Measurement of inclusive ep cross sections at high Q^sup 2^ at [SQRT]s = 225 and 252 GeV and of the longitudinal proton structure function F^sub L^ at HERA

Abstract

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

Inclusive ...... double differential cross sections for neutral current deep inelastic scattering are measured with the H1 detector at HERA. The data were taken with a lepton beam energy of ...... GeV and two proton beam energies of ...... and 575 GeV corresponding to centre-of-mass energies of 225 and 252 GeV, respectively. The measurements cover the region of ...... for ...... GeV...... up to ....... The measurements are used together with previously published H1 data at ...... GeV and lower ...... data at ......, ...... and ...... GeV to extract the longitudinal proton structure function ...... in the region ...... GeV.......

Eur. Phys. J. C (2014) 74:2814

DOI 10.1140/epjc/s10052-014-2814-6

Regular Article - Experimental Physics

H1 Collaboration

V. Andreev21, A. Baghdasaryan33, S. Baghdasaryan33, K. Begzsuren30, A. Belousov21, P. Belov10, V. Boudry24,G. Bradt37, M. Brinkmann10, V. Brisson23, D. Britzger10, A. Buniatyan12, A. Bylinkin20,r, L. Bystritskaya20,A. J. Campbell10, K. B. Cantun Avila19, F. Ceccopieri3, K. Cerny27, V. Chekelian22, J. G. Contreras19,J. B. Dainton16, K. Daum32,m,a, E. A. De Wolf3, C. Diaconu18, M. Dobre4, V. Dodonov10, A. Dossanov11,22,A. Dubak22,25, G. Eckerlin10, S. Egli31, E. Elsen10, L. Favart3, A. Fedotov20, J. Feltesse9, J. Ferencei14,M. Fleischer10, A. Fomenko21, E. Gabathuler16, J. Gayler10, S. Ghazaryan10, A. Glazov10, L. Goerlich6,N. Gogitidze21, M. Gouzevitch10,n, C. Grab35, A. Grebenyuk10, T. Greenshaw16, G. Grindhammer22, S. Habib10,D. Haidt10, R. C. W. Henderson15, M. Herbst13, M. Hildebrandt31, J. Hladk`y26, D. Hoffmann18, R. Horisberger31,T. Hreus3, F. Huber12, M. Jacquet23, X. Janssen3, A. W. Jung13,u, H. Jung3,10, M. Kapichine8, C. Kiesling22,M. Klein16, C. Kleinwort10, R. Kogler11, P. Kostka34, J. Kretzschmar16, K. Krger10, M. P. J. Landon17,W. Lange34, P. Laycock16, A. Lebedev21, S. Levonian10, K. Lipka10,q, B. List10, J. List10, B. Lobodzinski10,V. Lubimov20,, E. Malinovski21, H.-U. Martyn1, S. J. Maxeld16, A. Mehta16, A. B. Meyer10, H. Meyer32,J. Meyer10, S. Mikocki6, A. Morozov8, K. Mller36, Th. Naumann34, P. R. Newman2, C. Niebuhr10, G. Nowak6,K. Nowak11, B. Olivier22, J. E. Olsson10, D. Ozerov10, P. Pahl10, C. Pascaud23, G. D. Patel16, E. Perez9,o,A. Petrukhin10, I. Picuric25, H. Pirumov10, D. Pitzl10, R. Plaakyte10,q, B. Pokorny27, R. Polifka27,s,V. Radescu10,q, N. Raicevic25, A. Raspereza10, T. Ravdandorj30, P. Reimer26, E. Rizvi17, P. Robmann36,R. Roosen3, A. Rostovtsev20, M. Rotaru4, S. Rusakov21, D. lek27, D. P. C. Sankey5, M. Sauter12, E. Sauvan18,t,S. Schmitt10, L. Schoeffel9, A. Schning12, H.-C. Schultz-Coulon13, F. Sefkow10, S. Shushkevich10,Y. Soloviev10,21, P. Sopicki6, D. South10, V. Spaskov8, A. Specka24, M. Steder10, B. Stella28, U. Straumann36,T. Sykora3,27, P. D. Thompson2, D. Traynor17, P. Trul36, I. Tsakov29, B. Tseepeldorj30,p, J. Turnau6,A. Valkrov27, C. Valle18, P. Van Mechelen3, Y. Vazdik21, D. Wegener7, E. Wnsch10, J. ek27, Z. Zhang23,R. lebk27, H. Zohrabyan33, F. Zomer23

