# Measurement of the inclusive ep scattering cross section at low Q2 and x at HERA

**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.

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**ABSTRACT:**Self-similar properties of proton structure in the kinematic region of low values of the Bjorken variable x are introduced and studied numerically. A description of the proton structure function reflecting self-similarity is proposed with a few parameters which are fitted to recent HERA data. The specific parametrisation provides an excellent description of the data which cover the region of four momentum transfer squared , and of the Bjorken variable .European Physical Journal C 07/2002; 24(4):529-533. · 5.25 Impact Factor

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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 four-momentum transfer squared, and x, the fraction of the

proton’s longitudinal momentum carried by the struck quark. The reduced cross section for

electron-proton scattering in the one-photon 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

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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

10-5

10-3

Q2 = 6.5 GeV2

10-5

10-3

Q2 = 8.5 GeV2

10-5

10-3

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

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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

10-5

10-3

Q2 = 6.5 GeV2

10-5

10-3

Q2 = 8.5 GeV2

10-5

10-3

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).

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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 HERA-I 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. Schultz-Coulon 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.

DIS2007