In the following article we describe our measurement of the proton structure
function $F_2$ and of the gluon momentum density $xg$ in $ep$ collisions with
the ZEUS detector at HERA in 1993. The results for $F_2$ confirm our
measurement from the previous year but with much higher statistics and show a
strong rise towards small $x$. The gluon momentum density $xg$ is measured for
the first time in a range from $ 4 \cdot 10^{-4} < x < 10^{-2}$ at a value of
$Q^2 = 20$~GeV$^2$.Comment: 7 pages uuencode-gzipped postscript. LaTeX and individual figures can
  be found on http://ppewww.ph.gla.ac.uk/preprints/95/01/fleck.shtm

Fleck, J. I.

English

arXiv

In the following article we describe our measurement of the proton structure function F_2 and of the gluon momentum density xg in ep collisions with the ZEUS detector at HERA in 1993. The results for F_2 confirm our measurement from the previous year but with much higher statistics and show a strong rise towards small x. The gluon momentum density xg is measured for the first time in a range from 4 \cdot 10^{-4} < x < 10^{-2} at a value of Q^2 = 20~GeV^2

Fleck, I

CERN Document Server

H
EP
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X
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60
11
Department of Physics & Astronomy
Experimental Particle Physics Group
Kelvin Building, University of Glasgow,
Glasgow, G12 8QQ, Scotland
Telephone: +44 (0)141 339 8855 Fax: +44 (0)141 334 9029
GLAS{PPE/95{01
19
th
June 1995
MEASUREMENT OF THE PROTON STRUCTURE FUNCTION F
2
AND
THE EXTRACTION OF THE GLUON DENSITY AT SMALL x
ZEUS Collaboration
talk given at Photon'95, 8{13th April 95, by J. I. FLECK
Department of Physics and Astronomy,
University of Glasgow, Glasgow, UK.
E-mail: eck@desy.de
Abstract
In the following article we describe our measurement of the proton structure function F
2
and of
the gluon momentum density xg in ep collisions with the ZEUS detector at HERA in 1993. The
results for F
2
conrm our measurement from the previous year but with much higher statistics
and show a strong rise towards small x. The gluon momentum density xg is measured for the
rst time in a range from 4  10
 4
< x < 10
 2
at a value of Q
2
= 20 GeV
2
.
1 Introduction
In 1993, electrons of 26.7 GeV and protons of 820 GeV were brought into collision at
HERA. 84 paired bunches out of 210 possible were lled and in addition 10 electron and 6
proton bunches were left unpaired for background studies.
The measurements described here were made using the ZEUS detector, which is described
in detail in [1] and [2]. The main components used for our analyses were the vertex detector
(VXD), the central tracking detector (CTD), the uranium calorimeter (CAL), a lead scintillator
beam monitor (C5) and the luminosity detector.
With the data taken in 1993 a measurement of the proton structure function F
2
was
possible with high precision in a region of 7 < Q
2
< 10
4
GeV
2
and x values as low as 3 10
 4
.
The total integrated luminosity in 1993 was 0.54 pb
 1
.
2 Kinematics
The processes in deep inelastic scattering (DIS) are described by the following kinematic
variables.
Q
2
=  q
2
=  (k  k
0
)
2
; x =
Q
2
2P  q
; y =
P  q
P  k
(1)
k and k
0
denote the four-momenta of the incoming and the nal state lepton, P is the four-
momentum of the incoming proton and y is the fractional energy transfer in the proton rest
frame.
As the ZEUS detector is a nearly hermetic detector (99.7 %), there exist various methods
to reconstruct the kinematic variables. For our analysis we have used two dierent methods:
1. electron method; (in this method only the scattered electron is observed and its scattering
angle and energy are measured.)
2. double angle (DA) method; (this relies on the measurement of two scattering angles, that