1 I. Physikalisches Institut der RWTH, Aachen, Germany

2 School of Physics and Astronomy, University of Birmingham, Birmingham, UKc

3 Inter-University Institute for High Energies ULB-VUB, Brussels and Universiteit Antwerpen, Antwerp, Belgiumd

4 National Institute for Physics and Nuclear Engineering (NIPNE), Bucharest, Romaniak

5 STFC, Rutherford Appleton Laboratory, Didcot, Oxfordshire, UKc

6 Institute for Nuclear Physics, Cracow, Polande

7 Institut fr Physik, TU Dortmund, Dortmund, Germanyb

8 Joint Institute for Nuclear Research, Dubna, Russia

9 CEA, DSM/Irfu, CE-Saclay, Gif-sur-Yvette, France

10 DESY, Hamburg, Germany

11 Institut fr Experimentalphysik, Universitt Hamburg, Hamburg, Germanyb

12 Physikalisches Institut, Universitt Heidelberg, Heidelberg, Germanyb

13 Kirchhoff-Institut fr Physik, Universitt Heidelberg, Heidelberg, Germanyb

14 Institute of Experimental Physics, Slovak Academy of Sciences, Kosice, Slovak Republicf

15 Department of Physics, University of Lancaster, Lancaster, UKc

16 Department of Physics, University of Liverpool, Liverpool, UKc

17 School of Physics and Astronomy, Queen Mary, University of London, London, UKc

18 CPPM, Aix-Marseille Univ, CNRS/IN2P3, 13288 Marseille, France

19 Departamento de Fisica Aplicada, CINVESTAV, Mrida, Yucatn, Mexicoi

20 Institute for Theoretical and Experimental Physics, Moscow, Russiaj

21 Lebedev Physical Institute, Moscow, Russia

22 Max-Planck-Institut fr Physik, Munich, Germany

23 LAL, Universit Paris-Sud, CNRS/IN2P3, Orsay, France

24 LLR, Ecole Polytechnique, CNRS/IN2P3, Palaiseau, France

Measurement of inclusive ep cross sections at high Q2 at s = 225 and 252 GeV and of the longitudinal proton

structure function FL at HERA

2814 Page 2 of 26 Eur. Phys. J. C (2014) 74:2814

25 Faculty of Science, University of Montenegro, Podgorica, Montenegrol

26 Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republicg

27 Faculty of Mathematics and Physics, Charles University, Prague, Czech Republicg

28 Dipartimento di Fisica, Universit di Roma Tre and INFN Roma 3, Rome, Italy

29 Institute for Nuclear Research and Nuclear Energy, Soa, Bulgaria

30 Institute of Physics and Technology of the Mongolian Academy of Sciences, Ulaanbaatar, Mongolia

31 Paul Scherrer Institut, Villigen, Switzerland

32 Fachbereich C, Universitt Wuppertal, Wuppertal, Germany

33 Yerevan Physics Institute, Yerevan, Armenia

34 DESY, Zeuthen, Germany

35 Institut fr Teilchenphysik, ETH, Zurich, Switzerlandh

36 Physik-Institut der Universitt Zrich, Zurich, Switzerlandh

37 Department of Physics, Oxford University, Oxford, UKc

Received: 17 December 2013 / Accepted: 26 February 2014 The Author(s) 2014. This article is published with open access at Springerlink.com

Abstract Inclusive ep double differential cross sections for neutral current deep inelastic scattering are measured with the H1 detector at HERA. The data were taken with a lepton beam energy of 27.6 GeV and two proton beam energies of Ep =

460 and 575 GeV corresponding to centre-of-mass energies

Deceased

a e-mail: [email protected]

b Supported by the Bundesministerium fr Bildung und Forschung, FRG, under contract numbers 05H09GUF, 05H09VHC, 05H09VHF, 05H16PEA

c Supported by the UK Science and Technology Facilities Council, and formerly by the UK Particle Physics and Astronomy Research Council

d Supported by FNRS-FWO-Vlaanderen, IISN-IIKW and IWT and by Interuniversity Attraction Poles Programme, Belgian Science Policy

e Partially Supported by Polish Ministry of Science and Higher Education, grant DPN/N168/DESY/2009

f Supported by VEGA SR grant no. 2/7062/ 27

g Supported by the Ministry of Education of the Czech Republic under the projects LC527, INGO-LA09042 and MSM0021620859

h Supported by the Swiss National Science Foundation

i Supported by CONACYT, Mxico, grant 48778-F

j Russian Foundation for Basic Research (RFBR), grant no

1329.2008.2 and Rosatom

k Supported by the Romanian National Authority for ScienticResearch under the contract PN 09370101

l Partially Supported by Ministry of Science of Montenegro, no. 05-1/3-3352

m Also at Rechenzentrum, Universitt Wuppertal, Wuppertal,Germany

n Also at IPNL, Universit Claude Bernard Lyon 1, CNRS/IN2P3,Villeurbanne, France

o Also at CERN, Geneva, Switzerland

p Also at Ulaanbaatar University, Ulaanbaatar, Mongolia

q Supported by the Initiative and Networking Fund of the HelmholtzAssociation (HGF) under the contract VH-NG-401 and S0-072

r Also at Moscow Institute of Physics and Technology, Moscow,

Russia

s Also at Department of Physics, University of Toronto, Toronto, ON

M5S 1A7, Canada

t Also at LAPP, Universit de Savoie, CNRS/IN2P3, Annecy-le-Vieux,

France

u Now at Fermi National Accelerator Laboratory, Batavia, IL 60510,USA

of 225 and 252 GeV, respectively. The measurements cover the region of 6.5 104 x 0.65 for 35 Q2 800

GeV2 up to y = 0.85. The measurements are used together

with previously published H1 data at Ep = 920 GeV and

lower Q2 data at Ep = 460, 575 and 920 GeV to extract

the longitudinal proton structure function FL in the region 1.5 Q2 800 GeV2.

