Studies of TMDs at HERMES - hermes @ desy

Studies of TMDs at HERMES Luciano Pappalardo [email protected] (for the HERMES Collaboration)

JLAB, Newport News, Virginia USA , May 18-21 2010

Quantum phase-space tomography of the nucleon

σ

Longitudinal momentum structure of the nucleon 2

Quantum phase-space tomography of the nucleon Join the real 3D experience!!

σ

TM

Ds

by [fm]

G

s D P

bx [fm]

Longitudinal momentum structure of the nucleon

3D picture in coordinate space

3D picture in momentum space 3

The nucleon spin structure at leading twist momentum

helicity

transversity

+ +

-

Legenda (courtesy of A. Bachetta): Proton comes out of the screen photon goes into the screen

• functions in black survive integration over transverse momentum

4

The nucleon spin structure at leading twist momentum

helicity Boer-Mulders transversity

pretzelosity Sivers

worm-gear

Legenda (courtesy of A. Bachetta): Proton comes out of the screen photon goes into the screen

• functions in black survive integration over transverse momentum • functions in red are naive T-odd • functions in green box are chirally odd 5

TMDs can be studied by measuring azimuthal asymmetries in SIDIS

Distribution Functions (DF)

FF σ

DF

functions in green box are chirally odd

6

TMDs can be studied by measuring azimuthal asymmetries in SIDIS

Distribution Functions (DF)

FF σ

DF

DF The SIDIS cross section exhibits asymmetries in the azimuthal angles φ and φ S

Fragmentation Functions (FF) h D1 a U Unpol. FF d.

functions in green box are chirally odd

H1⊥ Collins FF 7

The SIDIS cross section up to twist-3 0 1 dσ = dσ UU + cos 2φ dσ UU +

d

1 1 2 3 cos φ dσ UU + λe sin φ dσ LU Q Q

   6 1 1 4 5 7  + SL sin 2φ dσ UL + sin φ dσ UL + λe dσ LL + cos φ dσ LL   Q Q   

{

8 9 10 + ST sin(φ − φS ) dσ UT + sin(φ + φS ) dσ UT + sin(3φ − φS ) dσ UT

1 1 11 12 + sin( 2φ − φS ) dσ UT + sin φS dσ UT Q Q   1 1 13 14 15  + λe cos(φ − φS ) dσ LT + cos φS dσ LT + cos(2φ − φS )dσ LT   Q Q  

How can we disentangle all these contributions ? EXPERIMENT: setting the proper beam and target polarization states (U, L, T) ANALYSIS: e.g. fitting the cross section asymmetry for opposite spin states and extracting the relevant Fourier amplitudes based on their peculiar azimuthal dependences.

8

0 1 dσ = dσ UU + cos 2φ dσ UU +


   6 1 1 4 5 7  + SLsin 2φ dσ UL + sin φ dσ UL +λ dσ LL + cos φ dσ LL  e Q Q  

Boer-Mulders effect •

{ ( x, p

⊥+ 1

∝h

8 9 10 ST sin( 2 φ − φ S⊥) dσ UT2 + sin(φ + φ S ) dσ UT + sin(3φ − φ S ) dσ UT

T

) ⊗ H 1 ( z , kT )

• correlation between parton transverse 1 momentum and parton transverse + sin( 2φ Q polarization in an unpolarized nucleon

− φ S ) dσ

11 UT

1 12 + sin φS dσ UT Q

  1 1 13 14 15  +λe cos(φ − φS ) dσ LT + cos φS dσ LT + cos(2φ − φS )dσ LT   Q Q   9

The Boer-Mulders effect Twist-2:

Cos 2φ dσ UU

ˆ ˆ   ⋅ ⋅ − 2 ( P k )( P p ) k T ⋅ pT ∝ cos 2φ ⋅ ∑ eq2 I  h ⊥ T h ⊥ T h1⊥ H1⊥ q  MM h q  

Boer-Mulders effect Twist-3:

Cosφ dσ UU

Cahn effect

ˆ ˆ   ( Ph ⊥ ⋅ pT ) ( Ph ⊥ ⋅ kT ) 2 2M ⊥ ⊥q ∝ cos φ ⋅ ∑ eq I − x h1 H1 − x f1 D1 + ... Q  Mh M q 

Accessed through azimuthal modulations in SIDIS with unpol. H and D targets

The Boer-Mulders effect Twist-2:

Cos 2φ dσ UU

ˆ ˆ   ⋅ ⋅ − 2 ( P k )( P p ) k T ⋅ pT ∝ cos 2φ ⋅ ∑ eq2 I  h ⊥ T h ⊥ T h1⊥ H1⊥ q  MM h q  

Boer-Mulders effect Twist-3:

Cosφ dσ UU

Cahn effect

ˆ ˆ   ( Ph ⊥ ⋅ pT ) ( Ph ⊥ ⋅ kT ) 2 2M ⊥ ⊥q ∝ cos φ ⋅ ∑ eq I − x h1 H1 − x f1 D1 + ... Q  Mh M q 

Accessed through azimuthal modulations in SIDIS with unpol. H and D targets analysis based on a multidimensional unfolding of data to correct for acceptance, detector smearing and higher order QED effects

The Boer-Mulders effect (Hydrogen target) cos( φ )

UU

∝ Ι[ − h1⊥ H 1⊥ − f1 D1 ]

negative cos(φ φ) amplitudes for both π+ and πcos( w φ )

UU

∝ Ι[ − h1⊥ H 1⊥ ]

cos(2φ φ) ampl. positive for πand slightly negative for π+ Similar results for D target

The Boer-Mulders effect (Hydrogen target) cos( φ )

UU

∝ Ι[ − h1⊥ H 1⊥ − f1 D1 ]

negative cos(φ φ) amplitudes for both π+ and πcos( w φ )

UU

∝ Ι[ − h1⊥ H 1⊥ ]

cos(2φ φ) ampl. positive for πand slightly negative for π+ Similar results for D target

Accessing the polarized cross section through SSAs Full HERMES transverse data (02-05 data with

PT ≈ 73% )

The Fourier amplitudes of the yields for opposite transverse target spin states were extracted through a ML fit alternately binned in x, z, and Ph⊥ but unbinned in φ and φS:

This is equivalent to perform a Fourier decomposition of the cross section asymmetry:

1 dσ h (φ , φS ) − dσ h (φ , φS + π ) A (φ , φS ) = | PT | dσ h (φ , φS ) + dσ h (φ , φS + π ) h UT

+ ... in the limit of very small φ and φS bins. I [...]: convolution integral over initial ( pT ) and final ( kT ) quark transverse momenta

14



Collins effect •

∝ h1 ( x,

   6 1 1 4 5 7  + SLsin 2φ dσ UL + sin φ dσ UL +λ dσ LL + cos φ dσ LL  e Q Q 2 ⊥ 2   p ) ⊗ H ( z, k ) 1

T

T

{

• correlation between parton 8 + sin( φ − φ ) d σ S transverse polarization in a S UT T transversely polarized nucleon and transverse momentum of the produced hadron Ph⊥

9 10 + sin(φ + φS ) dσ UT + sin(3φ − φS ) dσ UT

1 1 11 12 + sin( 2φ − φS ) dσ UT + sin φS dσ UT Q Q

h

  1 1 13 14 15  +λe cos(φ − φPS ) dσ LT + cos φS dσ LT + cos(2φ − φS )dσ LT   Q Q   h h⊥

15

Collins pions amplitudes

positive for π+ consistent with zero for π0 negative for π16

Collins pions amplitudes Non-zero Collins effect observed Both transversity and Collins function sizeable! Ampl. increase with x, i.e. towards the valence region Isospin symmetry fulfilled −

the large negative π amplitude suggests disfavored Collins FF with opposite sign:

positive for

measurement at e+e-

π+

consistent with zero for

π0

collider machines

negative for π17

pu bl is he d

so on !

Collins pions amplitudes

be

Both transversity and Collins function sizeable!

re su l

ts

to

Ampl. increase with x, i.e. towards the valence region

li n s

Isospin symmetry fulfilled −

Co l

the large negative π amplitude suggests disfavored Collins FF with opposite sign:

Fi na l

positive for

Non-zero Collins effect observed

measurement at e+e-

π+

consistent with zero for

π0

collider machines

negative for π18

2-D Collins pions amplitudes Kinematic dependencies often don’t factorize → correlations among variables bin in as many independent variables as possibles (multidim. analysis)

X vs. Z

X vs. Ph⊥⊥

19


1 1 2 3 Sivers cos φ dσ UU +effect λe sin φ dσ LU Q Q ⊥

{

D1 ( z , kT )7   •1 ∝ f1T (5x, pT ) ⊗  4 6 + SLsin 2φ dσ UL + sin φ dσ UL +λ dσ LL + cos φ dσ LL   e Q transverse •Qcorrelation between parton   momentum and nucleon transverse polarization 9 8 10 2

