Measurement of the inclusive ep scattering cross section at low Q2 and x at HERA
 The Collaboration
 F. D. Aaron
 C. Alexa
 V. Andreev
 B. Antunovic
 S. Aplin
 A. Asmone
 A. Astvatsatourov
 S. Backovic

 A. Baghdasaryan
 E. Barrelet
 W. Bartel
 K. Begzsuren
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 G. Brandt
 M. Brinkmann
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 L. Favart
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 E. Sauvan
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ABSTRACT A measurement of the inclusive ep scattering cross section is presented in the region of low momentum transfers, 0.2 GeV2 ≤Q2≤12 GeV2, and low Bjorken x, 5⋅10−6≤x≤0.02. The result is based on two data sets collected in dedicated runs by the H1 Collaboration at HERA at beam energies of
27.6 GeV and 920 GeV for positrons and protons, respectively. A combination with data previously published by H1 leads to
a cross section measurement of a few percent accuracy. A kinematic reconstruction method exploiting radiative ep events extends the measurement to lower Q
2 and larger x. The data are compared with theoretical models which apply to the transition region from photoproduction to deep inelastic
scattering.

 JHEP. 01/2013; 1307:032.
 [Show abstract] [Hide abstract]
ABSTRACT: We compute the longitudinal structure function of the proton (FL) at the nexttonexttoleading order (NNLO) approximation. For this purpose, we should know the flavorsinglet, nonsinglet and gluon distribution functions of the proton. We use the chiral quark model (χQM) to determine these distributions. Finally, we compare the results of FL with the recent ZEUZ and H1 experimental data and some fitting parametrizations. Our results are in good agreement with the data and the related fittings.Modern Physics Letters A 10/2012; 27(31):50179. · 1.34 Impact Factor
Page 1
Measurement of the Inclusive ep Scattering Cross
Section at low Q2and x at HERA
Andrea del Rocio Vargas Trevi˜ no
on behalf of the H1 Collaboration
DESY
Notkestrasse 85  22607 Hamburg, Germany
Measurements of the inclusive ep scattering cross section in the region of low four
momentum transfer squared, 0.2GeV2< Q2< 12GeV2, and low Bjorken x, 4×10−6<
x < 0.02 are presented. The results are based on two data sets collected in dedicated
runs by the H1 Collaboration at beam energies of 27.6GeV and 920GeV for positrons
and protons. These new measurements extend the kinematic phase space to lower
values of Q2by using non tagged radiative ep scattering events. The combination of
these new measurements with data previously published by H1 is presented.
1Introduction
The kinematics of inclusive deep inelastic scattering (DIS) are usually described by the
variables Q2, the negative fourmomentum transfer squared, and x, the fraction of the
proton’s longitudinal momentum carried by the struck quark. The reduced cross section for
electronproton scattering in the onephoton approximation, which is valid in the region of
this measurement, is given by the expression:
σr= F2(x,Q2) −y2
Y+FL(x,Q2)
Y+= 1 + (1 − y)2
(1)
where y is the inelasticity, given by y = Q2/sx, and s is the centre of mass energy of the ep
collision.
The proton structure function F2 is the dominant contribution to the inclusive cross
section, while FL contributes only at high values of y. The experiments at the HERA ep
collider have shown that the Q2evolution of the proton structure F2 is well described by
pQCD over a wide range in x and Q2[2, 3]. However, at low Q2< 2GeV2, the transition
to photoproduction takes place and the data can be only described by phenomenological
models. This note presents new cross section measurements of the H1 collaboration in the
transition region. A combination of the new measurements with previous H1 data with
comparable accuracy is also presented.
2Cross Section Measurements
Two dedicated runs taken in the years 1999 (MB’99) and 2000 (SVX’00) by the H1 exper
iment, were used to measure the cross section in the transition region. The MB’99 data
sample covers a kinematic phase space from 0.5 ≤ Q2≤ 12GeV2while the SVX’00 data
sample covers the lowest values 0.2 ≤ Q2≤ 3.5GeV2. The trigger configuration of the MB’99
data taking allows to measure the cross section towards high y = 0.75, into the region of high
sensitivity to FL. During the SVX’00 data sample, the interaction point of the ep collision
was shifted in the proton beam direction, such that larger positron scattering angles could
DIS2007
Page 2
be measured and hence lower values of Q2were accessed. In addition, the measurement at
even lower values of Q2was possible by using initial state radiative (ISR) events. In this
analyses the detection of the radiated photon was not required. The energy of the incoming
electron is reconstructed from energy and longitudinal momentum conservation, assuming
that the photon is radiated collinearly with the electron beam. Using the reduced incoming
electron energy, the kinematic variables are reconstructed with the so called Σ method.