1 Introduction

Deep inelastic scattering (DIS) data provide high precision tests of perturbative quantum chromodynamics (QCD), and have led to a detailed and comprehensive understanding of proton structure, see [1] for a recent review. A measurement of the longitudinal proton structure function, FL, provides a unique test of parton dynamics and the consistency of QCD by allowing a comparison of the gluon density obtained largely from the scaling violations of F2 to an observable directly sensitive to the gluon density. Previous measurements of FL have been published by the H1 and ZEUS collaborations covering the kinematic region of low Bjorken x, and low to medium four-momentum transfer squared, Q2,

using data taken at proton beam energies Ep = 460, 575

and 920 GeV corresponding to centre-of-mass energies of s = 225, 252 and 319 GeV respectively [24]. The new

cross section measurements at Ep = 460 and 575 GeV

presented here, and recently published data at Ep = 920

GeV [5] improve the experimental precision on FL in the region 35 Q2 110 GeV2, and provide the rst mea

surements of FL in the region 120 Q2 800 GeV2 and

6.5 104 < x < 0.032. As the extraction of FL and F2 is

repeated using all available H1 cross section measurements, the earlier measurements of FL and F2 [2,3] are superseded by the present analysis. Furthermore, in the determination of the systematic uncertainties of the published H1 FL measurements [3] an error has been identied in the proce-

/ Published online: pril 2014

8 A

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dure of averaging several measurements at xed Q2 which is corrected here.

The differential cross section for deep inelastic ep scattering can be described in terms of three proton structure functions F2, FL and x F3, which are related to the parton distribution functions (PDFs) of the proton. The structure functions depend on the kinematic variables, x and Q2 only, whereas the cross section is additionally dependent on the inelasticity y related by y = Q2/sx. The reduced neutral current (NC)

differential cross section for e+ p scattering after correcting for QED radiative effects can be written as

NC(x, Q2, y)

d2NC

dxdQ2

x Q4 22

1 Y+

[parenleftbigg]F2

y2 Y+

FL

Y

Y+

, (1)

where Y = 1 (1 y)2 and the ne structure constant is

dened as (Q2 = 0).

The cross section for virtual boson (Z/ ) exchange is related to the F2 and x F3 structure functions in which both the longitudinal and transverse boson polarisation states contribute. The FL term is related to the longitudinally polarised virtual boson exchange process. This term vanishes at lowest order QCD but has been predicted by Altarelli and Martinelli [6] to be non-zero when including higher order QCD terms. As can be seen from Eq. 1 the contribution of FL to the cross section is signicant only at high y. For

Q2 [lessorsimilar] 800 GeV2 the contribution of Z exchange and the inuence of x F3 is expected to be small.

A direct measurement of FL is performed by measuring the differential cross section at different values of s by reducing the proton beam energy from 920 GeV, used for most of the HERA-II run period, to Ep = 460 and 575 GeV.

The lepton beam energy was maintained at 27.6 GeV. The two sets of cross section data are combined with recently published H1 data taken at Ep = 920 GeV [5], and cross

section measurements at lower Q2 taken at Ep = 460, 575

and 920 GeV [3], to provide a set of measurements at xed x and Q2 but at different values of y. This provides an experimental separation between the F2 and FL structure functions.

Sensitivity to FL is enhanced by performing the differential cross sections measurement up to high y, a kinematic region in which the scattered lepton energy is low, and consequently the background from photoproduction processes is large. The cross sections are used to extract FL and the ratio R of the longitudinally to transversely polarised photon exchange cross sections. In addition a direct extraction of the gluon density xg(x, Q2) is performed using an approximation at order S.

This paper is organised as follows: in Sect. 2 the H1 detector, trigger system and data sets are described. The simulation programs and Monte Carlo models used in the analysis are presented in Sect. 3. In Sect. 4 the analysis procedure is

given in which the event selection and background suppression methods are discussed followed by an assessment of the systematic uncertainties of the measurements. The results are presented in Sect. 5 and the paper is summarised in Sect. 6.

2 H1 apparatus, trigger and data samples

2.1 The H1 detector

A detailed description of the H1 detector can be found elsewhere [710]. The coordinate system of H1 is dened such that the positive z axis is in the direction of the proton beam (forward direction) and the nominal interaction point is located at z = 0. The polar angle is then dened with

respect to this axis. The detector components most relevant to this analysis are the Liquid Argon (LAr) calorimeter, which measures the positions and energies of particles over the range 4 < < 154, the inner tracking detectors, which measure the angles and momenta of charged particles over the range 7 < < 165, and a lead-bre calorimeter (SpaCal)

covering the range 153 < < 177.