2

+ ST sin(φ − φS ) dσ UT + sin(φ + φS ) dσ UT + sin(3φ − φS ) dσ UT • requires orbital angular momentum

1 1 11h 12 + sin( 2φ q− φS ) dσ UT + sin φS dσ UT T Q Q qT

h  1 1 13 14 15  +λe cos(φ − φS ) dσ LT + cos φS dσ LT + cos(2φ − φS )dσ LT   Q Q   20

Ph ys .

Re

v. Le tt. 10 3

(20

09

)1

52 0

02 ]

Sivers amplitudes

Main features confirmed by new high-statistics results

an r ap eti [Ai

U-quark dominance suggests sizeable u-quark orbital motion!

et al. ,

First observation of T-odd Sivers effects in SIDIS!

21

Sivers pions amplitudes Slignificantly positive clear rise with z rise at low Ph⊥⊥, plateau at high Ph⊥⊥

Sligthly positive

Consistent with zero Isospin symmetry fulfilled

22

Sivers pions amplitudes Slignificantly positive clear rise with z rise at low Ph⊥⊥, plateau at high Ph⊥⊥

Sligthly positive

Consistent with zero Isospin symmetry fulfilled Large positive π+ signal is dominated by scattering off u-quarks: +

2 sin(φ − φS )

π+ UT

∝−

f1T⊥,u ( x, pT2 ) ⊗W D1u →π ( z , kT2 ) u →π + 1

f ( x, p ) ⊗ D u 1

2 T

2 T

( z, k )

→ u-quark Sivers DF < 0

null signal for π- indicates that d-quark Sivers DF > 0 (cancellation) Confirmed by phenomenological fits (Torino group) and theoretical predictions (Gamberg)!

23

2-D Sivers pions amplitudes Kinematic dependencies often don’t factorize → correlations among variables bin in as many independent variables as possibles (multidim. analysis)

X vs. Z

X vs. Ph⊥⊥

24

The pion-difference asymmetry π+

Contribution by decay of exclusively produced vector mesons is not negligible

a new observable

π−

+

+

π −π AUT

−

−

+

−

π π π π 1 (σ U ↑ − σ U ↑ ) − (σ U ↓ − σ U ↓ ) (φ , φ S ) ≡ + − + − S T (σ Uπ ↑ − σ Uπ ↑ ) + (σ Uπ ↓ − σ Uπ ↓ )

Contribution from exclusive ρ0 largely cancels out!

• significantly positive Sivers and Collins amplitudes are obtained • measured amplitudes are not generated by exclusive VM contribution

25

The pion-difference asymmetry π+

Contribution by decay of exclusively produced vector mesons is not negligible

a new observable

π−

+

+

π −π AUT

−

−

+

−

π π π π 1 (σ U ↑ − σ U ↑ ) − (σ U ↓ − σ U ↓ ) (φ , φ S ) ≡ + − + − S T (σ Uπ ↑ − σ Uπ ↑ ) + (σ Uπ ↓ − σ Uπ ↓ )

Contribution from exclusive ρ0 largely cancels out

(cancellation of FFs assuming chargeconjugation and isospin symmetry)

provides access to Sivers u-valence distribution! 26

Sivers kaons amplitudes Slignificantly positive clear rise with z rise at low Ph⊥⊥, plateau at high Ph⊥⊥

Sligthly positive

27

Sivers kaons amplitudes Slignificantly positive clear rise with z rise at low Ph⊥⊥, plateau at high Ph⊥⊥

Sligthly positive

test presence of 1/Q2-suppressed contributions separate each x-bin in two Q2 bins hint of higher-twist contributions to the K+ amplitude 28

The Sivers π+/K+ riddle π+/K+ production dominated by scattering off u-quarks: ∝−

⊥ ,u 1T u 1

f

u →π + / K + W 1 u →π + / K + 1

( x, p ) ⊗ D 2 T 2 T

f ( x, p ) ⊗ D

( z , kT2 )

( z , kT2 )

?

π + ≡ ud , K + ≡ us → non trivial role of sea quarks

?

impact of different kT dependence of FFs in the convolution int.