In Fig. 1 the cross section measure
ments are shown for the MB’99 and
SVX’00 data samples. A good agree
ment between the two data sets is ob
served in the overlap region 0.5 ≤ Q2≤
3.5GeV2.
The total error of the measurement
contains two types of error sources.
One error source affects the measure
ment bin by bin (uncorrelated), while
the another source affects the measure
ment as a whole (correlated). Exam
ples of correlated sources are the uncer
tainty on the measurement of the en
ergy, angular position of the scattered
electron, while uncertainties on effi
ciencies are examples of uncorrelated
sources. The dominant uncertainties
of the MB’99 and SVX’00 cross section
measurements are the vertex efficiency
(2%) and the uncertainty on the lumi
nosity measurement (3%), respectively.
The total error of the measurement for
the MB’99 sample varies from 10% at
low values of Q2to 2% for the bulk re
gion Q2> 2GeV2. The SVX’00 sample
has comparable precision for values of
Q2> 2GeV2, but is of limited precision for the lowest values of Q2.
The MB’99 and SVX’00 measurements are the final H1 DIS cross section measurements
in the low Q2transition region. These measurements have a comparable precision with the
previously published H1 data collected in 1997 (MB’97) [2]. For obtaining a coherent result
of minimum uncertainty, the data is combined using the procedure described below. The
agreement between the MB’99, SVX’00 and the published MB’97 measurement is good,
after a global 3.4% correction of the MB’97 data sample. This correction did result from a
detailed luminosity reanalysis of the MB’97 data taking.
0.2
0.4
σr
Q2 = 0.2 GeV2
H1 Preliminary
SVX' 00
MB' 99
H1 Preliminary
Q2 = 0.25 GeV2
Q2 = 0.35 GeV2
0.3
0.6
Q2 = 0.5 GeV2
Q2 = 0.65 GeV2
Q2 = 0.85 GeV2
0.4
0.8
Q2 = 1.2 GeV2
Q2 = 1.5 GeV2
Q2 = 2 GeV2
0.5
1
Q2 = 2.5 GeV2
Q2 = 3.5 GeV2
Q2 = 5 GeV2
0.55
1.1
105
103
Q2 = 6.5 GeV2
105
103
Q2 = 8.5 GeV2
105
103
x
Q2 = 12 GeV2
Figure 1: Reduced inclusive ep scattering cross sec
tions as measured with the MB’99 and SVX’00
data samples
3Combination of Data Sets
The combination of the three data samples is performed using a minimization procedure
[4]. The correlated and uncorrelated errors of the different cross section measurements are
taken carefully into account.
DIS2007
Page 3
Let Mibe a set of cross section measurements, the combined cross section measurement
Mcombcan be obtained by minimazing the χ2function:
χ2(Mcomb
i
,αj) =
?
i
?
Mcomb
i
−
?
Mi+?
σ2
i
j
∂Mi
∂αjαj
??2
+
?
j
α2
σ2
α2
j
j
(2)
where σiare the statistical and uncorrelated systematic uncertainties of the measurement.
The sensitivity of the measurement to the correlated uncertainties αjare taken by the term
∂Mi/∂αjinto account.
The χ2function of Eq. 2 has by
construction a minimum χ2= 0 for
Mcomb
i
= Mi and αj = 0. The to
tal uncertainty for Mcomb
i
determined
from the formal minimisation of Eq. 2
is equal to the sum in quadrature of
the statistical and systematic uncer
tainties.
The combination of the MB’99,
SVX’00 and MB’97 cross section mea
surements is performed using the pre
scription of Eq. 2. The published H1
data [2] were taken with a different pro
ton beam energy, Ep= 820GeV. Thus
a centre of mass energy correction is
applied to the published cross section.
The correction becomes sizable only for
the highest y analysis bins which for
the published data is at y = 0.75. The
combination of the three data sets is
shown in Fig. 2.The total error of
the combined cross section measure
ment has a precision varying with Q2
and x, for the central values of Q2
and x is about 2% but larger towards
the edges of the covered phase space.
