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A measurement of K0,K0->3pi0 and an improved test of CPT Author(s): Bargassa, Pedrame Publication Date: 1999 Permanent Link: https://doi.org/10.3929/ethz-a-003823132

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ETH Library

Diss. ETH No. 13246

K°,K°

A measurement of

—>•

3tt° and

an

improved

test of CPT

A dissertation submitted to the

SWISS FEDERAL INSTITUTE OF TECHNOLOGY for the

degree

of

DOCTOR OF NATURAL SCIENCES

presented by PEDRAME BARGASSA born 31 December 1968 in

accepted

on

Tehran,

the recommendation of

PD Dr. T.

Nakada, referent

Prof. Dr. H.-J. Dr. A.

Iran

Gerber, co-referent

Schopper,

July

co-referent

1999

ZÜRICH

Abstract

The CPLEAR

experiment

at CERN is aimed to

the neutral-kaon system. The neutral kaons

are

produced

in pp annihilations at rest

pp^K^K+77-,K0K-7T+

each event, whether the neutral kaon is of

a

K°

or

K°. This gives

a

:

.

sign of the accompanying charged kaon allows

The observation of the

in

study CP-, T- and CPT-symmetries

one

to determine for

to CPLEAR the

capacity

extracting relevant physical parameters through time-dependent asymmetries between the

rates of

initially

In this work

pure

an

K° and K° decaying into various final

analysis

of

K°,K°

to the determination of the real and are

measured to be

These

values, although

imaginary part

This

of the CP-violation

0.18±0.14(sta*)±0.06(sysi)

Im(r]ooo)

=

0.15

still

analysis has lead

parameter

77000 which

decay mode; they lead on

an

upper limit

j770001

states.

=

(1.8±5.1)-10-19GeV/c2.

difference is of the order of the inverse of the Planck scale and experi¬

mentally confirms the CPT-invariance

in the neutral-kaon system up to these scales.

1

Contents

1

2

INTRODUCTION

1

1.1

Discrete symmetries and kaons

1

1.2

Thesis outline

2

PHENOMENOLOGY OF THE £T°-MESON SYSTEM 2.1

2.2

2.3

3

3

2.1.1

Time evolution of the

2.1.2

The

Unitarity

Neutral-kaon

K°-K° system

3

relations

7

decays

8

2.2.1

Two-pion decays

2.2.2

Three-pion decays

11

2.2.3

Semileptonic decays

13

9

CPTTest

16

2.3.1

Indirect test of CPT

17

2.3.2

Direct test of CPT

19

EXPERIMENTAL APPARATUS

21

3.1

The method of the CPLEAR

21

3.2

The

3.3

The Particle Identification Detector

3.4

The

3.5

4

The neutral-kaon system

3

tracking

experiment

detectors

Electromagnetic

23

Calorimeter

(PID)

24

(ECAL)

26

3.4.1

Shower reconstruction

26

3.4.2

Photon detection

30

3.4.3

Detection

The

efficiency

efficiency

for six

photons from 37r° decays

Trigger

SEARCH FOR CP VIOLATION IN

31 33

K°,K0

-+

ttVtt0 DECAYS

37

4.1

Detection efficiencies for the K° and K°

4.2

Feasibility study

38

4.3

Event selection and reconstruction

42

4.3.1

Preselection

signal

37

42

ii

4.4

4.5

5

4.3.2

The constrained fit

4.3.3

77

4.3.4

Lifetime resolution

48

Pairing

Signal and background

51 54

determination

55

4.4.1

The pionic annihilation channel

4.4.2

K°, K°

4.4.3

Kaonic annihilation channels with

4.4.4

Summary of analysis

4.4.5

The

—3-

27T° decay with 2 secondary photons

signal

to

an

additional 7r°

58

64 65

cuts

66

background ratio

69

Determination of 77000

70

4.5.1

Components of the asymmetry

4.5.2

Fit of the

4.5.3

Systematic

errors

77

4.5.4

Final results and conclusions

80

74

Aooo asymmetry

83

INDIRECT CPT TEST 5.1

Assuming CPT-conservation

5.2

Without assuming CPT-conservation in

6

CONCLUSION

A

Neutral-kaon

in

83

decays decays

85

87

89

decay amplitudes

A.l

Two-pion decays

89

A.2

Three-pion decays

89

A.3

Semileptonic decays

90

Matching

B

Photon

C

Possibility of

D

44

a

91

13C-flt

93

C.l

The acceptance of signal

C.2

The

C.3

Decay-time resolution of the 13C-fit

96

C.4

The overall effect of the 13C-fit

97

related variables

99

signal/background

Photon-energy

94

ratio

95

111

Chapter

1

INTRODUCTION

Symmetry

is

one

of the most

often lead to observable

transformation

of

symmetries in

physics.

In this

nature. some

thesis,

are

physics [1]. Symmetries

They

can

dynamical

also generate conserved

quantities.

mechanism acting behind the current

and time reversal

inverted; C interchanges

a

laws

physical

of

consider three discrete transformations

we

(P), charge conjugation (C)

space coordinates

in

important concepts

Violation of symmetry often indicates

understanding

kaons

symmetries and

Discrete

1.1

particle

Parity

:

operation (T). Under P, all the

to its

anti-particle;

T

reverses

the

direction of time. In nature, both

electromagnetic and strong interactions

P and T and any combination of them. not invariant under

of the

P,

charged weak

so

called

current

Parity

was

However,

are

found to be invariant under

the weak interaction

C,

discovered to be

was

violation. This lead to the conclusion that the structure

of the type V-A

(vector

-

The weak interaction is also

axial).

non-invariant under C. An

unexpected

violation of CP

though the Standard Model [3, 4]

was

can

first discovered in the neutral-kaon accommodate this

through

complex

a

matrix, the Cabibbo-Kobayashi-Maskawa (CKM) matrix

[5, 6],

has been made to exclude mechanisms of CP violation

suggested by

yond the Standard Model. This areas

in

no

particular

CT, it has

reason

exists

been shown

Lorentz invariance lead to

a

the field of CP-violation is still

of those fundamental in

[7]

and

experimental

one

of the most active

that

a

few very fundamental

P, C, T, CP,

assumptions such

physics should stay

of violation indicates

a

breakdown of

assumptions. Therefore, the search for CPT-violation

assumptions, and have thus revived the interest for

1

test

theories which go be¬

nature has to remain invariant under

physics. The quantum gravity [8] and the string theory [9]

fundamental

mixing

mass

why

Any sign

Al¬

theoretically.

conclusion that the laws of the

under the CPT transformation.

subject

why

particle physics both experimentally

While TP and

is

as

decisive

no

decays [2].

is

no more

accurate

the

invariant

one

an

as

or

more

important

fulfil all these

experimental

tests

CHAPTER 1.

2

INTRODUCTION

of CPT.

as

in the

promising places

of the most

one

kaon system, the

K°-K° oscillations generate

differences. This makes this system For such

studies,

no

especially

an

interference effect that could

CP-violation in

improve this

amplify such

attractive.

poorly

has been observed.

Ks decays

measurement and

to be well

known parameters is 77000, the CP-violation parameter in

37T° decays; the determination of this parameter is all the

—+

the neutral-

parameters describing the neutral-kaon system have

many

measured. One of the most

K°, K°

CPT-violation would result

to look for CPT-violation.

decay width differences between particle and anti-particle. In

and

mass

in the neutral-kaon system, this system appears

already violated

Since CP symmetry is

investigate

more

interesting

since

The main motivation of the thesis is to

its influence

on

the

knowledge about

the

validity

of CPT invariance.

Thesis outline

1.2

One aim of this work is to test the

chapter, to do

in

Kg

a

we

will present this system and focus

test of CPT invariance.

—>

CPT-symmetry

7r°7r07r° decays

In the third

chapter

is

one

we

We will

see

on a

in the neutral-kaon

method

using

paid

discrimination of the

photon showers

describing

relations

CP-violation

of the important parameters for this test.

will present the CPLEAR

is devoted to the

attention has been

Bell-Steinberger

that the parameter 77000

detector,

the Calorimeter which is essential to reconstruct neutral-kaon

Chapter four

the

system. In the coming

analysis of

K°,K°

—*•

with

particular emphasis

decays into 7r°'s.

7r07r°7r°

to the reconstruction of the neutral-kaon

67 decays.

—>

decay

background; the photon-pairing problem and the

has been studied in detail. This

analysis

on

will lead to

an

use

Special

time and to the

of the

angles of

improved value

of the

the

newly

CP-violation parameter 77000In

chapter

five

finally,

we

will

measured value of 77000 leads to

viously obtained.

a

perform better

an

indirect test of

precision

on

CPT-symmetry where

the CPT-violation parameter than pre¬

Chapter

2

PHENOMENOLOGY OF THE

X°-MESON In this

chapter

we

will first

explain

The

study

of neutral-kaon

through the unitarity

an

of the neutral-kaon system and express it

dynamics

interesting

providing

way to

decays will permit

us

understanding

an

compute

some

to define the

of this system, the

of its relevant parameters.

input parameters

to

a

CPT-test

relations.

The neutral-kaon system

2.1

Time evolution of the K°-K° system

2.1.1 Let

the

In addition of

in term of observable states.

unitarity relations will give

SYSTEM

\K°)

and

\K°)

be the

stationary neutral-kaon eigenstates of the strong and electromagnetic

hamiltonian,

(Hs where

states,

Mq and Mq we

have

+

are

HE)\K°)

the rest

4>cp

introduces

is

a

masses

phase.

Since

=

{Hs

,

K°

e^cp |#°)

only phases when applied

By demanding

of

K° and K°

T\K°)

phases

M0\K°)

+

and K°.

HE)\K^) =Mo\K^) Since

K° and K°

are

CP-conjugated

:

CP\K°) where

=

that

CPT\K°)

=

=

CP\Kü)=e~^cp\K°)

,

are

to them

el't'T\K0)

stationary states, the T operator

as

:

T\KÖ)

,

TCP\K°),

defined

(2.1)

we

=

é^\K^).

obtain the

following

(2.2) relation between the

:

2cp

=

Jr-4>T3

(2-3)

4

CHAPTER 2.

PHENOMENOLOGY OF THE K°-MESON SYSTEM

Since the weak interaction does not into

a

final state without strange

shown in

figure

conserve

particles

as

strangeness, the neutral-kaon states

shown in

figure 2.1,

or

can

decay

oscillate to each other

as

2.2.

u

TV

W

K TV

71 d

Figure

2.1: K°

—*

d

7r°7r07r° decay through

diagram

w

d

K

first order

s

I

u,c,t

d

s

Figure

2.2: An

in the Standard Model.

example

of

K°-K° oscillations through second order diagram

in the Standard

Model. The

time-dependent general

|*(t)> where

a(t), b(t)

Cf(t)

and

Schrödinger equation

are

state is then

=

expressed

as

a(t)|iO+H*)l^}+Ec/(*)l/>

time

dependent functions.

This state is

(2.4)

a

solution of the

:

i-|*(t))

=

(Hs

where V is the weak interaction hamiltonian.

+

HE

+

V)\V(t))

(2.5)

THE NEUTRAL-KAON SYSTEM

2.1.

5

Since the weak interaction is much smaller than the other tion 2.5 states

interactions,

by applying perturbation theory. Furthermore, weak interactions

are

neglected (Wigner-Weisskopf approach [10]). It

can

solve equa¬

we can

between the final

be shown that

a(t)

b(t)

and

follow

i^\m)

Mm)

=

(2-6)

where

\m) and where A is

given by

non-hermitian 2x2

a

A where M and Y

(a{t)

=

may be

as

:

(2.7)

are

(7,vbnE^(f^)

My

=

Mo^

IV,

=

27T^(i\V\f)(f\V\j)ö(M0-Ef)

+

decomposed

M-%-T

=

hermitian. Their elements

are

matrix; A

(^

f with

i,j=l,

2 where 1

=

K°,

2

=

K° and V

From the first of the above equation also contributes to the demands Flavour

one can see

The second term of

mass.

Changing

at much

higher

represents second-order

2.2).

how the weak oscillation of the neutral kaon

M\% representing

a

energy scale

interactions,

can

[11].

The

conditions

(V)

[13]

We observe that T-violation

panied by

K°-K° transition,

generate such currents.

here oscillations

through

all

interaction

The third term of

possible

(see

virtual states

section

2.1.2)

we

[12] M\i

(fig.

to all

from the second equation.

as seen

If the weak interactions

following

direct

hypothetical superweak

The T-matrix is constructed from the decays of neutral kaons

real final states

the

principal part.

Neutral Currents in the first order and thus vanishes if

consider only the standard weak interaction

occurring

means

are

T-, CPT-

or

CP-invariant,

then the A matrix must

satisfy

:

T

:

|A12|

CPT

:

An=A22

CP

:

|Ai2|

(|Ai2| ^ |A2l|)

=

=

or

|A21|

(2.9)

|A2i|,Aii =A22. CPT-violation

(An ^ A22)

are

always

accom¬

CP-violation.

By assuming K° and K°

are

that CP-violation is small

[2],

the solutions of equation 2.6 for

initially

pure

given by

\K°(t))

=

|^ö(i))

=

-L[e-^|^)+e-îA^|^L)] el^1+^6T[(l 25)e-iAst\Ks) V2 -

(2.10) -

(1

+

25)e~lKLt\KL)]


CHAPTER 2.

6

where ex and Ö

T- and CPT-violation parameters and

are

&L,s

=

MLts-\vLiS

Mm

=

^^ J.

Tl(s) e~lMs>Lt

The

term in

e~Vs'htl2

while the

11

JL

"T"

2

decay

shows their

(+)lri2|'

=

oscillatory character of the K°-K° system,

2.10 exhibits the

equation

HIM12|

+

99

(2.11)

to final states.

The states

eigenvectors of the A matrix with eigenvalues As,l and states with definite

with es

\K£)

ex +

=

are

=

\Kl)

=

ex

=

decay

-^l(l

\Ks)

sw

=

eT

i(2Am =

is also

(ßsw

a

=

T-violation parameter

tan~1(2Am/AT)

the above

equation

(see

for

through

4A7n2

as

seen

and

4>m

iAT)

+

are

.

Ar2SW(^r-^M)

from

r

.

.

equation

The

2.9.

respectively

the

box

phase 4>sw

is defined

phases of Mi2 and Ti2.

that this CP-violation is in fact

one can see

between oscillations

final states

and

-

(2.13)

generated by

by

From

the interference

diagrams (fig. 2.2) which gives Mi2 and through

common

example fig. 2.3) which gives Ti2 [14].

The small CP-violation parameter

2Am + iAr 72Am + AT

(Tu -r22) -

4Am2 also violates CPT

through virtual violating effect states,

as

as

states can

tion to

can

represented by

be

the

AT2

a

K -K°

our

My

decay-matrix P,

is

+i(Mu

in

equation 2.8),

only present

occurs

section

an

1.1);

decays

M22)

a

new

and

oscillation

moreover, the

(see

in the M-matrix

of neutral kaons

transition

represents

possibly

through

we

(Fn

a

field

superweak interaction

second term of

My

will consider the =

CPT-

real final

weak interaction which is

through

investigation of CPT-invariance,

the CPT-violation in the

-

mass-matrix M

oscillation; however,

CPT-conserving (see

in

2

equation 2.9. Since the

third term of

in

CPT-violating

2.8). Therefore,

neglect

from

(see

occur

interaction and thus

which

seen

+

'

.,

P22)-

in equa¬

possibility

2.1.

