w' = l/x' = w+M2/Q2 = 1+W2/Q2 extended the range of W for which scaling of ....
Q2-dependent terms to F1 and F2 for 11 fixed values of x = l/w in the range 0.1 2
...
- 163 -
TESTS OF STRUCTURE FUNCTION SCALING
VII.
Introduction
VI1.A. Experimental
tests
fraught
with
scaling
may arise
photon
resonance
parton
from low-Q2
structure(
l-5, l6 freedom 1
of charmed
(72)
inal
hypothesis
' "
would
scale
tions
only
VW; was consistent W > 2.6 GeV.
which
) was that
of this
experimental
errors,
with
in w for
In this
= w+M2/Q2
scaling
with
l7
),
in section
= 1+W2/Q2
only
VI1.B.
and vW2(v,Q2)
the
become func-
extended
early
v/Q2 held data
for
Q2 2 1 GeV2 and
use of the
experiment,
of VW; was valid (61, 62, 75, variables
section,
2MWl(v,Q2)
v + 00, Q2 -+ 00, with
limit
w as Q2 -+ 00, have been proposed examined
dimensions(
w = 2Mv/Q2 (i.e.,
scaling
scaling
theories
) I or arising from the producBjorken's origor colored states. (73)
of w) in the the
light
They may obscure
by field
anomalous
in the
18
in the variable
Within
w' = l/x'
predicted
exact
s-channel
) of VW2' terms
are
two -
as
commutator.
),
from
effects
and non-leading
deviations
scaling
deviations
( 5g
turn-on
scaling
tion
function
such diverse
of the current
and asymptotic
fixed.
Apparent
contributions
cone expansion genuine
of structure
ambiguity.
exchange,
-
scaling
variable
of W for Other down to W = 1.8 GeV. (74) 76 ) all of which approach I to fit
In the
the variables
the range
the data;
remaining
they
scaling
are tests
w and w1 are used and
- 164 -
deviations
from
Only data scaling
scaling
These restrictions
tests.
were influenced
neither
and F2 = vW2(x,Q2)
method
functions
the
scaling
were independent of R.
a comparison
This
of kinematics.
that
( 36 ) and ( 37 ), in section
the extracted
of any assumptions
method
had the disadvantage
of limited
in R at each kinematic
the
in the
error
four
and the number of data somewhat
limited
in this
The second method was similar
to that
method
inelastic
points
the
suited
structure
structure
The range
of func-
as the
was propagated
functions. available
the
same range
precision,
point
two structure
structure
were best
of the
of extracting
VI1.A.
about
data
Q2-dependence
dom error
the
as given
d 2MWT, VW:, and 2MWt, and VW2 in the
functions
In this
reported
These "separated"
of the
tests
Fl = 2MW1(x,Q2)
and deuteron,
in Figures tests
the
electroproduction
functions
the proton
had the advantage
Q2-dependence
tions
for
that
of vW2.
structure
( XV ) and plotted
were used for
for
turn-on
low-Q2
The two independent
This
are examined.
insured
by the prominent
nor by the
in Table
variables
Q2 >, 2 GeV2 and W 1 2 GeV are used in these
for
resonances
in these
ran-
into of Q2
at each x were also
method. used to extract
used in earlier
the
structure
cross
section
the scaling
function data
using
structure tests.
functions -( 7, 20 1
vW2 was extracted equation
(1,3),
from and
- 165 -
assuming
a functional
kinematic
region
Whereas
the
cQ2/(Q2
(XIII fits
satisfies
proton
functional better
Inelastic
V)
sections
V.F.
values
2MW1 owing
to our assumptions
that
structure
always
less
the
accuracy
method was particularly functional
forms
A rough "extracted!' or versus mation
test data
x',
these
statistical large
describe
single
deemed for
uncertainty
in vW2 was
in 2MWl. Because
body of data for
for
a study
vW2, this
terms
by plots
in vW2.
of all
these
x, as in Figure
To a fairly
functions
of the
of the possible
scale-breaking
).
extracted
are presented
is provided
( 39
NAB = 1.010
R, was
VW;, VW:, and VW; versus
as in Figure data
in the about
error
appropriate
of scaling
from experi-
factor
The corresponding
of this
it
B were normalized
normalization
and no results
of Q2-dependent
for
sections
The uncertainty
function. than
statistical
A by the
method,
and that
it
R -+ 0 in that
from experiment
in section
in this
that
were used in
discussed
large
form,
and e-n cross
e-d,
from Table
two advantages
as Q2 + 0, i.e.,
of experiment
too
taken
constant
to those
of
the
had been measured.
coefficients
the
(Table
Cross
method.
throughout
sections
form has the than
e-p,
ments A and B only this
the cross
gauge invariance
limit.