⊗W

29

The Sivers π+/K+ riddle π+/K+ production dominated by scattering off u-quarks: ∝−

⊥ ,u 1T u 1

f

u →π + / K + W 1 u →π + / K + 1

( x, p ) ⊗ D 2 T 2 T

f ( x, p ) ⊗ D

( z , kT2 )

( z , kT2 )

?

π + ≡ ud , K + ≡ us → non trivial role of sea quarks

?

impact of different kT dependence of FFs in the convolution int.

⊗W

• Difference of π+ and K+ amplitudes • Separate each x-bin in two Q2 bins • only in low-Q2 region significant (90% c.l.) deviation is observed

?

Higher-twist contrib. for Kaons 30


pretzelosity  1

•

+

∝


  6 1 4 5 7  + SLsin 2φ dσ UL + sin φ dσ UL +λ dσ LL + cos φ dσ LL  e ⊥ 2 ⊥ Q 2 Q  h ( x, p ) ⊗ H ( z , k ) 1T

1

T

T

• correlation between parton transverse 8 9 parton transverse sin(φ − φand ) d σ + sin( φ + φ ) d σ ST momentum S UT S UT polarization in a transversely polarized nucleon 1

{

+

10 + sin(3φ − φS ) dσ UT

sin( 2φ − φS ) dσ

• can be linked to the shape Qof the nucleon (deviation from a sphere)

11 UT

1 12 + sin φS dσ UT Q

  1of Ph⊥ with14 1 •λ suppressed by two powers 13 15  + e cos(φ − φS ) dσ LT + cos φS dσ LT + cos(2φ − φS )dσ LT   respect to Collins and Sivers Q amplitudes Q   31

The sin(3φ-φS) Fourier component • Sensitive to pretzelosity • suppressed by two powers of Ph⊥ w.r.t. Collins and Sivers amplitudes • no significant non-zero signals oberseved


1 1 2 3 cos φ dσ UU + λe sin φ dσ LU Worm-gear (UL) Q Q ⊥

{

+ ST sin(φ

⊥

H1 ( z , k )7    1• ∝ h1L (5 x, pT ) ⊗ 4 6 + SLsin 2φ dσ UL + sin φ dσ UL +λ dσ LL + 1 cos φ dTσ LL  e Q Q   • correlation between parton transverse momentum and parton transverse polarization9 in a longitudinally polarized 8 10 − φS ) dσ UT + sin(φ nucleon + φS ) dσ UT + sin(3φ − φS ) dσ UT 2

2

measurements 1 • accessible in UT 1 11 12 + sin( 2φ − φsin(2φ+φ ) d σ + sin φ d σ through ) Fourier component S UT S UT S Q Q


The sin(2φ+φS) Fourier component • arises solely from longitudinal (w.r.t. virtual-photon direction) component of the target spin

• related to UL Fourier comp • sensitive to worm-gear

h1⊥L

• suppressed by one power of Ph⊥ w.r.t. Collins and Sivers amplitudes • no significant non-zero signal observed (except maybe for K+)


{

+ ST sin(φ

1 1 2 3 cos φ d σ + sin φ d σ λ Worm-gear (LT) UU LU e Q Q

• ∝ g ⊥ ( x, p 2 ) ⊗ D ( z , k 2 )  1T5 T 7  T 6 1 11 4 + SLsin 2φ dσ UL + sin φ dσ UL + d σ + cos φ d σ LL   λe between LL  • correlation parton Q Q    transverse momentum and parton longitudinal polarization in a 8 9 10 polarized nucleon − φS ) dσ UT + sin(φ +transversely φS ) dσ UT + sin(3φ − φS ) dσ UT

1 1 11 12 + sin( 2φ − φS ) dσ UT + sin φS dσ UT Q Q

• accessible in UT measurements through sub-leading sin(2φ-φS) Fourier comp.


The subleading-twist sin(2φ-φS) Fourier component • sensitive to pretzelosity, worm⊥ gear g1T and Sivers function:

• suppressed by one power of Ph⊥ w.r.t. Collins and Sivers amplitudes • no significant non-zero signal observed

The subleading-twist sin(φS) Fourier component ⊥

• sensitive to worm-gear g1T , Sivers function, Transversity, etc • significant non-zero signal observed for π- and K- !