THE NEUTRAL-KAON SYSTEM

7

K°

u

wy s

K°

Figure

2.3: An

w

/

K°-K° oscillation through

of

example

common

final state, here 7T+7T

,

in the

Standard Model.

electromagnetic interactions K° and K°,

From the eigenstates of the strong and defined the

states of the neutral kaon

physical

Ks

and

K^,

which

eigenstates

are

of

CPT-symmetry.

violation,

2.1.2

Kg, Ki,

it is

The

interesting

to

Expressing

we

identify

measure

the time

ex and

a

total

isospin 1^

same

exchange,

to an

even

37r° decay is

K°,K°

—>

=

the

(1^

and

a

=

0,2)

a

as

follows

(2-38) or

(1^

odd

an

the

7r+7r-7r° final

(CP=+1) vanishing by

CP-violation parameter

states with

3.

violation of the

=

1,3)

total

isospin,

symmetric wavefunction for the angular

pions; therefore

0

or

l^lV2. Therefore,

(ttWiiw even

1

angular

(nW\V\Ks)

as

state can have

an

integration

isospin 1^

=

mo¬

CP-

a

over

the

follows

jdn(K+^\v\Ks)(-K+K-Av\KLY

generally, only three-pion final

sample

:

-

an

lîn2.

=

(-1)^1-2+1.

=

—1 and any

antisymmetric part

_

Z7ri7r2+_>7ro

to the definition of the 77000 CP-violation parameter

antisymmetric

exchange

:

obtain

we

symmetric under the

CP-eigenvalue

two

'^l-K2

The

(2.50)

the initial

of neutral

kaons,

strangeness of the neutral kaon and

we

on

define four

semileptonic

the

of the

charge

R^(r)

=

R(K°t=0^(l+ir-v)t=T)

P_(r)

=

R(Kto

RZ(t)

=

R(Ktt=0->(l-ir+V)t=T)

R+(r)

=

R(Kl0^(l+7T-v)t=T).

->

(/-7r+ï7)i=T)

rates

depending

decay lepton

:

(2.51)


CHAPTER 2.

14

6

8

10

Neutral-kaon

12

14

decay time

W

A-ooo

0.006

b)

0.004

^—-^::iJ:^^—-~

-

yf

0.002 0

T!

^000

0.002

f

^000

0.004

'-

0.006

r

~~

_

M000

=

£T 2

£T

4

ET

0.008 :

,

,

I

,

,

,

,

I

,

,

,

I

,

,

,

6

I

,

,

1

,

8

,

,

10

,

!

,

,

1

,

,

,

1

,

14

12

,

,

1

,

16

,

Neutral-kaon decay time

Figure

2.4: Simulation of the

We denote I to be all

amplitudes

can

be written

(l-TT+V\V\K0}

means

to

are

20

various values of 77000-

muons.

The

semileptonic decay

as

(l+n-v\V\K°)=a +

where b and d

,

Kl

ôoo asymmetry for

possible leptons, electrons and

,

18

=

c

b

(r^+V\V\KQ)=a*-b*

,

+ d

CPT-violation terms and

{l+TT-vlVlK15}

,

c

=

(2.52)

c*-d*

and d violate the AS

=

AQ rule; this

that between the final and initial states, the difference of strangeness should be

the difference of

charge

(fig. 2.5). Therefore,

c_lér(l+>K-v\V\KQY

x

x

for the hadrons

(l+*-v\V\K*) =

|(Z+7r-z/|y|#°)|2

=

respectively.

=

AQ

rule in

In the framework of the Standard

decays

^

c* -d*

^

+ b

(2.53)

c*+d* a~b

\(l-ir+V\V\K°)\" describe the violation of the AS

_

equal

the quantities

a

r^(r«^\v\K°)*.(r*+v\v\KB)

rule

into

Model,

positive and negative leptons,

this rule holds in the first order

NEUTRAL-KAON DECAYS

2.2.

diagrams (fig. 2.5) it is

and

only be violated by the second

can

to be very small.

expected

15

In the limit of the AS

or

higher

=

AQ rule,

diagrams. Therefore,

order a

positive and negative

w+ K°

(

s=o

Q=0

Q=-l

2.5: First order

lepton

are

diagram

respectively

the

this property,

we

for the weak

decay K°

1+tt~v illustrating AS

—>

consider the difference between the number of K°

production (sign

neutral kaon at its time

(AS

r

=

of the

a

measure

Taking

(see

charged

P+(r)

of two time-reversed processes,

final state,

4.1),

we

a

into

know the strangeness of the

we

production point) and

kaon at the

at the

an

A^p(t)

(2.54)

P_(r)

+

of the time-reversal

measure

measure

decay

a

experimental asymmetry [24] which

ARe(eT

~

-

y

-

rate of

decay

measure a

and different efficiencies to

define

—1.

=

oscillating

^>-*fj

=

into account different efficiencies to

section

AQ

AQ rule). Therefore, the asymmetry

Mr) is

=

signature of the K° and K° decays.

K° and the number of K° oscillating into K°, given that

decay

n

S=+l

Figure

Using

)

.

is

initially

rate with

given by

a

(T)

invariance.

K°

pure

e~~ or

a

or

K°

e+ in the

:

xJ)

(2.55)

Re(x_)(e~AVl'/2

cos(Amr)) Im(x+)sin(Amr) cosh(ATr/2) cos(Amr) +

+

-

where y

holds. X-

=

=

—

|

describes CPT-violation in

The parameter x+

^p

oc

(be*

+

d*a)

For the results of this

=

^^

oc

ac* describes the violation of the AS

describes the violation of the

analysis, CPT-invariance

assumed. The asymmetry is shown in

figure

ttV) (AmPe(77oo)

+YLBr(KL

->

tt+tt-tt0) (AmPe(77+_o)

+

+YLBr(KL

-*

ttW) (AmPe(77ooo)

rim(77ooo))

5.1, the

=

^

ttZi/) (AmRe(eT •

precision

+

2YLBr(KL "

physical

Im(eT)

states =

and

^Re(eT).

->

error on

Im(8).

(2.61)

liru)x+

ro,r

[27/m(77+_o

-

-

5

5

-

-

er)

eT)

-

-

1]

1]

computations of appendix A have been used for the decay

also used the relations

\Kg)

y)+ YIm(x+))}.

compute the matrix element

[2zlm(77ooo

»

where calculations similar to the

-

+

rim(?7+_o))

77000 dominates the

we can

YLBr(KL-> tt+tt-tt0)

+

are

on

(eq. 2.22),

^le^gM'M

YIm(Voo))

•

->

current

-

•

2

amplitudes;

irlv)]

+YsBr(Ks

K°,K° basis,

T12

->

tt+tT) (AmPe(?7+_) -rim(77+_))

-»

+2YLBr(KL As discussed in section

(2.60)

x

YYLBr(KL

giving

\Kl) (inverting

eq.

the

\K°)

2.12).

and

The

\K°)

states

imaginary part

as

function of the

of ex is

given by


CHAPTER 2.

18

into account the small size of

Considering the imaginary part of this equation and taking all parameters,

$

=

we

2^

obtain the

x

Ts

angle $ defined

[2Br(KL

—Br(K]_,

—>

Tr+7r-Tr )Im(ex

2?7+_ +7700

(2.62)

77-1—0)

—

—

parameter ô depends

angle

(see

access.

In order to

the CPT-violation parameter

,

S±

_

=

unitarity relations 2.21,

calculate their difference

the

remove

8± defined r22

x -6-

we

-

can

neglected (AS

decay amplitudes,

we

J

2

depends only

on

77^

8

small parameters. The

Re(ex)

7700,

,

and the

Re(-£-)

parameter

this parameter, let

on

us

consider

=

iAT

-

(2.64)

T

Im(8).

£=

to

(see

ex

eq.

2.13).

Thank to

compute the matrix elements Tu and T22 and therefore

=

rZof-lAol2

re-express

-

Re(-^-)

(2.65)

\A37r\2

-

+

|I^|2

\A3no\2

-

\Al+\2

AQ)-violating

=

-8 +

terms in second order.

Having

calculated the

:

Re(—)

8±

=

(2.66)

+ E

ao

with

:

(2.63)

.

unknown CPT-violation

2Am

Tn

+\Ä^\2 have

-$|

+

\a0J

follows

as

[16]

as

+\Ä^\2

we

2.35)

77000)]

—

:

r22-rn

where

(—)

phase perpendicular

its

)Im(ex

tt

2.31 and

eq.

dependence of

-^r-

8± has

It has to be noted that the

$

7t0tt

—

experimentally determined parameters

on

indirectly determined parameter $; the remaining is difficult to

Br(Kja

+ Re

ex-8

3

=

2.62 that the

equation

:

irlu)Im(x+)

->

which contributes to the CPT-violation parameter 8

It has to be noted in

2.28

equation

in

:

rL ;[J3r{J\L Ar

[Br(KL

+Br(KL which, like , noticed that

can

be

->

-

tt+tt-tt0)Re(eT

TT0Tr0TT0)Pe(eT

-

-

(2.67)

7?+_0)

77000)

+

Br(KL

-+

l)Re(y)}

computed from experimentally determined parameters.

frequently

the S term in the

expression of Im(8)

is

ignored (see

for

It should be

example

ref.

[27]). Finally, from equations

2.63 and 2.66

2t7+_+77oo

^

we

obtain the CPT-violation parameter

3Ut

+

ö±

+

^$

+

e\.

When

with the

performed

K° remaining

difference between the number of

with

the

(AS

CPT-conservation in the neutral-kaon decays

parameters. In chapter five,

that

equation 2.63, but

in

4>sw)-

the 3 term should be

K°,

e

uncertainty

nation of the CP-violation parameters 77+_o and 77000 and of

Im(x+),

(2-69)

measured ?7+_ and 7700

sensitivity of this

The

+

the direct CP-violation parameter

use

obtain

we

-—^p——

+

+

[2Im(x+)

+

AIm(8)]e-fTsin(AmT)

e-r-Tcos(Amr)

and where second-order terms in small parameters have been

neglected. This asymmetry has the advantage of being independent from Re(y) while being


CHAPTER 2.

20

sensitive to CPT-violation parameter 8.

independent asymmetry

Moreover,

from any parameter determined

A$xp(t)

is shown in

figure

4

by

an

other

6

8

10

A^xp

versus

AgXp(x)

experimental asymmetry

is

experiment than CPLEAR [26]. The

2.7. The fit of this asymmetry

Neutral-kaon

Figure 2.7: The asymmetry

the

12

14

decay

the neutral-kaon

by equation

16

gives

:

20

time

decay

2.71

[rJ

time

(in

units of

ts).

The

solid line represents the result of the fit.

Re(5)

=

(3.0 ±3.4)

where statistical and systematic than

decay

Im(8) time

Im(ô)

-10"

errors are

=

(-1.5

±

2.3)

(r

1

—

20ts)

while

being

(2.72)

10"

taken into account; the precision

since the asymmetry is sensitive to the first parameter =

•

sensitive to the second

Using time-dependent semileptonic decay-rates,

only

the CPLEAR

over

in the

on

Re(8)

is better

the whole range of

region

r

~

2/Ys+Yt,.

experiment has, for

the first

time, directly determined the CPT-violation parameter 8 [26]. Both real and imaginary part of 8

are

compatible with

zero

within

one

standard

deviation, showing

no

sign of CPT-violation.

Chapter

3


The method of the CPLEAR

3.1

The CPLEAR

experiment

was

designed

neutral-kaon system. The neutral kaons rest

to are

study

experiment the

CP-,

T- and

CPT-symmetries

in the

produced by proton-antiproton annihilations

at

:

pp

with

a

golden

total

branching fraction

of the

antiprotons

~

ÏW+TT-

->•

K°K~ir+

0.42% [28]

:

(3.1)

these annihilations will be referred to

Due to the conservation of the strangeness in the strong

events.

charge sign

of

-f

are

charged kaon tags

the strangeness of the neutral

interaction, the

kaon, i-e, K°

provided by the Low Energy Antiproton Ring (LEAR)

as

and K°. The

at CERN at

a

rate of

1MHz. The

experimental

structed

using the

method to

time

study symmetries

dependent decay

rates of

is to

measure

initially

pure

asymmetries which

K° and K°

are con¬

:

R^j(t) RK°^f(T) R^j(t) + Rk°^(tY -

{) Then

•

(3'2)

:

If

/

into

•

_ -

If

/

=

/,

the asymmetry is

K°,f

of the difference between two

CP-conjugated

rates

final state and is sensitive to CP violation.

a common

=

a measure

=

K°,

the asymmetry is

a

measure

of two time

conjugated

rates and is

thus sensitive to T violation.

•

The

If

/

=

K°, f

advantage

=

K°,

the

asymmetry is sensitive

of this method is that the

to

CPT violation.

geometrical acceptance cancels

asymmetry, and only second order effects have

to be controlled

21

through

to first order in the

simulation studies.

22

CHAPTER 3.

The

longitudinal and transversal views of

and 3.2


the CPLEAR detector

are

shown in

figures

3.1

:

CPLEAR Detector

At support rings

Magnet coils

Electromagnetic calorimeter 1

Drift chambers Beam monitor

16barH2

m

target

\

200 MeV/c

^r Proportional chambers Streamer tubes

Cherenkov and scintillator counters

_^ Figure

3.1:

Longitudinal

view of the CPLEAR detector

Electromagnetic Calorimeter

Scintillator S2

Cerenkov

Scintillator SI

Streamer Tubes

Target Proportional

Chambers

Drift Chambers

Figure The

antiprotons (see

3.2: Transversal view of the CPLEAR detector

reaction

Their momentum is reduced with

3.1) provided by a

beryllium dégrader

target. Before reaching the target, the beam gives the iment

:

a

start

signal

to the

LEAR have

traverses

so

a

that

a

momentum of

they stop inside the hydrogen

scintillator

trigger electronics. Two different targets

spherical target of radius

200MeV/c.

7cm filled with 16 bar gaseous

(Beam Counter) were

which

used in the exper¬

hydrogen

was

used until

THE TRACKING DETECTORS

3.2.

1994 and then

spring

The

by

and momenta of the

charged

tracks

cylindrical tracking detectors. The charged tracks

tracking

designed

detector is

so

that the

a

hydrogen.