The LAr calorimeter consists of an inner electromagnetic section with lead absorbers and an outer hadronic section with steel absorbers. The calorimeter is divided into eight wheels along the beam axis, each consisting of eight stacks arranged in an octagonal formation around the beam axis. The electromagnetic and the hadronic sections are highly segmented in the transverse and the longitudinal directions. Electromagnetic shower energies are measured with a resolution of E/E 0.11/E/GeV 0.01 and hadronic

energies with E/E 0.50/E/GeV0.02 as determined

using electron and pion test beam data [11,12].

In the central region, 25 < < 155, the central tracking detector (CTD) measures the trajectories of charged particles in two cylindrical drift chambers (CJC) immersed in a uniform 1.16 T solenoidal magnetic eld. The CTD also contains a further drift chamber (COZ) between the two drift chambers to improve the z coordinate reconstruction, as well as a multiwire proportional chamber at inner radii (CIP) mainly used for triggering [13]. The CTD measures charged particle trajectories with a transverse momentum resolution of (pT )/pT 0.2 % pT /GeV 1.5 %. The

CJC also provides a measurement of the specic ionisation energy loss, dE/dx, of charged particles with a relative resolution of 6.5 % for long tracks. The forward tracking detector (FTD) is used to supplement track reconstruction in the region 7 < < 30 [14] and to improve the hadronic nal state (HFS) reconstruction of forward going low transverse momentum particles.

The CTD tracks are linked to hits in the vertex detectors: the central silicon tracker (CST) [15,16], the forward silicon tracker (FST), and the backward silicon tracker (BST).

x F3

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These detectors provide precise spatial track reconstruction and therefore also improve the primary vertex reconstruction. The CST consists of two layers of double-sided silicon strip detectors surrounding the beam pipe covering an angular range of 30 < < 150 for tracks passing through both layers. The FST consists of ve double wheels of single-sided strip detectors [17] measuring the transverse coordinates of charged particles. The BST design is very similar to the FST and consists of six double wheels of strip detectors [18].

In the backward region the SpaCal provides an energy measurement for electrons1 and hadronic particles, and has a resolution for electromagnetic energy depositions of E/E 0.07/E/GeV 0.01, and a hadronic energy res

olution of E/E 0.70/E/GeV0.01 as measured using

test beam data [19].

The integrated ep luminosity is determined by measuring the event rate for the Bethe-Heitler process of QED bremsstrahlung ep ep . The photons are detected in the

photon tagger located at z = 103 m. An electron tagger is

placed at z = 5.4 m adjacent to the beampipe. It is used

to provide information on ep eX events at very low Q2

(photoproduction) where the electron scatters through a small angle ( < 5 mrad).

At HERA transverse polarisation of the lepton beam arises naturally through synchrotron radiation via the Sokolov-Ternov effect [20]. Spin rotators installed in the beamline on either side of the H1 detector allow transversely polarised leptons to be rotated into longitudinally polarised states and back again. Two independent polarimeters LPOL [21] and TPOL [22] monitor the polarisation. Only data where a TPOL or LPOL measurement is available is used. When both measurements are available they are averaged [23].

2.2 The trigger

The H1 trigger system is a three level trigger with a rst level latency of approximately 2 s. In the following we describe only the components relevant to this analysis. NC events at high Q2 are triggered mainly using information from the LAr calorimeter to rapidly identify the scattered lepton. The calorimeter has a nely segmented geometry allowing the trigger to select localised energy deposits in the electromagnetic section of the calorimeter pointing to the nominal interaction vertex. For electrons with energy above 11 GeV this LAr electron trigger is determined to be 100 % efcient obtained by using LAr triggers red by the hadronic nal state particles.

At high y, corresponding to lower electron energies, the backward going HFS particles can enter the SpaCal and therefore trigger the event. In addition low energy scattered

1 In this paper electron refers generically to both electrons and positrons. Where distinction is required, the terms e and e+ are used.

Table 1 Integrated luminosities, L, and luminosity weighted longitu

dinal lepton beam polarisation, Pe, for the data sets presented here

Ep = 460 GeV Ep = 575 GeV

e+ p L = 11.8 pb1 L = 5.4 pb1

Pe = (42.3 0.8) % Pe = (41.8 0.8) %

electron candidates can be triggered by the Fast Track Trigger [2429] based on hit information provided by the CJC, and the LAr Jet Trigger [30] using energy depositions in the LAr calorimeter. These two trigger subsystems allow electron identication to be performed at the third trigger level [31,32]. This L3 electron trigger and the SpaCal trigger are used to extend the kinematically accessible region to high y where scattered leptons have energies as low as 3 GeV, the minimum value considered in this analysis. For electron energies of 3 GeV, the total trigger efciency is found to vary between 9197% depending on the kinematic region.