of the scattered electron and that for the nal hadronic state. In the naive Quark Parton
Model the latter is the angle of the scattered quark.)
Method 1 gives a better resolution in x at low Q
2
while method 2 is less sensitive to
the absolute calorimeter energy scale and gives better resolution over the whole x  Q
2
plane.
Comparing the results obtained by both methods gives a good systematic check of our analysis.
The range of x and Q
2
that is accessible with these two methods is shown in gure 1.
1
10
10 2
10 3
10 4
10 5
10-5 10-4 10-3 10-2 10-1 1
Figure 1: Distribution of events in the x and Q
2
plane. Also shown are the bins used and the
range covered by previous experiments.
1
3 Event Selection
The event selection is dominated by two selection steps, the trigger and the oine selection.
The ZEUS trigger is a three step algorithm and has an eciency greater than 95% for DIS events
in the x and Q
2
region discussed here. A total of 2  10
6
events passed the DIS trigger. To obtain
an event sample with little background and high purity, several cuts were applied. The most
important are listed below:
{ 35 <  < 60 GeV,  =
P
i
E
i
(1  cos 
i
), where E
i
denotes the energy deposit in calorimeter
cell i and 
i
the polar angle of the centre of the cell with respect to the event vertex; (For
fully contained DIS events   2E
e
= 53:4 GeV, whereas photoproduction events peak at
low values of , as the scattered electron remains within the rear beampipe.)
{ E
0
e
> 5 GeV; the energy of the scattered electron should be greater than 5 GeV for a reliable
electron nding and a low background from photoproduction;
{ y
JB
> 0:04 to ensure a good measurement of the hadronic angle and of x.
A total of 46k DIS NC events corresponding to an integrated luminosity of 0.54 pb
 1
survived all cuts.
ZEUS 1993 Data
0
2000
4000
6000
8000
155 160 165 170 175 180
0
1000
2000
3000
4000
0 50 100 150
0
2000
4000
6000
10 10 2 10 3
0
2000
4000
6000
10-5 10-4 10-3 10-2 10-1 1
Figure 2: Distribution of the primary measured quantities, a) angle of the scattered electron #
0
e
,
b) angle of the hadronic nal state 
H
, c) Q
2
, and d) x. The dots are the data and the shaded
areas represent the MC.
The distributions for the measured and the reconstructed variables for the DA method for
data and MC are shown in gure 2. The good agreement between the data and MC distributions
demonstrates our good understanding of the relation between MC and data. The structure
function used as an input for the MC distribution has been reweighted to the measured structure
function.
4 Background
The main source of background originates from photoproduction events. Figure 3 shows
the distribution of DIS and photoproduction events in a given x and Q
2
bin after all cuts, except
for the cut on , have been applied. To calculate the number of photoproduction events with
 > 35 GeV a t is made to the data, shown as black dots, in each bin of the x Q
2
plane. From
the total number of events in each bin, the number of photoproduction events as calculated
from the t, is subtracted. The photoproduction background can rise to 12% at high y, but is a
2
few percent for most of the bins. Other sources of background, like cosmic ray events and halo
muons, contribute much less and are eciently removed.
0
50
100
150
200
250
300
25 30 35 40 45 50 55 60 65
Figure 3: Distribution of DIS and photoproduction (php) events in a given x Q
2
bin. The black
dots show the data and the solid line represents the t that is applied to the data.
5 The Proton Structure Function F
2
The proton structure function F
2
is related to the double dierential cross section for
inclusive ep scattering including photon and Z
0
exchange via the following formula:
d
2