(if±,Tr=F)

are

detector, provided by

z-axis of the

magnetic field of 0.44T along the size of the

filled with 26 bar gaseous

cylindrical target

1.2cm

charge signs, positions

série of

a

a

23

are

curved in

provided

a

uniform

solenoidal magnet. The

of the neutral kaons below 20rs

decays

be measured.

can

identification is carried out

particle

The

consists of measure

by the Particle Identification Detector PID

threshold Cherenkov counter sandwiched

a

energy-loss dE/dX

the

and the time of

In order to select the desired final state,

decay

neutral-kaon

channels

flight Tof specific

TT

mean

by the energy-loss

decay tt°

netic

the

lepton and the

which

particle. the dominant

(3-3)

7T

TT

TT

,

7T

TT

TT

associated neutrino. The

in the PID. The neutral

77 where the

—»

S2)

itlvi

TT+TT-,TT

v\

and

it

:

K°,K°

where I and

to each

distinguish between

has to

one

(SI

two scintillators

by

:

photons

pions

are

are

l/n separation

reconstructed

is

performed

through the electromag¬

detected and measured

by

an

Electromagnetic

Calorimeter ECAL.

Finally,

due to the small

beam intensity, A

a

[28].

and present their

The

3.2 The

tracking

momentum.

In this

device

chapter,

we

the

they

a

high

fast and effective event selection.

position of charged tracks and to the outside of the

six drift chambers and two

Chambers

(PC)

[29]

are

experiment our

can

be

analysis

decay-length

layers of

cylindrical

Ks have

of 2.6cm. Therefore

only those neutral kaons which decayed outside

no

are

detector, three multiwire

streamer tubes.

chambers which contain

placed

a mean

significant

is

placed

momentum of

loss is made

axially

at 1.5cm

480MeV/c,

by triggering

of PCO. This is done for the final states with

charged particles by restricting the number of PCO hits very much. PCI and PC2

is used to determine their

strips. The proportional chamber PCO

radius from the centre of the detector. Since the a mean

and

detectors

anodes and helical cathode

have

(reaction 3.1)

will describe the salient subdetectors for

comprises, from the inside

Proportional

placed

a

events

of each of the subdetectors of the CPLEAR

provides

proportional chambers, The

golden

performances.

tracking

It

ratio of the

multilevel trigger system is needed for

complete description

found in ref.

branching

to be

two, reducing the trigger

at 9.5cm and 12.7cm radius. If

a

rate

track is reconstructed

by the drift chambers without associated hit originating the

position of charged tracks

helical cathode

in the transversal

(DC)

strips. They

in the transversal

[30]

are

a

Supposing

charged particles [31]. This

determined with

a

track is obtained with

resolution of a

The Streamer Tubes

a

are

precision

that

can

as

determine

can

340/jm.

wires and

right/left ambiguity

(5mm),

The size of the

originates from the

track

a

to be

rapidly

centre of the

the transversal momentum

rapidly compute

with the information of the PID

coupled

induces

a

better than 3m?7i

tube,

one

can

information

on

by

the

fast information

gas mixture

a

charged particle

a

the difference of the

determine the

a

The z-coordinate of each

plane.

by using the information of cathode strips.

on

the

operating

at

a

ionises the gas,

propagation

z-position of the

tracks.

56.8 and 62.0cm. Each ST consists

layers between radii

in two

streamer when

By measuring

in the transversal

[32] provide

(ST)

being placed

192 ST's

wire.

a

leading

to

a

pulse

high

on

the

to the both

ends of the

resolution of 1.4cm.

Providing

time of the

z-position of each track with

This

high-voltage.

pulse

z-position of the tracks, the ST's give the possibility of computing the

longitudinal component

by

resolution of

trigger

double-wire system where the distance between

information

300^ttt,

central anode wire surrounded

voltage

an

a

the

by the trigger for the identification of the kaon candidate. The position of the tracks

is used

of

with

The PC's

vertex.

to the size of the drift-cell

detector, the information of DC1 and DC6

There

plane

by

by the trigger requirement where the hit information has

delivered to the trigger system.

are

it will be considered

between 25.5cm and 51cm. The

by using

(0.5mm) compared

drift-cell is dictated

px of the

PC's,

cylindrical chambers with axially placed

also

placed

arc

is removed

plane

the wires is small

in the

secondary vertex, i-e, the neutral-kaon

from the

The Drift Chambers

of the momentum pz which is used in the online selection of events

the trigger. In the offline

analysis,

the hit informations of PCI and PC2 and all the six DCs

into account to reconstruct a


CHAPTER 3.

24

a

track

:

pattern-track; then, the quality of

in the

analysis.

resolution

3.3

Ap/p

The for

this track is

efficiency for finding a

a

improved by

track

by

such

a

the

trigger

a

a

fit

eight

taken

is demanded to have

leading

to

a

fit-track used

method is 99%. The momentum

track is between 5 and 10%.

The Particle Identification Detector

The task of the PID

provide

minimum of three hits out of

a

are

[33]

is to

(PID)

identify the charged pions and

fast information about the

charged

kaons and

kaon-candidate.

particularly,

to

It consists of 32

sectors located between radii 62.5 and 75cm.

The Scintillators a

(S)

All

charged particles passing through

signal which is used by the trigger

these

to count the number of tracks.

plastic scintillators give This

signal

is also used

THE PARTICLE IDENTIFICATION DETECTOR

3.3.

to

(PID)

compute the difference of time of flight STof between the

resolution of the

primary

~

0.26ns, this allows

vertex.

to

in the offline

Moreover,

ATof where

(8Tof)

(8Tof)th

and

are

The scintillator SI is also used to

length) dE/dX [33, 34]. between K

+

and

As

can

be

tt+, particularly

analysis,

(STof)exp

=

\ATof\

differences. We demand that

separate between

respectively the

The

by

a

270MeV/c,

CHAPTER 3.

26

by DCl

where px is measured

kaon

by the trigger

is lower than 0.6%

[31]

In order to reconstruct the

photons

2(3)tt°

dictated

are

4(6)7 decay

—>

the

by

pions with

a

for

principle

K° decay

of the

a

[35].

accurately

as

the

performances (position, angle for

planes. A

V-layers hit

:

requirement and

a

crystal

parame¬

a

layer

each

W-plane at

as

Csl. The

of lead sandwiched between two

(W)

of ±30°

direction. A total of 18 such

is then measured

of these tubes

is sandwiched

angle

an

space limitation

calorimeter such

the wire information

can

[36].

be found in ref.

and energy

are

resolution)

pattern-recognition algorithm

a

demanded to be considered

given by

same

by

minimum of 3 hits in at least two

from the U-V

the

W-projection

by

an

provide

U- and V-

(fig. 3.4.b) providing

layers, representing

In this section,

we

will focus

of the calorimeter which

fulfilling

projection

the

simulated pp

in

one

matching —>

tt

by comparing the =

W-layers

as a

set of hits in the

as a

and

a

six

are

on

of great

shower. For

a

of the

shower,

(fig. 3.5) The

5mm. In

are

spatial

K+K~2j decays.

=

longitudinal position

has to be at less than 3cm from the

reconstructed with

2.2mm and az

the

position calculated

is set for showers

having

planes.

condition.

—

W-, U- and V-

minimum of 2 hits in both U- and

projection (matching condition). An ambiguity flag

The shower-foot coordinates

be ar$

important

analysis.

our

A shower is defined

the

resolution when

Shower reconstruction

3.4.1

a

spatial

—>

full reconstruction of the shower in the space.

the ECAL

description of

importance

of

a

the K°

possible

as

electromagnetic shower which

plane;

longitudinal

radiation-length (6X0) permits A full

an

strips crossing the W-plane

in the

position information

following

(fig. 3.4.a);

in the transversal

consist of

design criteria for the

The calorimeter had to lie in between the end

rather than

converts the 7-ray in

position information

plane which

a

electromagnetic

an

7 interacts with the detector is the most

calorimeter is the

streamer tubes

layer of

The

studies have shown that the

design

vertex determination

sampling

layers of aluminium by

as

higher than 360MeV/c.

decays with tt°'s,

to reconstruct

lead/gas sampling calorimeter,

a

to be misidentified

pion

momentum

of the PID and the magnet coil at lm radius. Performance

lead to

a

CPLEAR experiment.

ability

vertex. The

measuring the coordinates where ter for the

for

in neutral-kaon

calorimeter has been included in the

calorimeter

probability

the

DC6,

Electromagnetic Calorimeter (ECAL)

The

3.4

and


The

obtained from the first

resolution of the ECAL is studied are

obtained

generated r(f>- and z-infor mations. They

are

found to

K°

—»

value in unit of a^

(computed

and

on

rcf>-

3tt° simulated data, for each photon,

generated conversion-point and r

by using

and ^-coordinates

error

coordinates of the

from

layer of the shower

a^)

can

and az

:

we

have the

thus compare it to the reconstructed in

figures

3.6.a and .b

we can

observe

THE ELECTROMAGNETIC CALORIMETER

3.4.

(ECAL)

27

a)

Figure

W-,

a)

3.4:

U- and

:

Transverse cross-section of the calorimeter,

b)

Geometrical arrangement of

:

V-planes.

that for almost 70% of the events the reconstructed coordinate of the shower-foot is within standard deviation from the

mainly

generated value. However,

due to limited wire and

strip granularity and

tails

can

be

observed;

to effects related to the

these tails

one

are

shower-pattern

recognition. The shower in the various

angles ($, ©)

planes [37] (fig. 3.5).

where the directions of the

the true direction of foot. are

The

error

respectively

that these

quality

a

photons

photon

of the

is

determined by The are

errors

on

well known

given by

shower-angle

in the interval

errors are

of the

are

taking these :

into account the hit distributions

angles

in the pp

the line between the

in the transversal and

[0.2,0.5\rad

and

were

—

determined with data

tt°

primary

—

vertex and the shower

longitudinal plane

[0.25,0.63]rad (FWHM);

decreasing with increasing photons energies. Some

shower-angle information

will be

K+K~2^y decays, A$ and A0

it has to be noted

consequences of the

presented in Appendix D.

The shower energy. Simulation studies have shown that the best energy resolution for

photons

of

a

few MeV energy to be detected in

the number of hits rather than

measuring the

a

sampling calorimeter

energy

deposited

is obtained

in the gas.

Thus,

by counting

measurement

28

CHAPTER 3.


0 •"-"'

"^

V

^ r

Figure

Transversal and

3.5:

shower-foot

given by X

10

and

longitudinal

vue

/x

of the calorimeter.

Geometrical definition of

shower-angles ($,©).

1 769

J

86 50 d

10

a

0 1793

10

0 9864

StnÂ,

1 15

z-coordinate

Simulated K°

(b)

fitted

by

the shower energy fitted

of the entire shower

the shower energy a

sample

of pp

—>

good precision (~ and

assuming

a

,

nil

10

(E

3.6:

21

937 9

W

Figure

/

2

—*

a

by

3tt° data.

in the interval

allows the number of W hits

To calibrate the number of hits

K+K~2j decays

4%)

with

missing tt°

a

[-2,2]. c)

:

angle (a) and

Pull distribution of

gaussian function in the interval [-4,1]

development

[36].

Etm Jav)

Pull distribution of the shower-foot

gaussian function a

-

is used. The

constrained fit

mass

demanding

as

a

(tubes fired)

function of the

photon

to be related to

photon

energy,

energy is determined with

a

energy and momentum conservation

at the annihilation vertex.


3.4.

The hit distribution for

photons

with different

(ECAL)

29

energies is shown

in

3.7. Low energy

figure

20

Hits

Figure of the

3.7:

c/jtt0

—>

K+K 2j data. Hit distribution for photons converting in the first layer

calorimeter, with energies going from 70Mey

photons give

less hits in the calorimeter than

high

to

270MeV.

This

photons.

energy

stood since the number of hits is in fact the number of electrons and

e"e+-pairs

be

can

easily under¬

positrons produced by

the interaction of

a

the energy of the

interacting photon [23]. At low energies the hit distribution is asymmetric

the lead. The number of

photon with

because of the low number of hits. tion of the

mean

the energy of

a

value of the number of hits

(w(E))

non-linear variation of

less hits than

a

a more

photon

The variance aE

on

the

layer

same

photon a

where o2 (E)

3.7)

at low

=

y/w(E),

energies;

layers

The variation of

(w(E))

of the ECAL is shown in

is not

totally

energy determined

a2(E)

E

+

:

as a

as

func¬

function of

figure a

a

3.8. The

photon which

contained in the ECAL and thus

energy which has converted in

gives

previous layers.

by this method is given by

2ü2(E)

O is of the order of 1.5 and 1 for

This method

to calibrate the energy

(3.5)

and Î7 takes into account the asymmetry of the hit distribution

200MeV, respectively. It

photons.

possible

reflects the moderate thickness of the ECAL

advanced

of the

it is

(w(E)).

converted in different

photon

has converted in

Therefore,

itself is increasing with

is clear that the relative

permits

to

have

a

photons with

error

on

an

energy is

moderate energy resolution

(fig.

energy of lOOMe^ and

greater for low energy

aE/E

=

13%/Ê(GeV)

CHAPTER 3.

30

Q

I

!

I

!

i

100

0

I

I

200

3.8:

(w(E))

4>tv°

as a

—>

K+K~2j

function of the energy for

calorimeter. The lines represent the calibration

[36].

This

error

is

a

good

structed value of the energy is within

3.6.c); however, are

this distribution is

reconstructed at

higher energies

Photon detection

3.4.2

The reconstruction of energy we

a

observe in

figure

shower reconstruction

the energy

have

no

a

bad energy

based

photons to

a

on

its left

generated

a

and

8*^ layers

function of

generated

side, showing

that

of the

(w(E)).

3tt° events, the

recon¬

(fig.

value

some

photons

energy.

the detection of hits in the

on

a

lower

probability

of simulated

^tt°

constant detection

is due to the limited

requirements (see

—>

section

W-ambiguities. When demanding

no

to

efficiency

calorimeter,

be detected.

K+K~2-y

radiation-length

assignment. Therefore in

90% for this decay mode.

as

of simulated

events.

of 97% for

a

a

low-

This is what Photons with

single photon.

of the calorimeter and to the

3.4.1).

Since the energy of each shower is derived from its W-hit

lead to

1st, 4th

standard deviation from the

than the

and has thus

3.9 where

inefficiency

value of the number of the hits

efficiency

energies above 200MeV reach The residual

one

mean

giving

gaussian only

photon being

photon gives less hits

(MeV)

nearly 66%

estimation since for

500

converted in the

photons

1

i

400

Variation of the

data.

I

I

300

Photon energy

Figure


our

distribution,

analysis,

W-ambiguity,

we

a

W-ambiguity

can

will demand all showers to

the detection

efficiency drops

to

(ECAL)


3.4.

lOO

20O

300

600

50O

400

31

700

800

Energy [Mev]

tt0

3.9: Simulated

Figure photon

K+K 27 data. Photon detection efficiency

—»

as a

function of the

efficiency of the ECAL

to reconstruct

energy.

In the perspective of

our

photons from 37r° decays

for six

efficiency

Detection

3.4.3

analysis,

we

determine the

exactly six showers originating from neutral-kaon decays. Given the size of the detector and the neutral-kaon momentum, around 96% of the

decay

[28].

outside the apparatus

consider

a

sample

if£

of simulated

flat lifetime in the interval

sample •

3tt°

—>

[0,50]rg,

momentum neutral kaons with

a

study the geometrical acceptance (fig.