R to be valid
VW; R = 0.18 was used to extract P we used the modified spin-l/2 form (70)
with
+ d2)2
the R data
for
value
tests,
This
).
in which
constant
in the earlier R=
form
good approxi-
of x or x',
faring
(38)'
-
166
-
h
0.20 0.1 5 0.10 0.05 0 0.45 0.40 0.35 0.30 uw; 0.25 0.20 0.15 0.10 0.05
0
0.2
0.4
0.6
0.8
Fi . 38. Values of VW;, VW;, and V against x. The errors 4 plotted shown are purely random.
1.0
-
167
-
0.50 0.45 0.40 0.35 0.30 lm,p 0.25 0.20 0.1 5 0.10 0.05 0 0.45 0.40 0.35 0.30 l/w; 0.25 0.20 0.15 0.10 0.05 0 0.70 0.60 0.50 l/w;
0.40 0.30 0.20 0.10 0
0
0.2
0.4
0.6 X’
0.8
1.0 lll,DIl
Fi . 39. Values of "4Jp2, VW;, and V against x . The errors d plotted shown are purely random.
- 168 -
better is
in the
limited,
lo-20%)
second
however, from exact
proposed
scaling
where
VII.C.,
functional be the
same for
tible
with
diet
a rise
larger
certain
values
in section
in the
0.1 2 x 5 0.8.
of Table
( XV
accuracy
of the
separated each x.
results
by fitting
using
had been extracted
suited
was limited
from
that
is not
the
must compa-
77 ) that
preat
at low x and a fall-off scaling
in w were further
functions 11 fixed
to this
with values
explicit of x = l/w
2MWl and vW2 data task,
but
the
accuracy of the 3 and the ranges of Q- available
studies
values
approach
The separated
functions
More extensive
were possible
from
is
term hi(Q2)
models ( 17, 18,
functions
) were ideally
structure
This
5.
where
of VW;, VW:, and VW;
the Q2-dependent
to F1 and F2 for
terms
range
scaling
func-
and in sec-
of such an approach
theory
Q2-dependent
VII.B.,
are compared,
from
of
V1I.D.
or a scale-breaking
used in section
Deviations
of x.
plots.
scaling
unity
structure
in these
5 is one of the proposed
deviations
field
in the
values
examined
all
be apparent
of
of the
variables
form assumed for
approach
(on the order
were provided
The disadvantage
are compared.
of this
by fits
is either
Such is the procedure
several
not
tests
, where
and h(Q2)
tion.
tion
deviations
would
scaling
VW2 = f(5)h(Q2)
variables,
The usefulness
as small scaling
More quantitative form
variable.
by the
of the Q2-dependence
of this
structure
interpolated
cross
function sections
at
of vW2 that using
the
- 169 -
fit
R = cQ2/(Q2
experiments
The normalized
A and B were first
to values the
+ d2)2.
interpolated
of E' corresponding
x - Q2 array.
extensive
tests
deviations
to the
These data
for
of the various
from exact VI1.B.
section
at fixed
11 values
uW2(x,Q2)
functional
Bjorken
from E and 8
of x used in
then forms
permitted proposed
for
scaling.
Comparison
The two independent
cross
of 2MWl and vW2
structure
functions
Fl = 2MWl(x,Q2)
and F 2 = vW2(x,Q2) reported in Table (xv ) were used in the scaling tests reported here. As mentioned earlier only data for Q2 ? 2 GeV2 and W 2 2 GeV were used in these tests. Scaling
in the
functions
two variables of the
and deuteron
form Fi(x,Q2)
data
for
f2 (5) = Cbj (l-l/