dx dQ
2
=
2
2
xQ
4
h
Y
+
F
2
(x;Q
2
)  y
2
F
L
(x;Q
2
) + Y
 
xF
3
(x;Q
2
)
i
(1 + 
r
(x;Q
2
)) (2)
with Y

= 1  (1   y
2
). F
L
is the longitudinal structure function, F
3
is the parity violating
term, and 
r
is the radiative correction. For comparison with other experiments we measure
F
2
containing only contributions from virtual photon exchange. Therefore we have to absorb
the contributions from the Z
0
exchange in a correction factor 
Z
. This correction is 6% for the
highest Q
2
bin shown in this analysis and lower for all the other bins. Also the corrections due
to the longitudinal structure function and the radiative corrections are small (lower than 15%
and 5% respectively), and can be absorbed in correction factors 
F
L
, from QCD prescriptions,
and 
r
, from the HERACLES Monte Carlo. This results in the following equation for F
2
:
d
2

dx dQ
2
=
2
2
Y
+
xQ
4
F
2
(x;Q
2
)(1  
F
L
+ 
Z
)(1 + 
r
) (3)
To derive F
2
from the observed double dierential cross section, an unfolding method is used.
The results for the DA method are shown in gure 4. Our most important systematic
check is the comparison of the values of F
2
for the DA and the electron method. These two
methods use overlapping data samples, but the reconstruction of the kinematic variables is
largely independent. Within the statistical errors there is very good agreement between the two
methods.
6 Gluon Momentum Density
In zeroth order, F
2
is constant in Q
2
and the gluons do not contribute to the cross section.
The scaling violations, as shown in gure 5, are a higher order process (called leading order,
3
ZEUS 1993 F2
1
2
3
1
2
3
1
2
3
1
2
3
10-4 10-2 10-4 10-2 10-4 10-2
Figure 4: Proton structure function F
2
as a function of x. The inner error bars show the statistical
error only, while the outer bars show the statistical and the systematic error added in quadrature.
Q
2
is given in GeV
2
.
LO, for our purpose). At small values of x, x < 10
 2
, they are dominated by quark pair produc-
tion from gluons leading to positive scaling violations with increasing Q
2
. Therefore the gluon
momentum density, xg(x;Q
2
), can directly be extracted from the slope dF
2
=d lnQ
2
.
We compare dierent methods, the approximate method of Prytz [5], EKL [6], and a t
making use of the full NLO GLAP [7] evolution equation.
The method of Prytz uses the approximation that at low values of x the GLAP evolution
equation is dominated by the gluonic terms. Consequently the quark splitting functions are
neglected and only the gluon splitting functions are considered. Using a LO result for P
qg
,
the gluon splitting function and making a Taylor expansion of the gluon momentum density
zg(z;Q
2
) at z = x=2 results in the following equation in LO:
xg(x;Q
2
) 
dF
2
(x=2; Q
2
)=d lnQ
2
(40=27)
s
=4
; (4)
where the gluon density at x is calculated from the slope of F
2
at x=2.
Equation 4 has been extended to NLO, still neglecting quark contributions. In the NLO
GLAP t, all the F
2
data from ZEUS taken in 1993 have been used. To make a constraint at large
values of x, NMC data [8] on F
2
were included. The t of the parton momentum distributions
as a function of x has been performed at a value of Q
2
0
= 7 GeV
2
assuming a functional form of
the parton distribution as used by many parametrisations [4].
The power of the rise of the gluon momentum density with decreasing x has been calculated
4
ZEUS 1993
0
0.5
1
1.5
2
10 10 2
x = 0.00085
Q2(GeV2)
F 2
(x,
Q2
)
0
0.5
1
1.5
2
10 10 2
x = 0.00155
Q2(GeV2)
F 2
(x,
Q2
)
0
0.5
1
1.5
2
10 10 2
x = 0.00268
Q2(GeV2)
F 2
(x,
Q2
)
0
0.5
1
1.5
2
10 10 2
x = 0.00465
Q2(GeV2)
F 2
(x,
Q2
)
Figure 5: Scaling violation of the proton structure function F
2
as a function of Q
2
for xed
values of x as given in the gure. The solid lines show a straight line t, while the dashed lines
show the result of the global NLO t. The arrows indicate Q
2
= 20 GeV
2
.
and found to be xg  A  x
 0:35
+0:10
 0:04
.
The results from the global t, from the method of Prytz and from that of EKL are
shown in gure 6 for Q
2
= 20 GeV
2
. The shaded band shows the error on the global t. The
inner error bars on the points show the statistical error only, while the outer error bars show the
statistical and the systematic error added in quadrature. A good agreement between all methods
is observed.
7 Conclusions
With the 1993 ZEUS data the strong rise of F
2
with decreasing x already observed in the
previous year has been conrmed and is clearly visible over a large range of Q
2
. The measured
values of F
2
are in agreement with the parton distribution parametrisations from GRV, MRSA
and CTEQ2D
0
. The observed scaling violations have made it possible to derive the gluon mo-
mentum density in a new regime of x at Q
2
of 20 GeV
2
. xg(x;Q
2
) shows a steep rise at low x
when compared to the measurements from NMC at large x.
References
[1] The ZEUS Detector, Status Report 1993, DESY 1993.
[2] ZEUS Collaboration, M. Derrick et al., Phys. Lett. B 293 (1992) 465.
[3] ZEUS Collaboration, M. Derrick et al., Z. Phys. C 65 (1995) 379.
[4] ZEUS Collaboration, M. Derrick et al., Phys. Lett. B 345 (1995) 576.
[5] K. Prytz, Phys. Lett. B311 (1993) 286 and B332 (1994) 393.
[6] R.K. Ellis, Z. Kunszt and E.M. Levin, Nucl. Phys. B420 (1994) 517.
[7] V.N. Gribov and L.N. Lipatov, Sov. J. Nucl. Phys. 15 (1972) 438, 675;
L.N. Lipatov, Sov. J. Nucl. Phys. 20 (1975) 94;
G. Altarelli and G. Parisi, Nucl. Phys. B126 (1977) 298.
5
ZEUS 1993
0
5
10
15
20
25
30
35
40
10-4 10-3 10-2 10-1
MRSD
-
/
MRSD0
/
NMC Gluon
NLO GLAP Fit
Prytz NLO
Q2 = 20 GeV2
x
x
g(x
,Q
2 )
EKL NLO (ω0=0.4)
x
g(x
,Q
2 )
Figure 6: Gluon momentum density as a function of x at Q
2
= 20 GeV
2
[8] NMC Collaboration, P. Amaudruz et al., Phys. Lett. B 295 (1992) 159 and preprint CERN
PPE/92-124.
6


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