To

events with

the upper limit

maximal

photons generated

of data toy simulated data. For this acceptance,

The absence of

form of of

a

end-caps

barrel without

one or more

photons

of the ECAL. In no

in the ECAL

figure 3.10.b,

photon pointing

simulated events

:

to the we

a

end-caps have

we

solid

can

be

detector;

coverage of

will contribute to the

represented

the

we

will call this :

explained by

the

nearly 75%. The loss

geometrical inefficiency

generated

lifetime of events with

to the flat lifetime of all

observe that the absence of

20% when requiring six detected photons from variation in lifetime

angle

end-caps, normalised

can

in 4'Kst. and with

take into account two effects

we

we

The CPLEAR calorimeter is constructed in the

:

end-caps, with

in these

the

3.10.a),

to the lifetime of low-

corresponding

decay-length inside

KL's

if£

—>

end-caps gives

3tt°

—>

K\

an

—>

3tt° toy

efficiency

of

67 decays. The absence of

isotropic decay of tt°'s

in the neutral kaon

frame and the neutral-kaon momentum distribution. The finite volume of the detector of the

mainly

if£

—>

3tt° decay

because of the

represented

the

vertex is below

is

greater than

incapacity

generated

given the internal radius of the ECAL, if the

:

of

lifetime

Rmax normalised

a

value

disentangling

(toy

Rmax-, the

event cannot be

the showers. In

simulated

data)

detected,

figure 3.10.C,

we

of events for which the

to the flat lifetime of all

KL

—>

vertex

have

decay

3tt° toy simulated


CHAPTER 3.

32

events

:

we

efficiency

observe that the finite volume of the detector diminishes the detection

can

for

high lifetimes. The global

detection

53.3%.

to this effect is

efficiency due

The value of Rmax has been determined in order that the combined effect of finite

volume of the calorimeter and absence of

KL

3tt°

—>

67

—>

events

(fig. 3.10.a);

the acceptance of simulated

end-caps reproduce

this value is found to be

(43

2)cm showing

±

given the dimensions of the ECAL (inner radius of 77.5cm) and the neutral-kaon

that

K\

momentum range, the effective volume to detect

3tt°

—>

67 decays

—

is

a

sphere of

43cm radius.

40

30

True neutral-kaon

50

decay

time

[x„]

c) !

^'

.

S-0T5

-

G

,

-

05

S

*

*

—

US

W 0 25

1 t

-

H t

,

•t«,

r !

1

.

t

1

1

30

40

True neutral-kaon

Figure

(see

section

(line)

a)

3.10:

The acceptance for

4.4.4),

—»

3tt°

Taking without

W-ambiguity)

(dots) taking

we

ÜT£

derive the

—>

3tt° data,

calorimeter, taking

probability

3.4.2, and the

we

for

a

derive the

the

signal

the detection to

efficiency

background ratio,

,'

1

decay

time

[ts]

3tt° events, after analysis

—>

(b)

and

(c).

The

efficiency for

(c)

obtained from toy simulated data.

(for

showers

energy distribution of each of the six

photons

as a

function of the energy

probability

a mean

due to the

is 40%

cuts

into account the absence of ECAL in

for each

six-shower event to be detected

acceptance for reconstructing photons has

Finally,

,

50

into account

photon detection efficiency

from section

,

generated decay-time obtained from simulated data

the finite volume of the latter

into account the

from simulated

detecting K°,K°

function of the

events in the

end-caps (b) and

Then,

a

as

and from toy simulated data

detecting K® the

:

,

photon

to be detected.

by the calorimeter; this

value of 24%.

analysis

(normalised

cuts

(section 4.4.4),

which

improve

to the total number of events

in the

33

THE TRIGGER

3.5.

Kl

3tt°

—

shown in

67 simulated data).

—>

figure

These cuts

The different detection efficiencies of the ECAL

acceptance of

~

11% is the

independent

are

Detection

Absence of

Analysis

factors. For the

40. ±1.

of the

efficiency

if£

—

3tt°

—

The

—>

ing ratio of the golden

3tc°

events is

Moreover,

an

1%.

events

(3.1)

the need of

is very small

high

statistics

as

(~ 0.42%), requires

Early one

Decision

Logic (EDL),

of which should be

among kaon candidates

in the Cherenkov without

track

IDL

a

depending

can

pp annihilation rate

(1MHz)

multilevel hardwired processor system

provided by

the CPLEAR

:

which demands at least two hits in the SI scin¬

kaon-candidate. The amount of low-momentum an

SC S

signal)

is reduced

by

a

cut

on

pions

the transversal

since low-momentum kaons

Logic (IDL) which

uses

are

stopped

the hit information of each

computation and classify them

whether

they

have

a

hit in the PC's

select events with different number of

3. The HWP1 which

a

high

firing the S2 scintillator.

first track on

are

mainly the pions

2. The Intermediate Decision

chamber to do

a

(also giving

momentum px; this cut affects

this,

a

this event selection has to be very

function of all informations

subdetectors. The main levels of this trigger

tillator,

is the total number of events in the

important step in the CPLEAR experiment. Since the branch¬

is used to select the events

1. The

function of different

cuts the normalisation is the total number of events

and the selection has to be very fast. To achieve

(HWP)

as

Trigger

The online event selection is

effective.

calorimeter

67 simulated data.

efficiency for detecting KL

3.5

electromagnetic

geometrical acceptance, the normalisation

toy simulated data and for the analysis in the

efficiency [%]

23. ±1.

cuts

Table 3.1: The detection

geometrical

53.3 ±1.0

reconstructing photons

for

cuts.

20.0 ±0.4

Finite volume of the ECAL

Acceptance

analysis

:

in the ECAL

end-caps

the acceptance

in table 3.1. The

reported

Source

Geometrical acceptance

:

factor for the detection of desired events. The overall

limiting

most

lifetime

events which have survived the

(solid line) represents

3.10.a

are

performs

a

checks the number of primary

primary

tracks;

or

and

better track reconstruction

as

primary-

not.

or

secondary-

Several levels in the

secondary

tracks.

(Track Parametrisation)

and

it demands the total number of tracks not to


CHAPTER 3.

34

with

a

the HWP1

Finally,

exceed four.

performs

a

rapid

check of

compatibility of the

this check takes into account the number of

golden event;

tracks,

event

kaon candidates

and the sign of tracks.

X'+TT^-pair

dE/dX-

into account the

HWP2, taking

4. The

Tof-information, improves the

and the

identification.

5. For events with

only

two

HWP2.5 level of the

primary tracks, i-e, neutral final

trigger

can

states of reaction

(3.3),

the

demand different minimum number of clusters no in

the calorimeter. The full level of the

of the information flow and

logical-path trigger

shown in

are

figure

With

3.11.

CPLEAR Fast

>

PID sectors

SI. C, S2

wires

the time needed

rejection factor of

total

a

~

by each 1100,

an

Trigger 60 ns, Rate reduction: 4.1

Early Decision Logic N(K)>0, Ntrack>l

>

DCl, DC6

particularly

t

Fast Kaon Candidate

|

400 ns, Rate reduction: 3.1

pTcut

TE PC, DC, PED sectors

PC-, DC-,

ST-

wires

h

Intermediate Decision

tracks

|

Track Follower

h


Logic

K, primary, all charged

Track Validation

Pattern

Recognition

|

1.9 us, Rate reduction: 1.4

JL Track Parametrization Curvature, , z, approach

Momentum Calcul.

Distance of min.


-*5-

j£ Missing

Mass

Kinematics

wires

1.9lis, Rate reduction: 6.4

Fast ECAL Processor

>

SI TDCs C ADCs

in Cerenkov

Particle Ident.

500 ns, Rate reduction; 1.5

KCAL

SI ADCs

dE/dx, TOF, N(e)

const.

PK+PTI=

N(shower)>

Shower Calculation

no

17 jj.s, Rate reduction: 2.9

Read-out starts

J.

after 34

Root Read-Out

Figure

3.11:

Logical path

To

average beam rate of 800kHz and

One of the of the

trigger

we

have

advantages can

be

a

taking

read-out of

~

450

of the CPLEAR

changed.

rate

This has

trigger. For each

reported.

are

(about 25%)

of the data

events/second.

trigger

is that the decision of different levels

permitted for example

through the study of

trigger requirements used

to obtain the data of this

:

drive

into account the dead-time

subdetectors of CPLEAR

decisions

Tape

of all subdetcctor informations in the CPLEAR

step, the needed time for online analysis and the reduction

acquisition system,

us

to calibrate the different

various channels like pp

—>

analysis corresponds

4>ir°. to the

The main

following

35

THE TRIGGER

3.5.

EDL

•

requirements

candidate; •

transversal momentum of

At least

primary

kaon

requirements

3

4, the total number of tracks should

or

:

:

one

tracks greater than

one

at least

be 2, 4 and 4

The total momentum of the

kaon

270MeV/c.

candidate; if the number of primary tracks

IDL

HWP1 requirement

•

A minimum of two scintillators SI fired and at least

:

is 2

or

respectively.

primary kaon and pion greater than

700MeV/c. HWP2.5 requirement

•

It is

an

triggers;

(see 4.2.1).

In

we

can

do this

figure 3.12.a,

and P29. While other we

=

6 clusters

seen

triggers

on

in the ECAL.

the data. To do

observe

comparison for

we can

and

similarity

having survived the preselection

applied

for the P29

are

same, IDL decision

between these distributions.

five, the other trigger conditions being

a

major effect

to each

period.

Therefore,

on our

we

cuts

periods P27

was

In

not

figure

3.12.b

the same;

we

cuts

on

can

again observe

a

also

for the

respectively

six

similarity between

conclude that different selections criteria of the

analysis and the applied

we

(see Appendix C)

and P27 where the minimal number of clusters no in the ECAL is

these distributions. not

us

compare the neutral-kaon momentum for the

trigger conditions a

events

compare the distribution of the invariant-mass of the six showers

periods P24

that, let

important variable of the analysis for different data taking periods corresponding

to different

data;

A minimum of no

to evaluate the effect of different

important

consider

:

trigger have

the data do not have to be

specific

36

CHAPTER 3.


600

800

1000

Neutral kaon momentum

[ Mev/c ]

b)

37r°

—>

67

(open triangle)

Invariant

mass

data,

a)

:

of six showers for no

[ Mev/c

Neutral-kaon momentum for periods P27

where the IDL

where the minimum number of showers

Mass

requirements

are

respectively

(full

active and

periods P24 (full dot) and P27 (open dot)

in the ECAL is

respectively

six and five.

Chapter

4


KG, K° In this

chapter,

parameter

77000

ttVtt0

->

we

will present the

using the

[39, 40]

The tools of ref.

We will discuss the

Then, the

we

analysis leading

asymmetry of initially

rate

our

our

this

conditions and how

procedure

event selection

to

our

K° decaying

to

a

different detection

K+ and

a

they affect

difference of detection

probabilities

probabilities

we

Ç

for

=

a

K° and

R^) R») R$(t) + Rfo(t)

where R~

=

a

(t)

are

the observed

-

+

material,

e(K+ir~) ^ e(K~7T+).

K°. Therefore, the

ratio defined

Event selection and reconstruction

4.3

we

K°,K°

the definition of

of the two tracks must be

PC must be touched

one

by

a

track,

in section

see

3.2).

zero.

both tracks.

kaon candidate

(for

the definition of

a

kaon

candidate,

see

3.3).

For both

K^ and ir?, the number of hits

in the PC's and the DCs must be

more

than

more

than

four.

•

For both

K± and 7^, the number of hits

in the

Z-plane

of the DCs must be

two.

•

The charged kaons with momenta less than than 50% because

scintillator; thus, momenta

Pk

interacting

to have

a

300MeV/c

in the Cherenkov and

better

quality for

must be in the range

having

the kaon

[350,800] MeV/c.

have

a

detection

efficiency

less

difficulties to reach the S2

candidates,

we

require that their

4.3.

43

EVENT SELECTION AND RECONSTRUCTION

a)

b)

y

Figure

4.4:

Data events.

K°

(a)

and

y

K° (b) decays into

apparatus. The charged kaons and pions respectively give

PID;

the

photons give

six

The momenta of the the

energy-loss

electromagnetic showers,

charged pions P^

an

37t°,

detected in the CPLEAR

SC S and

an

SC S

signal

in the

detected in the ECAL.

must be in the range

[100, 750]MeV/c.

of the kaon candidate should be at less than four standard deviations

from the theoretical

energy-loss

of

a

kaon with the

same

momenta.


CHAPTER 4.

44

K°,K°

-

ttVtt0 DECAYS

Selection of the neutral showers

•

the

By strong interaction,

charged particles

their interaction point in the calorimeter. showers at

a

•

Due to

gas flow

a

produce large

ter

a

additional

some

we

photons around

define neutral showers

charged pion

and 50cm from

a

[41]

as

charged

demand six neutral showers.

we

problem

in

running periods,

some

[42], i-e, they produce

noise

candidates. We demand

no

some

sections of the calorime¬

anomalously high number of shower

an

shower to be in those regions.

The constrained fit

4.3.2

The neutral-kaon

vertex is determined

decay

struction of the annihilation pp

7r07r°7T° see

Therefore,

distance greater than 25cm from

kaon. For each event

produce

can

—>

67 through

[43]).

ref.

The fit

flight direction

a

K°(K°)K±7rT

—»

(for

constrained fit

that the six

assumes

of the neutral

by

a

full

a

and the

more

detailed

•

the momentum pk of the

figures

4.5.a and

charged

•

the

and the

(ce-s)

the

decay

point along the vertex.

:

kaon and the momentum jv of the

reconstructed in the

photons

(see figures

energies Ei of the six photons

equality of

a common

charged pion (see

.b),

the shower-foot coordinates of the

are

are

—>

primary vertex,

•

The constraints

recon¬

description of constrained fits,

the unknown neutral-kaon

The measured quantities used in the constrained fit the coordinates of the

and kinematical

neutral-particle cascade K°,K°

photons originate from

kaon, namely

•

geometrical

4.5.c and

.d)

measured in the ECAL.

energy- and momentum-conservation at the

Kît^ missing-mass

equality of the

with the neutral-kaon

77 invariant-mass with the

7r°

mass

ECAL,

mass

vertex

(01-4),

the

primary

vertex

(05)

primary at the

for the three

couples

of

photons

:

6

cx

:

2mp-(EK

+

En

J2Ei)

+

=

(4.8)

0

i=l 6

C2-4

"•

PK + Pit +

^Pi

=

0

i=\

m2K0

c5

-

C6

:

2m^°

c7

:

-mlo

es

:

2m^°

(2mp -EK- E^f

~

I -

_

(-^1^2

+

Pi

P2)

=

0

p3

pY)

=

0

(E5Eô -P5-Pe)

=

0

(E3Ei

-

-

(pK

+

pV)2

=

0

4.3.


45

b) I

RMS

SB3Î

1200

800

600 400

/

r

200

r

-

0

200

400

Primary pion

600

momentum

i

800

,

,

1

,

400

c)

.