2.3 Data samples

The data sets used in the measurement of the reduced cross sections correspond to two short dedicated data taking periods in 2007 in which the proton beam energy was reduced to 460 GeV and 575 GeV, and the scattered lepton was detected in the LAr calorimeter. The positron beam was longitudinally polarised with polarisation Pe = (NR NL)/(NR + NL),

where NR (NL) is the number of right (left) handed leptons in the beam. The integrated luminosity and longitudinal lepton beam polarisation for each data set are given in Table 1. The lepton beam polarisation plays no signicant role in this analysis.

The extraction of the FL structure function in Sect. 5.2 uses the cross section measurements presented here and e+ p measurements with Pe = 0 at Ep = 920 GeV in which the

scattered positron is detected in the LAr calorimeter (Tables 22 and 26 of [5] scaled by a normalisation factor of 1.018 [33] which arises from an error in the determination of the integrated luminosity used for this data set). In addition the FL extraction also uses cross section measurements from H1 at Ep = 460, 575 and 920 GeV with the positron detected in

the SpaCal as it is described in [3]. The two detectors provide access to different kinematic regions and the corresponding measurements are referred to as the LAr and SpaCal data for each of the three values of Ep.

3 Simulation programs

In order to determine acceptance corrections, DIS processes are generated at leading order (LO) QCD using the Djangoh 1.4 [34] Monte Carlo (MC) simulation program

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which is based on Heracles 4.6 [35] for the electroweak interaction and on Lepto 6.5.1 [36] for the hard matrix element calculation. The colour dipole model (CDM) as implemented in Ariadne [37] is used to simulate higher order QCD dynamics. The Jetset 7.410 program [38] is used to simulate the hadronisation process in the framework of the string-fragmentation model. The parameters of this model used here are tuned to describe hadronic Z decay data [39].The simulated events are weighted to reproduce the cross sections predicted by the NLO QCD t H1PDF2012 [5]. This t includes H1 low Q2 NC data and high Q2 neutral and charged current (CC) data from HERAI, as well as inclusive NC and CC measurements from H1 at high Q2 based on the full HERAII integrated luminosity at Ep = 920 GeV [5]. In

addition the Compton 22 [40] MC is used to simulate elastic and quasi-elastic QED Compton processes, and replaces the Compton processes simulation available in Djangoh.

The detector response to events produced by the various generator programs is simulated in detail using a program based on Geant3 [41]. The simulation includes a detailed time dependent modelling of detector noise conditions, beam optics, polarisation and inefcient channel maps reecting actual running conditions throughout the data taking periods. These simulated events are then subjected to the same reconstruction, calibration, alignment and analysis chain as the real data.

4 Experimental procedure

4.1 Kinematic reconstruction

Accurate measurements of the event kinematic quantities Q2,

x and y are an essential component of the analysis. Since both the scattered lepton and the hadronic nal state (HFS) are observed in the detector, several kinematic reconstruction methods are available allowing for calibration and cross checks.

The primary inputs to the various methods employed are the scattered leptons energy E e and polar scattering angle e, as well as the quantity = [summationtext]

The most precise kinematic reconstruction method for y [greaterorsimilar] 0.1 is the e-method which relies solely on E e and e to reconstruct the kinematic variables Q2 and y as

Q2e =

(E e sin e)2 1 ye

, ye = 1

E eEe sin2 [parenleftbigg]

e

2

, (2)

and x is determined via the relation x = Q2/sy. This method

is used in the analysis region y > 0.19 since the resolution of the e-method degrades at low y. The method is also susceptible to large QED radiative corrections at the highest and lowest y. A cut on quantity E Pz = + E e(1 cos e)

ensures that the radiative corrections are moderate.In the -method [45], y is reconstructed as /(E Pz)

and is therefore less sensitive to QED radiative effects. The e -method [46] is an optimum combination of the two and maintains good resolution throughout the kinematic range of the measurement with acceptably small QED radiative corrections. The kinematic variables are determined using

Q2e = Q2e =

(E e sin e)2 1 ye

, ye = 2Ee

[E Pz]2

, (3)

and x is determined as for the e-method above. The e -method is employed to reconstruct the event kinematics for y 0.19 in which is determined using

hadronic jets dened using the longitudinally invariant kT jet algorithm [47,48].

4.2 Polar angle measurement and energy calibration

The detector calibration and alignment procedures adopted for this analysis rely on the methods discussed in detail in [5] which uses the high statistics Ep = 920 GeV data recorded

just prior to the 460 and 575 GeV runs. The detector was not moved or opened between these run periods. The alignment and calibration constants obtained at Ep = 920 GeV are

veried using the same methods [5] for the data presented here.