The behaviour of the cross section data,
which extend from photoproduction to
the DIS region, can be analysed within phenomenological models. As an example, the data
in Fig. 2 is compared to the fractal model [5], in which F2is parameterised exploiting self
similarity features of proton structure at low x. FLis expressed via F2and the cross section
ratio R = FL/(F2−FL). A good fit is obtained with R ? 0.5 in the whole Q2range covered
which corresponds to F2? 3FL.
0.2
0.4
σr
Q2 = 0.2 GeV2
H1 Preliminary
SVX' 00,MB' 99,MB' 97 comb.
Fractal Fit
Q2 = 0.25 GeV2
Q2 = 0.35 GeV2
0.3
0.6
Q2 = 0.5 GeV2
Q2 = 0.65 GeV2
Q2 = 0.85 GeV2
0.4
0.8
Q2 = 1.2 GeV2
Q2 = 1.5 GeV2
Q2 = 2 GeV2
0.5
1
Q2 = 2.5 GeV2
Q2 = 3.5 GeV2
Q2 = 5 GeV2
0.55
1.1
105
103
Q2 = 6.5 GeV2
105
103
Q2 = 8.5 GeV2
105
103
x
Q2 = 12 GeV2
Figure 2: Reduced inclusive ep scattering cross
section measurement obtained by combining the
MB’99, SVX’00 and the published MB’97 cross sec
tions (see text).
DIS2007
Page 4
4λ Extraction
0
0.05
0.1
0.15
0.2
110
C
Q2/GeV2
H1 Preliminary
0
0.05
0.1
0.15
0.2
110
λ
Q2/GeV2
SVX' 00,MB' 99,MB' 97 comb.
Linear fit
0
0.2
0.4
0.6
0.8
1
110
FL
Q2/GeV2
H1 Preliminary
SVX' 00,MB' 99,MB' 97 comb.
FL Fractal fit (R=const)
Figure 3: Coefficients c, λ and FL de
fined in Eq. 3 determined from a fit to
the H1 preliminary data (Fig. 2) as a
function of Q2.
The rise of the structure function F2at low values
of x can be described by a power law in x, F2∼
x−λ. The coefficient λ increases approximately lin
early as a function of lnQ2for Q2> 2GeV2. The
rise of F2above 1GeV2increases with lnQ2. This
parametrisation can be used at low x to fit the
reduced cross section σr, allowing the extraction
of λ and FLsimultaneously. Assuming that FLis
constant for a given Q2, the reduced cross section
from Eq. 1 can be written as:
σr(x,Q2) = c(Q2)x−λ(Q2)−y2
Y+FL(Q2) (3)
The global normalisation c(Q2), the power law ex
ponent λ(Q2) and FLare three parameters which
are obtained by fitting the reduced cross section.
The result of these fits are shown in Fig. 3.
5Summary
New inclusive cross section measurements of ep
collision in the Q2transition region from photo
production to DIS are presented. The data from
dedicated runs in 1999 and 2000 are combined here
with previously measured data, leading to a coher
ent result for the low Q2cross section data mea
sured by H1 in the HERAI data taking period. The systematic uncertainty for a large part
of the phase space is about 2%.
6Acknowledgments
I would like to acknowledge the work of all members of the H1 Collaboration, in particular
I would like to thank to O. Behrendt, S. Glazov, M. Klein, K. Krueger, V. Lendermann,
A. Petrukhin, H. SchultzCoulon and D. Wegener, for their help and support during the
preparation of these results.
References
[1] Slides: http://indico.cern.ch/contributionDisplay.py?contribId=25&sessionId=8&confId=9499
[2] C. Adloff et al. (H1 Collab.), Eur. Phys. J. C 21 (2001) 33;
[3] S. Aid et al. (H1 Collab.), Nucl. Phys. B 470 (1996) 3; M. Derrick et al. (ZEUS Collab.), Z. Phys. C
72 (1996) 399; C. Adloff et al. (H1 Collab.), Phys. Lett. B 393 (1997) 452.
[4] S. Glazov, in ”13th International Workshop on DIS, DIS2005,” edited by W. Smith and S. R. Dasu,
AIP Conference Proceedings, 2005.
[5] T. Lastovicka, Eur. Phys. J. C 24 (2002) 529.
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