800

kaon momentum [Mev/c]

Primary

[Mev/c]

,

600

d)

.aoooo

1

Men

39JS

I

RMS

23 41

2500

RMS

E8000

IM7

M

o

2000

il

T-r

6000

1500

"

4000

1000 .

2000

rn

-,,,,i,, 0

,,i

100

50

150

0

Minimal energy of photon [Mev/c]

Figure

37r° simulated data.

4.5:

7

500

-

i

i

-

,7Wu

i

,

200

400

Maximal energy of

600

,

1

,

,

800

photon [Mev/c]

Momentum distribution of the primary pion

primary kaon (b). Distribution of photons with minimal (c) and maximal (d)

where mp, mô and m„-o fit with

photons of the

eight are

are

constraints and

the one

deduced from their

K° which

pairings and sorted according to the

We will discuss this The

chi-square

xpKim

ls a

are

fifteen

to the

possibilities

probability

pairing; therefore the

question of pairing

of the

7C-fit,

x%q,

primary vertex

to form three

previous paragraph

in

energy

more

2

sCprim

i

'

repeated

E{ of the

of the six vertex

six

xlec

over

to the

2

as

,

Xsec

*s a

error on

photons.

the fifteen

possible

The constraints C6_8

are

photons affects the pairing.

'

follows

:

2

(4.9)

A,c

primary tracks, namely their momentum;

function of measured

the energy

by

a

physical

quantities

namely their energies and shower-foot coordinates; however, the relative

being smaller

with six

pairs

is the neutral-kaon momentum and the

energy and momentum conservation,

foot coordinates

pi

detail in the next section 4.3.3.

be written

can

is

of the fit result.

function of measured quantities of

the unknown at the are

The momenta

energies, their shower-foot coordinates and the decay

Xtc where

energy.

K° and the 7T° respectively. This

unknown is called the 7C-fit.

the 7C-fit described in the

directly related

and the

is the unknown of the constrained-fit.

One should note that there

Therefore,

of the proton, the

mass

(a)

error on

factor 100

(see

constraints

of

photons,

the shower-

section

3.4.1),

CHAPTER 4.

46

2

X.

is

more

K°,K°


sensitive to the energy and

can

be written

ttVtt0 DECAYS

as

'É!c-Ex

E

Xsec

->

(4 10)

2=1

where E% and a% and

Ejc

fitted

are

subset of the

the

are

photon

photon

energies and their

x2ec

energies.

photon-physics.

measures m

figures

In

errors

fact the

4.6.a and 4.6.b

determined

as

performance

we can

by

the calorimeter

of the 7C-fit in the

see, for the best pairing

pairing giving the highest probability), the probability distribution of the 7C-fit and the

secondary-probability

A

-

10

Prob(x2ec). Finally x\

distribution

is

a

(the

Prob(x2c)

function of both kind of

a)

3

\ 10

2

Î,

,

,

1

,

,

,

02

1

,

,

04

,

1

,

,

1

,

,

,

08

Best 7C fit 1

,

06

02

1

06

04

probability

08

1

Secondary probability

c)

09 08 07

06 05

04 03 02

01

0 01

02

03

04

05

06

07

08

09

1

Primary-probability

Figure versus


4.6.

from very

charged

(PK, P~ir

the

and

ProKx2ec) 03)- (c)

ProHx2ec)

:

possible correlation between charged and neutral hemispheres Apart

particular mechanisms like albedo photons

to the neutral

and Pk°

=

—

hemisphere (see

(pk +Ptt))

because different detectors

precision

are

is

proven

4.4.2),

a

photon

is sent back from the

the measurement of

used to reconstruct charged and neutral

charged quantities

is

quantities (see sections 3 2 and 3

charged parameters independently

vanish. This

section

where

charged quantities

does not affect the measurement of neutral

of measurement of

measurement of neutral

the

Prob(x2c) (a)

Prob(x2prim)

variables, revealing

the

Best

much

quantities; this

is

particles. Furthermore,

higher than

4). Therefore,

from neutral parameters and

the

precision

of

the 7C-fit determines we

expect the

by figure 4.6.c where the secondary-probability is displayed

x\

versus

t°

the


4.3.

primary-probability

:

one can

observe that there is

proving that the output parameters related not

affected

2

The property of the 7C-fit described

mass

apply

a

cut of

squared spectrum

Prob(x2ec)

10%

_

2

hemisphere (see relation 4.10)

are

Prob(x2ec)

on

at the

and

on

primary vertex;

the K°

region corresponding

Prob(x2c)

in order to be able to monitor the

(see

section

secondary

4.4.5),

to

while

(4.11)

by the above relation

as

can

seen

from this

in

while

Prob(x2ec)

in the

the

to reduce

figure

4.7

Kîr^ missing-

figure, cutting

cutting

analysis

our

background through

on

seen

and observe the

distribution,

Therefore,

mass.

cutting

be

also be

can

Prob(x2c)

does not affect the missing-mass squared

distribution

variables,

L2 ' Xsec

Xprim

selects the

from the

the neutral

to

:

X7C

we

correlation between this two

by charged parameters.

The relation 4.9 then becomes

where

no

47

we

on

on

Prob(x2c)

will not cut

on

missing-mass squared

background originating

vertex.

>

Missing

Figure

4.7:

(solid line)

3tt° data. Kîr^ missing and after

the lifetime interval

channels

(see

where,

section

a

cut

on

7C-fit

[—1, 20]ts-

The

mass

squared [

GeV /c

square distribution after

probability (dashed line). peak

in addition to the neutral

4.4.3).

Mass

in the

kaon,

a

a

]

cut

on

energy

probability

Events have been selected in

higher missing-mass region corresponds 7T° has been produced

at the

primary

to

vertex


CHAPTER 4.

48

improve the quality of the selected events,

In order to

•

The fit for the

The momentum of the

primary The

secondary-probability

Prob(x2ec)

•

Due to the limited lifetime

resolution,

4.3.4);

ative lifetimes

(see

quirements

mainly reconstructed

to

are

study both

the

K^,

by

7r°7T07r° DECAYS

following

severely

on

as

the

computed by

750MeV/c, 670MeV/c

cuts

:

probability

events.

the fit for the

750MeV/c.

and

should be greater than 10%.

some

the at

signal

events

are

also reconstructed at neg¬

background channels which negative lifetimes (see

signal and background

lifetime t-jq reconstructed

tt^ and K°

smaller than

•

section

the

->

missing-mass spectrum when selecting

primary particles

respectively be

vertex must

apply

vertex has to converge. We do not cut

primary

of this fit in order to not affect the

•

we

K°,K°

in the

fulfil the 7C-fit

section

4.4.5). Therefore,

largest lifetime region,

the 7C-fit for the best

pairing

re¬

demand the

we

[—40, 60]t,s

to be in the

range.

4.3.3 In

our

Pairing

77

analysis

we

want to reconstruct the

two neutral showers with the

pair of

not know beforehand which

With

a

simulation

study,

pairings is correlated with on

preselection

a

we

correct

37r°

—>

67 decays. For this,

cuts of section 4.3.1 for each

require

we

tt°. However,

we

do

evaluate how the

pairing, and then

probability see

of the 7C-fit for different

the consequence of wrong pairings

the lifetime reconstruction.

of

Matching

generated and reconstructed photons

Monte-Carlo Data. For this

photons

and

particularly

between the conversion

sample,

we

we can

between

generated

a

in the calorimeter.

and reconstructed

pairing found by the 7C-fit is

photons,

see

pairing rate,

reconstructed

photon

in the transversal

at less than 2.5cm from the

study,

we

a

Pairing

Repeating

probabilities

plane

:

a

the

conversion

correct

(for

the

we

7C-fit,

can

matching

a

should not take into account events

generated photon. In figure 4.8

generated photon and

we can

the shower-foot of

around 80% of the showers

are

a

reconstructed

can

be observed. at less than

point.

procedure described above for the pairings given by the we

37r°

the reconstructed

generated photons; however, non-negligible tails

generated photon

of

the distance

Computing

require that all the six reconstructed shower-foots should be

lcm from

of the

point of

sample

Appendix B).

shower has been reconstructed far from

the distance between the conversion

For this

point

a

concerning the generated MC

points of generated photons and the shower-foot of

In the determination of the correct

for which

We consider

have all the informations

their conversion

determine whether the

showers,

see

—>

photons originates from which tt°.

two

can

K°,K°

determine in how many

cases

they

n

highest

match with the correct


4.3.

49

'E c

W

10"

3

10

2

10

-15

-10

-5

0

5

10

15

Transversal shower-foot difference [cm]

Figure

3tt° simulated data. Shower-foot difference

4.8:

and reconstructed

pairing

of the

function of

in transversal

plane between generated

photons.

generated

In table

events.

decreasing probability

4.1,

we can see

for the different

the percentage of correct

pairings

of the 7C-fit. One

Pairing

of 3

highest probability

15. ±2.

Pairing

of 4

highest probability

9.±1.

Pairing

of

5th highest probability

7. ±1.

our

Proportion

The question to

us

of correct

is 60%

analysis (see

highest probability

Let

24. ±2.

gives the right pairing by

the cuts of

us

2nd highest probability

of

highest 7C-fit probability

allow

40. ± 1.

Pairing

Table 4.1:

the 7C-fit

highest probability

of

to

now

improve

a

than the rate

:

observe that

pairings of the 7C-fit.

the correct

pairing

rate

given by the

given by the 2nd probability. Applying

the percentage of correct

pairing for the

55%. is if there is

on

the

a

criteria other than the

highest probability which would

pairing.

consider the 7C-reconstructed lifetime

ECAL)

various

manner

4.4.4) improves

where ta is the reconstructed lifetime

the

decisive

higher

section

pairing for

as

[%]

Correct pairing rate

Pairing

can

pairing

by

T^c(i)

for the

ith highest probability and

the intersection of shower directions

and the neutral-kaon flight direction

(see Appendix C);

ta is

(as

ta,

measured in

pairing independent.

We

can

then build the

pairing-dependent

variable

At (i)

rate is

correct

higher

This is what

one.

for small values of

At(i)

ttVtt0 DECAYS

->

:

(4.12)

T7C(i)-rA.

=

The smaller this difference of lifetime for

pairing is the

K°,K°


CHAPTER 4.

50

given pairing, the higher the probability that this

a

observe in

we can

Ar(i). However,

for

a

figure

4.9.a where the correct

value of lifetime

given

pairing

difference,

the

a)

40

35

*

30

:

25

:

•

Q

20

6

-

•

15

Û a

10

7

A

A

A A

5

7

7 5

10

12 5

15

17 5

20

22 5

25

09

1

b) •

• -

•

0

-

1

O

•

[

0

Q

--

,,,,!,.,.

01

02

04

03

05

06

07

08

AProb

Figure

4.9:

a)

for the first

Correct-pairing

:

(full circle),

second

rate

(open circle),

(full triangle) highest probability, difference AProb

(of

second and the third

correct-pairing of the

eq.

4.13)

(i

+

ith highest probability;

l)th

highest probability

is

of the

probabilities

corresponding pairings;

Prob7c(i)

Correct-pairing

it is thus not

AProb(i) where

:

rate

forth

ta

(of

(open square)

function of the

as

(full circle)

we

=

+

1),

the

pairing

possible

to

never

exceeds the

improve the

7C-fit, there could be

is not

eq.

4.12)

and fifth

probability

and between the

big, revealing

Prob7C(i) +

i has

1). a

-

We

cases

rate

pairing.

where the difference

the weakness of the 7C-fit to choose

Prob7C(i can

correct-pairing

correct

thus consider the difference of

higher than Prob7c(i

higher than Prob7c(i

(full square),

between the first and the second

probabilities

between two consecutive between the

b)

third

~

(open circle) highest probability.

rate of the

When sorting the

function of the time difference t7q

as

+

probability

1)

estimate that if

big probability

:

(4.13)

Prob7c(i)

to be the correct

one.

is much This is

4.3.


what

we can

however,

observe in

it is

again

not

not found

Having

a

4.9.b where the correct

figure

possible

criteria which allows to

correct

improve

the

AProb(i);

increasing with

rate is

pairing

improve the total

to

51

pairing. correct-pairing rate,

will

we

pairing associated with the highest probability of the 7C-fit.

the

Lifetime resolution

4.3.4

The effect of

bad pairing

a

4.10.a and 4.10.b

:

+5ts, for the

and

pairing

have

we

a

on

pairing

we

have

resolution function of

the lifetime resolution and the

photons through

When

.b),

and

pairing

be understood will result in

C6_s

of the event

K^tt^)

which could favour

of such

effects,

a

pairing and

we

t) given by

the

or

highest probability, for

the

RMS of

that the lifetime resolution

pairing. This correlation between

by equation

4.8

:

a

bad association

badly reconstructed decay

a

kinematical

bad association between

pairing (figures 4.10.a

same

configuration

photons. In order

of

to be

2nd probability gives the

(r7c(2)—t)

photons

figures

photon-

correct

4.11.a and .b

(t7c(1)

we

observe

that the deterioration of the lifetime resolution is

mainly

given by

due to

a

bad

=

t

—

t, where

aa,

gaussian function where 1.5,

we

obtain aa

corresponding when the

7,

a

a

and N

to the

in table 4.2. correct

It is

of

a

gaussian distribution;

pairing, there is

we can

r

a

—

x.

t. There

the

good pairing.

even

Fixing ß are

7C-fit;

a

kind of

at 0.7 and 7 at

five such distributions

each distribution is filled

In the limit of

ß

=

probabilities

if all five lifetime resolutions

0, the is

aa

reported

correspond

slow deterioration of the lifetime resolution towards lower

the event

topology

also affects the lifetime resolution.

conclude that the lifetime resolution is

but also decreases with

This function is

its value for the various

to observe that

probabilities, which indicates that Therefore,

the

("4)

increased with

highest probabilities given by

interesting

a

:

free parameters.

distribution of

corresponding probability gives cr

are

symmetrically

is

by fitting g(x)

to the five

parameter is the

a

the

ß,

—

pairing.

9(*)=N^[2J(::lxV)\ x

and

independent

with the lifetime resolution

events. In

The best function to fit the lifetime resolution is

with

vertex.

correct-pairing probability than for the highest probability,

better lifetime resolution for the

confirming

(geometrical

compare the lifetime resolution

(greater

deterioration of the lifetime resolution could

select those events for which the

we

5ts

—

1.5ts, while for the bad

events for correct and bad

comparing different events; the

topology

be due to the

figures

the

gaussian between

~

a

we can see

events with correct

can

a

events in the tails

more

figure 4.10.C,

in

the constraints

3ts with

~

comparing the lifetime resolution of

we are

by comparing

seen

resolution function of

a

o

improves when increasing the number of

between

be

can

lifetime resolution distribution with

fitting the

correct

the lifetime resolution

distribution). Moreover,

the resolution

to

use

decreasing

7C-fit

probabilities.

mainly

a

function of the

The final lifetime resolution

pairing

(see figure

CHAPTER 4.