In this analysis the scattered lepton is detected in the LAr calorimeter by searching for a compact and isolated electromagnetic energy deposition. The polar angle of the scattered lepton, e, is determined using the position of its energy deposit (cluster) in the LAr calorimeter, and the event vertex reconstructed with tracks from charged particles. The relative alignment of the calorimeter and tracking chambers is veried using a sample of events with a well measured lepton track [49] in which the COZ chamber provides an accurate z reconstruction of the particle trajectory. The residual difference between the track and cluster polar angles in data and simulation is found to be less than 1 mrad, and this value is used as the systematic uncertainty of the scattered lepton polar angle.

i (Ei pz,i) determined from

the sum over the HFS particles assuming charged particles have the pion mass, where Ei and pz,i are the energy and longitudinal momenta respectively [4244]. At high Q2 and low y the HFS is dominated by one or more jets. Therefore the complete HFS can be approximated by the sum of jet four-momenta corresponding to localised calorimetric energy sums above threshold. This technique allows a further suppression of hadronic noise in the reconstruction arising from electronic sources in the LAr calorimeter or from back-scattered low energy particles produced in secondary interactions.

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An in situ energy calibration of electromagnetic energy depositions in the LAr calorimeter is performed for both data and simulation. Briey, a sample of NC events in which the HFS is well contained in the detector is used with the Double Angle reconstruction method [50,51] to predict the scattered lepton energy (ED A) which is then compared to the measured electromagnetic energy response allowing local calibration factors to be determined in a nely segmented grid in z and .The residual mismatch between ED A and E e after performing the calibration step are found to vary within 0.3 1 %

depending on the geometric location of the scattered lepton within the LAr calorimeter. An additional 0.3 % correlated uncertainty is considered and accounts for a possible bias in the PT,D A reconstruction and is determined by varying e and a measurement of the inclusive hadronic polar angle, h, by the angular measurement uncertainty. This has been veried by comparing the residual global shifts between data and MC in the kinematic peak of the E e distribution.

At the lowest electron energies the calibration is validated using QED Compton interactions ep e p with E e of

3 8 GeV in which the lepton track momentum Ptrack is

compared to the measured energy E e of the cluster. The simulation on average describes the data well in this low energy region. For energies below 11 GeV an additional uncorrelated uncertainty of 0.5 % is included to account for a possible nonlinearity of the energy scale.

The hadronic response of the detector is calibrated by requiring a transverse momentum balance between the predicted PT in the DA-method (PT,D A) and the measured hadronic nal state using a tight selection of well reconstructed events with a single jet. The calorimeter calibration constants are then determined in a minimisation procedure across the detector acceptance separately for HFS objects inside and outside jets and for electromagnetic and hadronic contributions to the HFS [52]. The potential bias in the PT,D A reference scale of 0.3 % is also included as a correlated source of uncertainty.

The mean transverse momentum balance between the hadronic nal state and the scattered lepton both in data and simulation agree to within 1 % precision which is taken as the uncorrelated hadronic scale uncertainty. The hadronic SpaCal calibration is performed in a similar manner and a systematic uncertainty of 5 % is adopted.

4.3 Measurement procedure

The event selection and analysis of the NC sample follows closely the procedures discussed in [5]. Inelastic ep interactions are required to have a well reconstructed interaction vertex to suppress beam induced background events. High Q2 neutral current events are selected by requiring each event to have a compact and isolated cluster in the electromagnetic part of the LAr calorimeter. The scattered lepton candidate is

identied as the cluster of highest transverse momentum and must have an associated CTD track. For high electron energies the track condition is relaxed as detailed in 4.3.1. The analysis is restricted to the region 32 < Q2e < 890 GeV2.

The quantity E Pz summed over all nal state particles

(including the electron) is required by energy-momentum conservation to be approximately equal to twice the initial electron beam energy. Restricting E Pz to be greater

than 35 GeV considerably reduces the photoproduction background and radiative processes in which either the scattered lepton or bremsstrahlung photons escape undetected in the lepton beam direction. Topological algorithms [53] are employed to suppress non-ep and QED Compton backgrounds ep e p.

The photoproduction background increases rapidly with decreasing electron energy (corresponding to high y), therefore the analysis is separated into two distinct regions: the nominal analysis (ye 0.38), and the high y analysis

(0.38 < ye < 0.9). In the high y region dedicated techniques are employed to contend with the large background. The analysis differences in each kinematic region are described below.

4.3.1 Nominal analysis

At low y 0.38 the minimum electron energy is kine

matically restricted to be above 18 GeV. The forward going hadronic nal state particles can undergo interactions with material of the beam pipe leading sometimes to a bias in the reconstruction of the primary interaction vertex position. In such cases the vertex position is calculated using a stand alone reconstruction of the track associated with the electron cluster [53,54]. For the nominal analysis the photo-production contribution is negligible, and the only sizeable background contribution arises from remaining QED Compton events which is estimated using simulation. The electron candidate track verication is supplemented by searching for hits in the CIP located on the trajectory from the interaction vertex to the electron cluster. This optimised treatment of the vertex determination and verication of the electron cluster with the tracker information improves the reliability of the vertex position determination and increases the efciency of the procedure to be larger than 99.5 %.