The subleading-twist sin(φS) Fourier component ⊥

• sensitive to worm-gear g1T , Sivers function, Transversity, etc • significant non-zero signal observed for π- and K- ! Q2 dependence observed in π- signal:

Conclusions The existence of an intrinsic quark transverse motion gives origin to azimuthal asymmetries in the hadron production direction

• Non-zero Boer-Mulders effect observed for identified charged pions → clear evidence of non-zero Boer-Mulders function and Collins FF

• significant Collins amplitudes observed for charged π-mesons → enabled first extraction of transversity and Collins FF

• significant Sivers amplitudes observed for π+ and K+ → clear evidence of non-zero Sivers function → (indirect) evidence for non-zero quark orbital angular momentum → hint of non-trivial role of sea quarks and of higher-twist contrib. for positive kaons

• additional Fourier components recently extracted → no evidence of non-zero pretzelosity (though amplitude kinematically suppressed) ⊥ → first glimpse on worm-gears h1⊥L and g1T related observables h → significant non-zero sin(φS ) UT amplitudes for negatively charged mesons 39

Back-up slides

40

The HERMES experiment at HERA

TRD, Calorimeter, preshower, RICH: lepton-hadron > 98%

hadron separation

Aerogel n=1.03

C4F10 n=1.0014

π ~ 98%, K ~ 88% , P ~ 85% 41

The Boer-Mulders effect analysis based on a multidimensional unfolding of data to correct for acceptance, detector smearing and higher order QED effects = Kinematic range of integration

= signal not expected and not observed

x

= signal expected and observed

= signal expected but not observed

The Boer-Mulders effect for π+ Hydrogen vs. Deuteron target data The two samples are compatible

The Boer-Mulders effect for πHydrogen vs. Deuteron target data The two samples are compatible

Standard cuts

0.1 < y < 0.95

y < 0.95

0 .2 < z < 0 .7

Collins moments: Pion-kaon comparison •

K+

and

π + amplitudes

consistent (u-quark dominance) •

− K − and π amplitudes with

opposite sign (but

K − (u s )

originates from

fragmentation of sea quarks)

46

Siver samplitudes: additional studies

No systematic shifts observed between high and low Q2 amplitudes for both π+ and K+ No indication of important contributions from exclusive VM

47

2-D moments for Collins

π±: z vs. Ph⊥ Sivers

48

An alternative channel to access transversity Interference FF

ep→ →e’h1h2X

(does not depend on quark transv. momentum)

Chiral-odd

T- odd

Correlation between transverse spin of the fragmenting quark and the relative orbital angular momentum of the hadron pair.

Describes Spin-orbit correlation in fragmentation

h1

azimuthal asymmetries in the direction of the outgoing hadron pairs.

• Independent way to access transversity • No complications due to convolution integral → interpretation more transparent • ...but limited statistical power (v.r.t. single-hadron SSAs) • published on JHEP 06 (2008) 017

The extraction of the Distribution Functions dφS d Ph ⊥ sin(φ +φ S ) dσ UT ∫ = ∝I 2 ∫ dφS d Ph⊥ dσ UU 2

sin(φ + φS )

h UT

 kT ⋅ Pˆh ⊥  2 ⊥q 2 h1 ( x, pT ) H1 ( z , kT )   Mh 

Convolution integral on transverse momenta

pT and kT

dφS d Ph ⊥ sin(φ −φ S ) dσ UT  pT ⋅ Pˆh ⊥ ⊥ q  ∫ 2 q 2 = ∝I  f1T ( x, pT ) D1 ( z , kT )  2  M  ∫ dφS d Ph⊥ dσ UU 2

sin(φ − φS )

h UT

Experiment: only partial coverage of the full Ph ⊥ range (acceptance effects) Theory: difficult to solve h1 ( x) h1 ( x, p ) ≈ e 2 π pT ( x) 2 T

Gaussian ansatz −

pT2 pT2 ( x )

H

⊥q 1

H1⊥ q ( z ) ( z, k ) ≈ e 2 π kT ( z ) 2 T

(extraction assumption-dependent)

−

kT2 kT2 ( z )

50

Extraction of transversity and Sivers function form global analyses sin (φ +φ S ) AUT ∝ h1 ( x) ⊗ H1⊥ q ( z )

sin (φ −φ S ) ∝ f1,⊥T ( x) ⊗ D1q ( z ) AUT

Known

lp → l ' hX

ld → l ' hX

e + e − → h1h2 X lp → l ' hX

First extraction of Transversity!

ld → l ' hX

Anselmino et al. Phys. Rev. D 75 (2007)

Anselmino et al. Eur.Phys.J.A39 (2009)