52


a) RMS

2 726

X'/ndf

55 78

Cons DM

loo

/

RMS

:

18

02838

"1

30

r

40

20

j-

'

20

i

L

10

1

ll

if

"

JIT -20

20

Resolution

60

'S3 o

,

20

[xs]

Resolution

[x ]

u t

~-

\

R

•c

„r",l

-20

c)

:

50

-uu^

ill.

In,

0

70

2999

1

40

60

^

IB

43 76

S„.~

C

W

/

1 023

50

•4—1

80

30 11

Constant GO

1507

Sigma

1998

XVndf

72 B3

Mean

1)

W

ttVtt0 DECAYS

->

b)

a

a

K°,K°

\

1

40

M M

»

30

o

Ü

20

10

r

,,,,!,,,!

0

10

15

20

25

30

l7C(l)

Figure

3tt° simulated data.

4.10:

pairing

events,

b)

:

1st pairing of 7C-fit

Lifetime resolution for bad

function of the percentage of correct

4.12.b),

includes both correct

resolution of bad

a

~

pairing

:

Lifetime resolution for correct

events,

c)

:

Lifetime resolution

(4.10.a)

and bad

pairings (4.10.b), resulting

2.6ts- The tails of the lifetime resolution distribution

in

section

In

with very few hits in the

3.4.1) resulting

figure 4.12.a,

we

lated data after all the

in

a

bad

are

mainly due

lifetime

calorimeter,

their energy is

in

cuts

(see

next

our

section).

detector

(see

gives non-negligible number of signal

a

to

a

momentum of

since neutral-kaons of low momentum

pairing and though

includes the effect of the acceptance of resolution which

:

have the reconstructed neutral-kaon

analysis

a

total lifetime

a

pairing. We have slightly improved this resolution by demanding that the

low-energy photons

as

pairing for the highest 7C-fit probability.

the neutral-kaon must be greater than 180MeV7c

(see

a)

:

t[xj

badly

give

reconstructed

bad lifetime reconstruction.

decay-time from K°

This lifetime is the section

3.4.3)

—>

3tt° simu¬

Kt, lifetime which

and the limited lifetime

events reconstructed in the

negative

region.

In order to

improve the lifetime resolution and thus the statistical

error

of the fitted

4.3.


53

a) 50

|

RMS

3 238

40 I

I

30

J

20

10

1

\

r -,

,

1

,

„

.

„^^.

.^

i

.S^r-u

,

,„.

,

r,

1

,

20

(T7C(2) t) [T ] -

b) 1

RMS

20

a

C 17 5

rV

q

«

15 12 5

10 75

M

5 25

uzM

0

cdL

ni h n,n

-20

,

n

10

lin n n 20

(MU-t)lTj

Figure

4.11:

when the


2nd gives the

correct

2nd (a) and lsi (b) probability

Lifetime resolution of the

pairing.

"o-

Lifetime resolution of 1st

probability

0.68 ±0.01

Lifetime resolution of

2nd probability

0.68 ±0.02

Lifetime resolution of

3rd probability

0.72 ±0.02

Lifetime resolution of 4th Lifetime resolution of

Table 4.2: The aa parameter of the 7C-fit

[ts]

probability

0.76 ± 0.03

5th probability

0.76 ± 0.03

correct-pairing lifetime resolution (eq. 4.14) for

various

probabilities.

parameters

-Re(?7ooo)

with the measured

improves slightly

and

im(?7ooo))

angles

we

have studied the

of showers in the ECAL

the lifetime

resolution,

while

possibility of reconstructing the

(see Appendix C).

losing signal events,

C. This 13C-fit will therefore not be included in

our

analysis.

as

Such

a

events

constrained-fit

discussed in

Appendix


CHAPTER 4.

54

K°,K°

-

7t07t07t0 DECAYS

a) S

500

S

400

27T° decay with

annihilations,

In the pp

Percentage of pionic background

4.17:

function of

period

secondary photons

2

the neutral kaon

can

decay

produced by secondary interactions, giving pp->

as a

into

thus the total

Kü(K°)K±iv^

27T°

27r° and

->

+

two additional

photons

photon multiplicity

6

can

:

2lsec.

47

Considering 27r° simulated data, by matching generated and reconstructed photons (see Ap¬

pendix B), photons

we can

and

Before

among the six reconstructed showers the two

tag

describing The

the mechanisms

for 37T with

mean

~

giving secondary photons, let

point which characterises all of them

photons. In figure 4.18,

energy of

we

energy of

can see

that the

photons from

156MeV for the six

the

mean

K°

—->

photons of 27r°

events, each photon having less available

computing the

invariant invariant

from

secondary

study their characteristics.

characteristics.

while the

originating

mass

mass

invariant

corresponds for

2tt0

the neutral-kaon

mass

in the final

we

data,

+

mass

to the

27sec.

energy of

is that

We

is

in

photons

use

of this property

photons (see Appendix D); this

from the

mass

a

higher

K° decay already give

In order to reduce the amount of

require that the invariant

a mean

is around 127MeV

mean

make

energy

131MeV

~

167MeV, resulting

can

common

they produce low

of the neutral-kaon for 37r° events and to

events where the four

(see figure 4.19).

~

events while this

of the six reconstructed mass

discuss their

secondary photons

27T° decay is

energy.

us

27r°

+

27sec.

events

of the six showers should be smaller than

SIGNAL AND BACKGROUND DETERMINATION

4.4.

59

300

350

400

[Mev]

Mean énergie

4.18: Simulated data. Mean energy for

Figure

generated photons

four

MeV/c2.

27r°(b),

According

to the

variables

now

each event

showers

are

we

~

the

~

27% of the 27r° + 2n/sec

6% of the signal.

not to count

demand six showers with

e+e_ pair in

probability gives

some

of such

two

producing secondary photons and

charged a

showers

the

m

around their interaction

the total number of

distance greater than 25cm from

Among

a

and

conversion for

can

thus

a

entering the calorimeter,

a

photons,

tt^ and

e+e~ pair.

a

photon

with

an

two

are

photons

detected

can

for

50cm

by

are

convert

the minimal

40%

[23].

indistinguishable

from

energy above lOOMeV is

showers into the calorimeter which

27r°,

some

(Cherenkov, Scintillators);

give the total photon multiplicity

the four 7 of the

convert in

Before

massive part of the detector

electromagnetic

photon showers •

27r°(a),

27r° (dashed line) and the six

produced by charged primary particles

Showers from 7 conversions

This

of the

K^.

a

a

of the

cut suppresses

the three different mechanisms

point in the ECAL. In order

into

secondary photons

permitting their further reduction.

"Charged"

from

photons

simulation, this

background while suppressing only We describe

the six

the two

37r° (solid line) (c).

of the

generated photons

800

of the

:

6 in the

following

cases

:

the calorimeter and the two other

CHAPTER 4.

60

6y Invariant

Figure

a)

4.19:

Simulated data

:

(dashed line), b)

•

Among

:

37T° data

albedo

•

a

photon (for

a

possible that

because

being

(see

a

67 Invariant

27r°,

three

mass

photons

the

by

in the

one

3.4.3),

[ Mev/c

calorimeter,

ECAL,

27T°,

among the four 7 of the or

next

can

has

a

while three other

broad distribution with

observe in

figure

characteristics of both we

the

require 27T°

+

mn > 12

photons

as

additional

paragraph).

convert in

mean

a

value of

clear ~

by the calorimeter

e+e~ pairs.

mass

mn out of all

peak below

lOMeV/c2

possible

while the

31MeV/c2 (see figure 4.20,a).

signal and 2?t0 + 27sec background. In

MeV/c2. According while

The albedo

and detected in the ECAL to be detected

an

photon

One

4.20.b that the distribution of this variable for the data reflects the

27sec background

"Albedo" showers

a

27sec

because pointing outside the geometrical accep¬

pairs (see Appendix D), such background shows

signal

+

the fourth

while there is

is not detected

When computing, for simulated events, the minimal 77 invariant 77

ttVtt0 DECAYS

for data events.

see

photon

Mass

->

37r° (solid line) and for 27r°

for

detected

are

seen as

mass

definition of albedo photons,

low energy

section

67 Invariant

:

e+e~ pair

It is also

tance

:

the four 7 of the

has converted in

K°,K°


as

to the

suppressing only photons

are

those

neutral showers

neutral shower is

roughly 9%

order to reduce this

simulation, ~

~

48% of

12% of the signal.

produced by charged tracks but

(see figure 4.21);

[41].

background,

this cut suppresses

the

probability

for

sent back a

photon

SIGNAL AND BACKGROUND DETERMINATION

4.4.

61

a) g

5512OO

:]

-

c

,§1000 800

r\

';

1 i|

600

;:

_p-uL^.

^j^ffT :s^r"^

400 200

1,

,

,

,

1

,

,

,

^^S^

[

''

'-~~']

,

1

30

27T°

a)

4.20:

Figure

Simulated data

:

27sec (dashed line), b)

+

:

showers) photon

and the cut of 12MeV

conversions into

very similar to the

photons

of 2tt0 +

is not

possible

K°

3tt°

—>

these

—>

to

one

e+e~), of

figure

27sec events;

:

,vritrT1rr*^-.L, 60

70

.

.

1

.

SO

remaining

4.18.a with

..

100

Minimal YY Invariant Mass

[ Mev/c ]

Minimal vy Invariant Mass

[ Mev/c ]

events

mass

have

a mean

with variables the

,

90

for

mass

27 minimal invariant

mass

energy very

to find

a

(solid line)

and for

for data events

(mainly eliminating charged

photons

computed with

us

3tt°

(mainly eliminating

mn is done

remaining photons

is what motivates

us

compare the direction of

tracks with the direction of rection of

flight of

~(P~K

—

probability, ter,

,

50

and 25c77i around tt^ is done

distinguish between

67 decay. This

1

,

the 7 7 minimal

on

the

,

with

an

energy distribution

comparable

with the

the energy of the

and those

one

of

photons

it

originating from the

geometrical variable

to characterise

photons.

Let

(Pk°

K^

,

minimal invariant

27

:

,

40

3tt0 data

Once the cut of 50cto around

^W

'

lt

1

we

+

and

flight

flight

reconstructed

possible

P~k))- Using

the

corresponding directions of

the associated

to the

flight

decay

aß (i),

($,0)

Let

a

the

charged

be the di¬

plane given by the charged tracks

and shower-foot coordinates in the calorime¬

pair of photons

to obtain three

vertices of the three

7r°'s;

we

we can

independent "secondary

independent "secondary

then define

of the neutral-kaon in the transversal

vertex and the three

errors

the six showers.

using

pairing of the six photons obtained with the highest 7C-fit

using the shower-angles

using the primary

using

the neutral-kaon in the transversal

intersect the directions of each

vertices"

of the neutral-kaon reconstructed

plane,

vertices".

ß(i)l=its

as

three

directions obtained

Having calculated

compute the weighted direction of flight of the K° in the

CHAPTER 4.

62

K°,K°


->

ttVtt0 DECAYS

ECAL

Figure

Albedo showers

4.21:

originating

from the

transversal

plane given by

decay

of

the

(black) a

neutral

It is

now

interesting

to

that for

background mean

(4.22.b)

of neutral-kaon

are

represented

is

the two

(4.16)

plane (x, y)

a

and

ß,

of the detector

angles

uncorrelated.

are

flight-directions given by photons,

the

The

peak

27r°+27sec. background;

but

events.

We

can

similar effect for

define the

angle

8

signal

\a

=

—

ß\

which

measures

angles giving the neutral-kaon flight-direction. For signal a

distribution with

a

clear

distribution for 27t° + 27sec. with 8 to the ~

2n +

sec. y s

„o o K —» 3ti

o

n

-

.

,

K

,

30000

—> 271

pionic

£

25000

data

15000

-

result of the fit 20000

^

12500

10000

15000

L*-, 7500

10000 5000

2500

0.1

Neutral-kaon

0.1

0.2

0.3

decay

time

0.4

0.5

mass

squared

interval

[0.15, 0.35]GeVr2/c4.

in the lifetime intervals

spectra (points)

are

channels

are

decay

0.4

Fits to the measured

with the fit result

shown.

0.3

0.5

0.6

0.7

Luev/c

J

0.4

time distribution

[-20, -10]rs (b), [-10,0]r5 (c)

compared

0.3

Missing-mass squared

Fits to the measured neutral-kaon

4.25:

background

0.2

[ GeVz/c


Figure

0.2


(crosses) ;

and

(a)

in the

missing-

K^tc? missing-mass squared

[0,20}ts (d).

The measured

the contribution of the

signal and

CHAPTER 4.

68


K°,K°

Channels

Pionic

Signal

2tt°

7r037T0

7T027T0

77/71"°

1.

-0.04

-0.68

0.02

-0.09

1.

-0.32

-0.21

0.16

1.

0.03

-0.09

1.

-0.51

Signal 2tt° 7r037T0 7r027T°

PP-

-

pp-

pp-

-*

pp--+ PP-->

Table 4.4:

K^K^K+tt* K°(K°)

errors are

7T+7T

channels.

Contribution -

3tt0

Contribution

KÜ(K°)K±^ KîK0)^^ K*(KQ)K±^

[—1,20]rs

[%]

24.9 ±0.5

77,71

statistical.

[%]

50.0 ±0.8

:

Contribution of

time interval


:

Backgrounds ->

ttVtt0 DECAYS

1.

Table 4.3: Correlation between

Signal

-»

+

secondary photons,

K°(K°)

—>

2tt°

16.5 ±0.3

+

7i°, KQ(K0)-,3vr°

4.9 ±0.2

+

ir°,KÔ(K0)-^277°

3.7 ±0.2

signal and backgrounds

and within

a

missing-mass

to the final data

square interval of

sample

in the

decay-

[0.15,0.35]Gey2/c4.

The

69

DETERMINATION OF mo

4.5.

Determination of 7/000

4.5

The real and imaginary part of the CP-violation parameter 77000 in cays

are

dependent asymmetry

T=TO&S

Rooo(r)

i?ooo(r)

and

given by equation

observed lifetime

Koo(r)

-

=;obs

the observed

are

figure

4.6 and shown in

(4.17)

R^(r)

ld(r) +

Rqqq(t)

to the

7r°7r07r0 de¬

—>

:

A$?0(t) where

(2.50)

extracted from the fit of the theoretical asymmetry

K°,K°

rates of

decay

initially

pure

K° and K°

states

Therefore, the observed asymmetry depends

4.26.

on

a) 1200

A

f, 1000

w

800

600

400

;

-

,/

200 1

1

-20

-10

0 -40

-30

,

-,

.

....

.

10

0

.

*. 1

20

30

40

50

decay

Reconstructed neutral-kaon

60

time

[xs]

b) ,

f 800

#t

~~

600

200

\

/

L

400

r >"

0

1

1

1

-40

1

1

1

-30

1

1

1

1

1

1

1

1

.

1

-10

-20

.

I

1

,.

0

I

1

1

1

1

.

10

1

1

1

1

20

.