For the region y < 0.19 the hadronic noise has an increasing inuence on and on the transverse momentum balance PT,h/PT,e through its effect on PT,h where PT,h, PT,e are the hadronic and scattered lepton transverse momenta respectively. The event kinematics reconstructed with the e -method in which the HFS is formed from hadronic jets only, limits the noise contribution and substantially improves the PT,h/PT,e description by the simulation. The jets are found with the longitudinally invariant kT jet algorithm [47,48] as implemented in FastJet [55,56] with radius parameter R = 1.0 and are required to have transverse momenta

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Fig. 1 Distributions of PT,h/PT,e, jets and E Pz for

(a) Ep = 460 GeV and (b)

Ep = 575 GeV for y < 0.19

data (solid points) andsimulation and estimatedbackground (histograms)normalised to the integratedluminosity of the data. Theestimated QED Comptonbackground contribution isshown as shaded histogram T,e

H1 Collaboration

H1 data, E

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PT,jet > 2 GeV. In Fig. 1 the quality of the simulation and its description of the Ep = 460 GeV and Ep = 575 GeV

data for ye < 0.19 can be seen for the distributions of the PT,h/PT,e, jets, and E Pz where all HFS quantities are

obtained using the vector sum of jet four-momenta. The simulation provides a reasonable description of both sets of distributions. The MC simulation is normalised to the integrated luminosity of the data.

4.3.2 High y analysis

In the high y region (0.38<ye<0.9) the analysis is extended to low energies of the scattered electron, E e>3 GeV. At these energies photoproduction background contributions arise from 0 decays, from charged hadrons being

misidentied as electron candidates, and from real electrons originating predominantly from semi-leptonic decays of heavy avour hadrons. These contributions increase rapidly with decreasing energy of the electron candidate. Therefore additional techniques are used to reduce this background.

The background from 0 decays leads to dif

ferent electromagnetic shower proles compared to electrons of similar energy. In addition genuine electrons have a momentum matched track associated to the cluster. Four cluster shape variables and the ratio of the candidate electron energy E e determined using cluster information, to the momentum of the associated track pe, are used in a neural network multilayer perceptron [57] to discriminate signal

from background. Additional information using the specic ionisation energy loss, dE/dx, of the track is also used to form a single electron discrimination variable, Dele, such that a value of 1 corresponds to electrons and a value of 0 corresponds to hadrons. The neural network is trained using single particle MC simulations, and validated with samples of identied electrons and pions from J/ e+e and

K 0s + decays in data and MC [31,32]. For the region

E e < 10 GeV isolated electrons are selected by requiring Dele > 0.80 which is estimated to have a pion background rejection of more than 99% and a signal selection efciency of better than 90 % [31]. For the region E e > 10 GeV the scattered electron is identied as in the nominal analysis.

The scattered lepton candidate is required to have positive charge corresponding to the beam lepton. The remaining background is estimated from the number of data events with opposite charge. This background is statistically subtracted from the positively charged sample. However, a charge asymmetry in photoproduction can arise due to the different detector response to particles compared to antiparticles [58,59]. The charge asymmetry has been determined by measuring the ratio of wrongly charged scattered lepton candidates in e+ p to e p scattering at Ep = 920 GeV data and was

found to be 1.03 0.05 [5]. This is cross checked in the

Ep = 460 and 575 GeV data using photoproduction events

in which the scattered electron is detected in the electron tagger. In this sample fake scattered electron candidates passing all selection criteria are detected in the LAr calorimeter with both positively and negatively charged tracks associ-

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Fig. 2 Distributions of E Pz, Dele, and E e/pe for the sample of

events with E e < 6 GeV. The selection requirements on E Pz and

Dele are shown as vertical lines with all other selection criteria applied. The distributions are shown for a Ep = 460 GeV and b Ep = 575 GeV

for data (solid points) and simulation and estimated background

(histograms) normalised to the integrated luminosity of the data. The estimated background is shown as shaded histogram and includes the photoproduction contribution estimated using wrong charge scattered lepton candidates as well as the QED Compton contribution

ated to the electromagnetic cluster. The charge asymmetry is obtained by comparing the two contributions. The results obtained are consistent with the asymmetry measured in the Ep = 920 GeV data, however due to the lower statistical

precision of the Ep = 460 and 575 GeV data sets, the uncer

tainty of the asymmetry is increased to 0.08. The asymmetry is taken into account in the subtraction procedure. The efciency with which the lepton charge is determined is well described by simulation within 0.5 % and is discussed in Sect. 4.5.

The control of the background in the most critical region of E e < 6 GeV is demonstrated in Fig. 2 for both data sets.