1

VT'il'T-rYv^v^^

30

40

Figure

37T° data

4.26:

background

:

contamination

the resolution function

T(t

the normalisation factor

leaving

the

Lifetime-distribution of i\°

K°/K°

(see —

t,t),

K°/K°

factor

as

table

a

decay

time

and K°

[xs]

(b) decays including

ou/o

4.4).

the amount of

and,

(a)

60

50


in second

background,

order,

on

the

background shape bckg(r),

the acceptance function

free parameter in the fit of the asymmetry,

we

e(t).

While

should know

these functions and parameters in order to extract the information about the CP-violation

parameter

77000 contained in the theoretical rates

RoQ0(t)

and

i?ooo(*) (equations

2.48 and

2.49). We will first

metry. Then, our

we

study

and determine these

will present the fit

analysis and present

our

"components",

procedure;

final result.

we

will

necessary to the fit of the asym¬

finally

discuss the

systematic

errors

of

Components

4.5.1

T(t

—

—

t)

t,

varies

a

as a

simulation

addition,

parametrise

the resolution function is the

where

x

=

(compare

parametrisation

to

the

Nexp[-

following function

=

L2a2(l

1rs),

we

seen

from t

:

figure 4.27,

+

the

the RMS of the

4.815 for large decay-times. t. We

:

(x-uf

(4.18)

ß\x\-7x)Sl

asymmetric tails of the lifetime resolution

with resolution function given in equation

generated lifetime (Ai

be

generated lifetime

decay-times

T—t. This function takes into account the

distribution of

—

can

asymmetric and this asymmetry also varies with

decay-time resolution by

p(x)

study. As

function of the

resolution distribution varies from 4.2T5 for small In

ttVtt0 DECAYS

t, t) in reconstructing the neutral-kaon decay-time

We derive the resolution function from

T(r

->

of the asymmetry

The resolution function

resolution function

K°,K°


CHAPTER 4.

70

4.14). Moreover,

for each bin

(eq. 4.6) by

specific p(x)

will fold the theoretical rates

a

in order to take into account the variation of the resolution distribution with

t.

Figure

4.27:


The

decay-time

resolution for four different

decay-time

regions. The solid line shows the parametrisation (eq. 4.18) of the decay-time resolution. Uncertainties in the lifetime section 4.5.3.

resolution, resulting

in

systematic

errors

will be discussed in

4.5.

DETERMINATION OF 77000

The amount of

background contributing

of the observed rates

given by table 4.4. taken into account

(eq. 4.6),

The

in

as

systematic

dE/dX-study

for the

errors

-40

-20

0

40

60

-40

expression


We obtain the lifetime distribu¬

-40

-20

a

neutral-kaon

decay,

A fit to these distributions is shown

parametrisations which fit best these

0

20

40


[ts]

C)

decay

time

[xs]

d)

-20

0

20

40

Reconstructed neutral-kaon decay time

The

(bckg(r))

fit intervals and the

20

In the

in section 4.5.3.

pionic background.

Reconstructed neutral-kaon decay time

4.28:

K°

of K° and

know the level of all contributions will be

we

function of lifetime

figure 4.28, together with the

Figure

sum

channels from simulated data for channels with

background

and from the

of

to the

take into account the amount of

we

precision with which

as a source

Shape of background tion for the

71

60

-40

decay-time distribution

-20

0

20


[xs]

of the

40

decay

time

60

[xs]

pionic (a), 27r° ± 27sec. (b), 7t°3vt0 (c) and

7T°27r0 (d) background channels. The solid lines show used parametrisations. lifetime

for the lifetime

shapes

Having

determined

bckg(r)

region [—1,20] ts (see table 4.5). from

simulation,

bckg(T)

=

we

abckg

obtain

bckg(r) through

bckg(T)

where abckg is the normalisation of the relative contribution of

signal;

it will be determined

In order to fit the

by

the method

explained

study the effect of the parametrisation

decay-time distributions

in section 4.5.3.

of

the relation

:

(4.19) background

in the next as a source

to the

K° and K°

paragraph.

of systematic errors,

background channels with different functions,

as

we

will

discussed

CHAPTER 4.

72

Channel

2tt°

+

exponential

exponential

27sec.

can

be

seen

7r°27T°

exponential

on

equations 4.6 and 4.19. In figure 4.29

background

structed

contributions,

time for all

justifies that

interval tion of

we

[—1, 20]ts-

background

to the

this in

we can

a

large

as

a

to the

for each channel and

separately

for K°- and

thus determine

can

and for the

data, a

we

it

that, within statistics, recon¬

decay-time ([—20,20]ts); in the fit

K°/K°

repeat the simultaneous

we

obtain the number of K°- and

(sec

K°-events

4.6).

table

normalisation

1.13 ±0.02

2tt0 + 27sec.

1.14 ±0.05

7T03îT0

1.16 ±0.04

7r°27T0

1.18 ±0.06

Pionic

1.18 ±0.02

background

to the

K° and K° signal

obtained from the simultaneous lifetime and

fit.

that for

signal

a37ro

unity

=

£[1

+

4Re(es)]

is dominated

K°. More generally, for

by

and that es

10~3,

we can

observe that

the difference of the detection

probabilities

any channel with

a

~

neutral-kaon

decay,

by £, the difference of detection probabilities for K° and

is dominated

a

possible CP-violation effect

expected

as

if°-data. With this method, which fits

Signal

a

is

interval of

for each contribution

background channels,

the deviation of 0:3^0 from for K° and

observe

time-independent parameter

Table 4.6: Normalisation of the relative contribution of

Recalling


K° and K° signal for all contributions,

Channel

missing-mass

The

To derive the absolute value of the normalisation of the relative contribu¬

reference distributions to simulation and

signal

for

K° and K° signal is independent of the

consider this normalisation

fit described in section 4.4.5

for the

K° and K° signal

to the

K°/K°

the normalisation

the relative contribution of

this

decay-time of background channels.

signal and background contributions

from

decay

exponential

+

gaussian ± gaussian

depends

7r°7T°7T0 DECAYS

+ constant

7T037T0

Table 4.5: Parametrisation of the

observed asymmetry

-

Parametrisation

Pionic

Difference of

K°,K°


to be

equal

of the order of

for all channels

10-3.

involving

a

Therefore,

the

the normalisation

K°,

but also includes

K°/K°

normalisation

neutral-kaon that has been

tagged by


4.5.

73

K°->3tx0

xVndf

—

o

,

4+^1-!-!++

U'+rfTT+rf -30

T+'T-r-r-

1

1

1

1

1

+ -hM-

1

1

-+"

+ -1"'1

'I

.+.

1

1

—

1

1

-10

-20

K° -> 2TC°+sec.

y

'

'1 1

46.65

..

'

1

1

1

1

1

1

1

1

,

I

I

I

1

I

v0

0

7t

,

K

_

->

1

1


decay time [xs]

I

I

45.51

H++J+++.

4-t-t-+

3-

I

3I

I

I

I

I

I

I

0

-10

-20

-30

-+-_+.+

,

1

s

J-+;i-Tf^+++

-H

,

1

30

10

X2/nd

i± +.

,

1

40

20

0

Î4 o

,

.

,

^

1

1

/

/

40

rh

+1 » .t-h

Jri-fifl 20

30


decay time [xs]

10

-0

3rc

XVndf

45.48

/

40

O

+--+— -

+, ,4-+'-HI.1

_=t. 1

1

1

1

1

-30

1

1

1

1

1

1

1

1

1

1

-10

-20

1

1

1

0

.-,—>-,

;

1

1

1

1

1

1

1

[

1

1

1

1

20

30


decay time [ts]

10

7i°,K%2/ 46.08

XVndf o

1

1

1

1

-30

1

1

1

1

-20

J

I

J2 I

I

-10

I

I

40

V^+'î^

,

1

/

•y I

L

0

20

10


30

decay

time

[ts]

33.16

/

8

Pionic

XVndf

—

o

IW -

1

1

1

1

1

1

1

[

1

-20

-30

1

1

1

1

1

-10

1

1

1

1

1

0

1

1

1

1

10

1

1

1

data) the

4.29: The normalisation

and for the

pionic

contribution

accompanying charged

kaonic

backgrounds

Therefore,

we

are

K°/K°

kaon and

for contributions with

(from pion

the

:

a

a

4.6,

of the

we

signal (aô) and leave

1

1

decay

time

[xs]

kaon-decay (from

can

simulated

it

asymmetry. However, for the pionic background,

as a

we

observe that the a's of all

signal within their statistical

will consider the atcfcc,. normalisation of all kaonic

the normalisation of the

1

dE/dX-study).

in table

compatible with the

1

30


Figure

1

20

backgrounds

free parameter

have

a

a

to be

error.

equal

in the fit of the

charged pion instead

of

a

to

Aooo

charged

74

CHAPTER 4.


kaon at the

primary

:

can

priori lead

a

Therefore,

(see

the strong interaction acting

Aooq asymmetry,

in the fit of the

in the determination of

uncertainty

generated

lifetime t from

event has

reconstructed at

and im (77000).

systematic

simulation

a

Due to

negative

negative lifetimes

a

However,

lifetimes

as

as seen

[—1, 20]t5 by minimising

the

^4ooo asymmetry given by

JVj and N%

This

signal

errors on

and

is

region also

signal

—

events

the fit interval to

errors on

Re (77000)

mainly present increases the

in the

errors

on

the fit interval has been chosen to be

imôoo),

maximum likelihood method. The likelihood that

=

respectively

i?ooo(T)

and

through

we

^2Nt-lnRt + '52Wt-lnB~.

will

the number of events in the

iôoo(T) (see

e

4.30 shows the

the

(530.7 Ki

of the

±

1.3)

mean

x

are

given

lO7^-1 and

life is fixed at tt, are

We

(a.

can

—

I)/(a

+

1) (see

we

can

only put

The limited lifetime

use

27sec, tt°

free parameter a; for the

+

K°

—>

3ir° and

pionic background,

To fit the observed asymmetry

(89.22

=

as

fix the

±

±

mass

0.10)ps

0.4)ns

as

difference and the Ks

as

determined in ref.

given by

Re(vooo)

=

0.18±0.14stat.

im(?7ooo)

=

0.15±0.20siai.

mean

[45];

by

life at

the value

ref.[23]. Re(r)QQo), im(?7ooo)

free parameters in the fit. The fit

yields

:

(4.23)

is statistical. The correlations between fitted

parameters

eq.

observe that the measured asymmetry has

one can

to

a

an

upper limit

a

better

on

correlation of p

=

are

the CP-violation parameter 77000

resolution, coupling strongly the

of this strong correlation

2.45, and get

a

total

4.4).

observe that the obtained values for the CP-violation parameters

equation 2.50, leads make

we

(51.7

=

error

±

For all channels with

in table 4.7.

with zero;

4.5.4).

ts

left

Given the obtained value for a, offset of

as a

2tt°

—>

K° and K° signal

to the

4.19).

4.6 and

eq.

experimental asymmetry Aqoq.

1.10 ±0.03 where the

=

to

table 4.6.

given by

and the normalisation factor

a

4.5.1).

background

the K°

signal,

maximising the likelihood of equation 4.22, =

(see

rates

2tt° decays, this factor is left

it is fixed at the value

Figure

and

(eq. 4.6).

decay, namely

neutral-kaon

e(t) (fig. 3.10)

background channels bckg(T) (tab. 4.5) contributing

background decay

and

signal

for

with

section

the normalisation of the relative contribution of

•

the acceptance

in tab. 4.4.

signal and background given

•

Am

(eq. 4.6) by

rates

79% between

by fixing Re(77000)

at

compatible

(see

section

sinus and the cosine term in

i?e(?7ooo) Re(es)

precision for im(77ooo); however, there

is

and

as

no

Im(rjooo).

We

can

suggested by equation

experimental

value of

CHAPTER 4.

76


7 5

Figure

4.30:

The measured

pure K° and K° into

37T°,

12 5

lO

Neutral-kaon

decay

K°,K°

15

->

IV 5

time

W DECAYS

tt

20

t-^sl

time-dependent CP asymmetry between decay

between —1 and 20ts-. The dots

are

the

rates of

initially

experimental asymmetry

and the solid line shows the result of the fit to the data.

Re (77000)

im(77ooo)

a

1

0.79

-0.09

1

-0.56

-Re(77ooo) im (77000)

1

a

Table 4.7: Correlation coefficients between parameters obtained from the fit of the

Aooo

asym¬

metry.

Re(es).

In order to be able to

use

the measurement of the

semileptonic charge asymmetry

[23]: T(KL

we

have to

then fix

assume

Re(r]ooo)

to

->

TT-Z+i/)

-

CPT-conservation

Si/2

=

statistical precision of the

Re(er)

=

T(KL

(x_

=

Re(es)

Im(rjooo) by

im(77ooo)

a

-

y

=

8

=

0,

.

\/l

—

p2

.

fAni^

nn

see

sections 2.1 and

in the fit of the asymmetry.

factor

=

TT+I-V)

This

2.2);

we

can

improves the

:

-0.05 ± 0.12rtat

(4.25)

77


4.5.

Systematic

4.5.3

in the fit of the asymmetry

"components"

The

errors

(section 4.5.1)

known with

are

To take into account the effects of these uncertainties in the final

component of the asymmetry within its

error

result,

interval and observe the

some

uncertainty.

will vary each

we

resulting variation

on

the fitted CP-violation parameters.

•

Neutral-kaon

time resolution

decay

In order to take into account the simulation

a

possible underestimation of the lifetime resolution by

study, the resolution function has been increased by 10% in each bin of

generated decay-time;

the

error on

aa is below

10%,

parameter which

where aa is the

represents the width of the resolution function given by equation 4.18. This has of 0.01

on

ite(77000)

both

Moreover, possible

and

1777,(77000)

deviations in the

resolution function

•

Lifetime

shape

In order to will fit the

4.8).

of

the effect of the

parametrisation of

The effect of the variation of the

Pionic

exponential exponential

27sec.

7r°37T0

gaussian

+

negligible.

Background

contribution

systematic

signal and background,

we

the

induced

error

replace

where its amount is

determined

fixed,

of

a source

exponential

decay-time for

systematic

different functions

the simultaneous fit

background

various

we

(tab.

by

an

channels,

to determine the level of

independent missing-mass

proportions

of


proportions given by the simultaneous

pionic background is obtained from

in each bin of lifetime and

by the dE/dX-study

errors,

+ constant

by the method used

channels agree within better than 3% with the The level of the

as

Parametrisation 2

and lifetime fit to the reference distributions. The

(table 4.4).

a

exponential

parametrisations of

found to be

fit

The effect of such

parametrisation of lifetime-distributions has been

Parametrisation 1

To evaluate the

a

time.

background channels with

Channel

Table 4.8: Alternative

decay

the asymmetry with

negligible.

decay-time distributions

+

of the

by fitting

background channels

study

2tt°

•

decay-time dependence of the resolution function

(fig. 4.12.b) independent

variation has been found to be

effect

•

from the simulation have been considered

(fig. 4.27)

an

a

simultaneous fit

squared missing-mass,

in each bin of momentum

(see

section

at the level

4.4.1);

the level


CHAPTER 4.

78

4.4). Therefore,

to determine the

the level of contributions with

a

systematic

decay by ±3%,

kaon

Variation of the amount of the contribution

2tt0

and

im(?7ooo),

we

and reduce the level of the

vary

pionic

AIm(77ooo)

AIm(7?ooo)Äe(77000)==ße(e:r)

±0.01

±0.01

±0.00

±0.00

±0.01

±0.01

±3%

:

7T°37T°

:

±3%

±0.01

±0.01

±0.01

7r°27T0

:

±3%

±0.00

±0.00

±0.01

-0.01

±0.01

±0.02

n7i°

:

-7%

Table 4.9: Contribution of the variation of the level of errors

when

•

i^ôoo);

Re (77000),

on

Re(rjQoo)

=

background

normalisation of

for K° and the

K°/K°

left

as

only

the

kaon

a

a

K°/K°

systematic

in

error

systematic

on

iTn (77000)

to the

K° and the K° signal

errors on

Re(77000)

normalisation within ±5% for

a

and im (77000)

signal

kaon are

decay

then evaluated

background

and

all

are

channels

decay. We recall that the mechanism giving different detection efficiencies K° is expected

to be the

normalisation of the

free parameter

take the

biggest

a

same

and

signal

in the fit of the

error on

Re(rjooo)

for all channels with

background

is determined with in

a

precision

of 2%

a

neutral-kaon

channels with

a

kaon

decay;

decay

asymmetry; therefore, for these channels,

and

is

we

im(?7ooo) (table 4.10).

The normalisation of the relative contribution of

uncertainty

background

signal and background channels with

compatible within 5%; the systematic

with

and

Re(ex).

K°/K°

by varying

signal

the last column represents the

The relative contribution of The

(see

AÄe (77000)

±3%

27

+

Re(r]ooo)

errors on

(table

fit

4.9).

table

:

regular

into account the correlations between all contributions

background by 7%, taking

Signal

ttVtt0 DECAYS

-

is then 7% smaller than the result of the

pionic background

of the

K°,K°

pionic background

(table 4.6). Taking

into account the

determining the level of the pionic background,

isation of this channel within ±5% to evaluate the

K° and K°

to the

we

systematic

systematic

also vary the normal¬

errors

on

Re(rjooo)

and

Im(r]QQo). We

can

Q!n7ro

the

•

observe that these

(table 4.10).

errors are

dominated

This is due to the fact that the

by uncertainties

pionic and the 27r°

+

on

a27ro and

27 channels

are

dominating backgrounds (table 4.4).

Uncertainties related to The variation of on

systematic

Am,

Am,

tl and ts

tl and ts within their

the result of the fit.

errors

(ref. [23, 45])

have

a

negligible

effect


4.5.

Variation of OJ27r°

a

a37r0 i

=

79

for each contribution

Ai?e (77000)

Aim(?7ooo)

Aim(77ooo)Äe(r?ooo)=jRe(eT)

±0.035

±0.01

±0.035

5%

a7r037r°

=

a3n° ±

5%

±0.00

±0.01

±0.00

a7r°27r°

=

a37T° ± 5%

±0.02

±0.01

±0.01

±0.04

±0.01

±0.03

anô

=

1.18 ± 5%

Table 4.10: Contribution of uncertainty

Uncertainties due to

•

decay

A summary of the

systematic

the

K°/K°

times where the

systematic

error on

errors on

Re (77000),

Re(r]ooo)

we can

shape

K°/K°

of

Am,

and

of

background

channels

ts

Contribution of systematic

when

Re(i]ooo)

fix

Comparison ity (eq. 4.7)

with

=

at

reported

are

by

in table 4.11. For

the

uncertainty

on

0.01

«0.01

«0.01

«0.01

«0.01

0.02

0.02

0.02

0.05

0.01

0.05

«0.01

«0.01

«0.01

«0.01

«0.01

«0.01

0.06

0.03

0.05

feasibility study

in table

as

errors

on

Re(ï]Q0Q)

and

Aim (77c

im(77ooo),

and the ITEP

parameters due

4.12;

are

also

to the

reported

experiment

and

on

im(77ooo)

decay-time resolution

the total intrinsic

The intrinsic sensitiv¬

and due to

4.23 and

background

sensitivity of the CPLEAR

derived from the total number of events and the statistical

Im(rjooo) (eq.

)00)ße(Woo)=ße(eT)

Re(ex).

to the fitted

reported

errors

on

Re (77000)

4.25).

The numbers of table 4.12 agree within 3% for relation

Im(r]ooo)

negligible

(fig. 4.1).

is maximal

and

is

0.01

backgrounds

Table 4.11:

and

im(?7ooo)-

Aim(77ooo)

Total

experiment

and

A-Re (77000)

contribution

Regeneration

are

by CPLEAR [46]

measured

observe that it is dominated

resolution

Background

we

Re(7]ooo)

errors on

normalisation.

Decay-time

TL

as

Aqqo asymmetry

Source

Lifetime

systematic

regeneration effects

The effect of neutral-kaon regeneration short

in

on a

C(Re(riooo))

and

:

C(fl)cPLEAR C(î])ldeal

^

C(rj)Background

C'("o)Resolution

C (r}) ideal

C(r])ideal

C(im(?7ooo))

with the

CHAPTER 4.

80

Background

Resolution

CPLEAR

ITEP

C(Re(mo))

2.8

4.9

10.2

18.4

4.5

C (Im (77000))

5.6

9.3

16.2

26.3

6.8

C(Im(moo))Re(n)=ReleT)

4.7

8.0

7.9

15.8

4.5

Intrinsic

derived from the

and ITEP

sensitivity

due to

cance

a

our

a

Re(r]ooo)

on

and

background of 50% and for

are

also

a

statistical

finite


and

background

CPLEAR,

K+ + Xe

K°

-

neutral-kaon

decay-length

contamination.

Imôoo) events

despite more

being

Therefore,

than CPLEAR

only

reconstructed

is known with

this

are

(for a

events, the CPLEAR experiment has

a

4.5.4

a

(table 4.12). However,


[25].

targeted by

It is a

a

bubble-chamber

K+-be&m, producing

:

67

->

6(e-e+)

the intersection of six e~e+

Moreover,

due to the very low total of 6

a

there is

no

better intrinsic sensitivity to

x

probability

better

sensitivity

background and

to detect such reason

why,

but with 30 times

-Re(77ooo)

on

pairs, the

Re(r]ooo)

106 Kg). This is the

background contamination,

and

Im(rjooQ).

Final results and conclusions

Determining the CP-violation parameters Re(r)ooo) reconstructed

K°,K°

where the total

between

error

—»

7r°7r07r°

is

and

to

Jm(?7ooo),

the final result from 17'300

Re(vooo)

=

0.18 ±

O.U8tat.

im(77ooo)

=

0.15 ±

0.20stot. ± 0.03sysi.

is dominated

i?e(77ooo)

and

:

by the

Im(rjooo)

±

0.06sysi.

(4.26)

statistical error; the correlation coefficient

(see

table

is 0.79.

This is the first determination of 77000

decaying

signifi¬

to have searched for CP violation

following

accuracy.

experiment has

632 events have been collected

finite

high

a

->

through

and

a

analysis

p

3tt°

«^

vertex

our

contamination.

37r° is the ITEP experiment ref.

neutral-kaons K°. The signal event to reconstruct is the

secondary

like in

The total sensitivities for the CPLEAR

experiment without magnetic-field where Xenon nuclei

The

(no background,

case

well understood in terms of loss of intrinsic

errors are


of neutral-kaons in

for ideal

given.

The only experiment up to date, apart from

decays

im(77ooo)

feasibility study (section 4.2).

experiment

This shows that

4.7)

ttVtt0 DECAYS

->

Ideal

perfect resolution), for

in

K°,K°

Intrinsic sensitivity

Table 4.12:

as


using the

7t07t07t0 [38] and is independent

on

rate

any

asymmetry of initially pure K° and K°

assumption

on

CPT invariance. We have

4.5.

the best sensitivity for 77000 since as

81


On this

4.31.

figure

shown in

we

improved the previous

have

figure

[25] by

represented the equal likelihood

also

are

measurement

~

24%

contours in

"

0.4

"

j

/ ( •

-O 2

/

CPLEAR

"

/

/

y

^y

3cr

!

/

/

ITEP

-0.4

'

/

/

/ "

2.a

'"

/

/

A

0

/

/ /

0.2

la

~

1

1

1

...

K-=Cri000)

Figure 4.31: The

contour

for

plot

Re(r]QQo)

and

im(77ooo)

obtained in

systematic uncertainties added

bars represent the statistical and

our

analysis;

the

quadrature. For

in

error

compar¬

ison, the result of ref. [25] is also shown. the 77000 remains

that

our

complex plane an

:

the correlation

ellipse representing

statistical

observe that up to three-standard

can

one

(~ 80%)

of two

deviation, the

gaussian parameters. It

in the fit of the asymmetry is not altered

approach

contour

by

any

proves

systematical

effect.

Upper limit

for

Assuming CPT invariance,

BKs__>37ro

in the fit of the asymmetry,

obtaining

im(77ooo) Given the order of

be 5

•

10-2

,

magnitude

we can

branching

=

Re(ex) (eq. 2.45)

(4.27)

-0.05±0.12stet. ±0msyst.

-Re(?7ooo)2

fixed at

Re(ex)

+

Im{rlQoo)'1

-

Ks decaying in 3tt°

T(KS -

at

~

10

3,

and

im(?7ooo)

measured to

:

ratio of

OKc-,3ir°

Äe(77ooo)

:

Re(rjQoo)

consider that

|?7ooo|2 and compute the

of

=

fix

we

-,

T(KL

3tT°) T-TTT

^7T7 -»

3tt°)

X

Imôoof as

Y(KL

follows -

Tl

37T0)

(4.28) :

^

Tl Ts

(4.29)

CHAPTER 4.

82


|2

I =

where the T's

branching

Bkl->Ztt°

the

are

ratio of =

(21.12

ratio of the Ks

—

partial

Kl ±

—>

and full

from ref.

7t07t07t0 decay

decay

[25]

—

widths of neutral-kaons and

[23],

we

the

Bkl_^ô

is the

approximation of equation 4.28 and

deduce

an

upper limit for the

branching

:

90% confidence level, which is

surement of

3„o X

Using

BKs^3ir° at the

ttVtt0 DECAYS

TL

7t°7t07t° decay.

0.27)%

->

TS

d

x BK

Ivooo]

K°,K°

an

r

and

argAÂo (see

eq.

is found to be

$

(6.1

=

±

10~5rad

11.7)

(5.1)

where correlations between

are

Am and

•

0+-,

•

Re(ex)

and

(f>sw (determined

im(a:_|_) (measured

taken into account in the

parameter 8 is then found

error

[45])

from the fit of calculation.

Ae^v)

The

imaginary part

of the CPT-violation

to be

Im(8) From the definition of 8

from ref.

(eq. 2.14)

=

(1.3±3.6)-10"5.

(5.2)

it follows that

MKo-Mj^

=

(1.8±5.1).nr19GeV/c2.

(5.3)

WITHOUT ASSUMING CPT-CONSERVATION IN DECAYS

5.2.

We

emphasise

experimental

that the results of

precision of the phase

the

uncertainty

5.2 and 5.3 have been obtained

equations 5.1,

values of CP-violation parameters 77-1—o and 77000, with The

decay amplitude.

and CPT-conservation in the

differences $

as

85

be

it

can

$

[rad.]

assumptions of unitarity test is dominated

precision of this seen

from table

5.2, mainly

Im(8)

ITEP

(-0.3±2.0)-10"4

(-1.2±5.5)-10"5

ITEP and CPLEAR

(6.1 ±11.7) -lO"5

(1.3 ±3.6) .10"5

Table 5.2: Values of the

phase difference $ and CPT-violation parameter Im(8)

of different

values of 77000

experimental

From the result obtained in be derived to be

If

77000

assume

=

V-\

leading

0,

level,

that there is and

we

-

Mj^\

If

we

Re(y) and

upper limit

on

the neutral-kaon

difference

•

10-19GeU/c2

which represents the best limit I

no

=

3

decay amplitude

(5.4)

on

the

K°-K°

mass

three-pion decays,

in

difference.

it follows that

$

=

(1.4±7.7)-10~6rod

Im(5)

=

(-0.3

±

1.9) 10-5 •

to

Ptt+F) [-1

-

2i2e(y)

+

i27m(ï)

+

i2/m(

^7tz^),

we

A*L,fAs,i

—>

lJrix~v)

=

Br(KL

—>

l~ir+T>)

=

finally obtain =

2TLBr(KL^lnv)-[Re(eT)-Re(y)+iIm(x+)+iIm(8)}.

(A.10)

Appendix

Matching

Photon

For

matching the

conversion

B

six

generated photons with

the reconstructed

photons,

first consider the

we

point of the the generated photon (see figure B.l).

Primary Vertex

ECAL

Figure B.l:

Conversion

point of the generated photon and reconstructed shower.

We define the transversal distance between as

the

following

Rshower

generated photon

and

a

reconstructed

one

:

8(r(j>)i where

a

=

(B.l)

Rsh, ower-wYi

is the reconstructed shower-foot radius and

constructed shower-foot and the

generated

conversion

91

S(f>

point

is the

angle

between the

in the transversal

plane.

re¬

The

APPENDIX B.

92

distance in three dimensions is then

given by

PHOTON MATCHING

:

^(8(r^))2 + (82 where 8z is the

longitudinal

distance between the conversion

the shower-foot of the reconstructed between six

generated and

(B.2)

photon. Then,

six reconstructed

generated photon and

compute the

we can

photons

of the

point

sum

of all distances

:

(B.3) For six

generated photons,

structed

sponds

photons;

to

the

have 6!

we

among these 720

720

=

possibilities

to combine

pairing possibilities, the

generated

and

giving the smallest A

one

recon¬ corre¬

right combination.

In order to

appreciate

the

tions of the transversal and

quality

of this

matching-method,

longitudinal distances

matched reconstructed photons

we can

between the 6

consider the distribu¬

generated photons

and their

:

s

JJ4000

iS 4000

E

'-

c

M2000

2000

; 05

1

15

2

i

05

15

A(yl) [cm]

«4000 £.

2

A(f2) [cm]

g4OO0

J-i

-

W

2000

:

0 05

1

15

2

3

05

15

A(y3) [cm] =

=s U4000

6000

a

-h

u

C4OO0

c

c

ta

m 2000

-

2000 -

!~!±rr-

T+-

L

...

15

I

0

L.

2

1

A(ï5) [cm]

Figure

B.2: 3tt° simulated data. Transversal

between the 6

One

can

generated photons and

observe that the widths

those of the calorimeter simulation

2

A(y4) [cm]

15

2

A(y6) [cm]

(full line)

and

longitudinal (dashed lines)

their matched reconstructed

are

very

study given

comparable (ar

and the true

flight

angles ($,0),

their

function of the

U\rue.

direction

respective

secondary

good approximation