The MC simulation is normalised to the integrated luminosity of the data. In all cases the background dominated regions are well described in shape and overall normalisation, giving condence that the background contributions can be reliably estimated from the wrong charge sample. At low E Pz a peak is observed arising from QED initial state

radiation (ISR) which is reasonably well described. The cut E Pz > 35 GeV suppresses the inuence of ISR on the

measurement. The Dele distribution show two populations peaking at zero and unity arising from hadrons and real electrons respectively. The peak at Dele = 1 for the background

indicates that there are real electrons in the remaining background sample.

The e-method has the highest precision in this region of phase space and is used to reconstruct the event kinematics. Figure 3 shows the energy spectrum and the polar angle distribution of the scattered lepton, and the E Pz spectrum

of the high y sample for the Ep = 460 and 575 GeV data

before background subtraction. The background estimates are shown together with the contribution from the remaining QED Compton process. The NC simulation provides a good description of these distributions.

In the scattered lepton energy spectrum a small discontinuity at 8 GeV can be seen. This is a consequence of suppressing electron candidates with E < 8 GeV if a second electron candidate is found with E > 8 GeV. This criterion efciently suppresses background from the QED Compton process in the region E e < 8 GeV.

4.4 Cross section measurement

The simulation is used to correct the selected event samples for detector acceptance, efciencies, migrations and QED radiation effects. The simulation provides a good description

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Fig. 3 Distributions of E e, e and E Pz for a Ep = 460 GeV and b

Ep = 575 GeV for high y data (solid points) and simulation and esti

mated background (histograms) normalised to the integrated luminosity of the data. The estimated background is shown as shaded histogram

and includes the photoproduction contribution estimated using wrong charge scattered lepton candidates and the QED Compton contribution (dashed line)

of the data and therefore is expected to give a reliable determination of the detector acceptance. The accessible kinematic ranges of the measurements depend on the resolution of the reconstructed kinematic variables. The ranges are determined by requiring the purity and stability of any measurement bin to be larger than 30 % as determined from signal MC. The purity is dened as the fraction of events generated and reconstructed in a measurement bin (Ng+r) from the total number of events reconstructed in the bin (Nr). The stability is the ratio of the number of events generated and reconstructed in a bin to the number of events generated in that bin (Ng). The purity and stability are typically found to be above 60 %. The detector acceptance, A = Nr/N g, corrects the measured

signal event yields for detector effects including resolution smearing and selection efciency.

The measured differential cross sections (x, Q2) are then determined using the relation

(x, Q2) =

th(x, Q2)

. (5)

The cross section measurements are nally corrected for the effects of lepton beam polarisation using the H1PDF2012 t to yield cross sections with Pe = 0. This multiplicative

correction does not exceed 2.5 % in the region considered.

In order to optimise the measurement for an extraction of the structure function FL, the cross sections are measured in y, Q2 bins for y > 0.38 at Ep = 460 GeV, and y > 0.304 at

Ep = 575 GeV. At Ep = 920 GeV the y, Q2 binned cross

sections are published for y > 0.19 (Table 22 of [5]). This binning is constructed specically for a measurement of FL with ne segmentation in y. The lower limits in y for each proton beam energy are chosen such that they have the same x for all three values of Ep. Below these y boundaries for each of the three proton beam energies the cross sections are measured in Q2, x bins. The bin boundaries and bin centres in

[integraltext][integraltext]

bin dx dQ2 th(x , Q2 )

N B

L A C [parenleftBig]

1 + QED[parenrightBig]

, (4)

where N and B are the selected number of data events and the estimated number of background events respectively, L

is the integrated luminosity, C is the bin centre correction,

and (1 + QED) are the QED radiative corrections. These

corrections are dened in [60,61] and are calculated to rst order in using the program Heracles [35] as implemented

in Djangoh [34] and veried with the numerical analysis programs Hector [62] and Eprc [63]. No weak radiative corrections are applied to the measurements.

The bin centre correction C(x, Q2) is a factor obtained

from NLO QCD expectation, th(x, Q2), using H1PDF2012

[5], and scales the bin integrated cross section to a differential cross section at the kinematic point x, Q2 dened as

C(x, Q2) =

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2814 Page 10 of 26 Eur. Phys. J. C (2014) 74:2814

Table 2 Table of applied systematic uncertainties and regions of applicability.Uncertainties which are considered point-to-point correlated are labelled corr., and all other sources are considered uncorrelated. The effect of these uncertainties on the cross section measurements is given in the tables of Sect. 5 (except for the luminosity uncertainty)

Source Region Uncertainty

Electron energy scale zimp 150 cm 0.5 % unc. 0.3 % corr.

150 < zimp 60 cm 0.3 % unc. 0.3 % corr.

60 < zimp +20 cm 0.5 % unc. 0.3 % corr.

+20 < zimp +110 cm 0.5 % unc. 0.3 % corr.

zimp > +110 cm 1.0 % unc. 0.3 % corr.

Electron scale linearity E e < 11 GeV 0.5 %

Hadronic energy scale LAr and tracks 1.0 % unc. 0.3 % corr.

SpaCal 5.0 % unc. 0.3 % corr.

Polar angle e 1 mrad corr.

Noise y < 0.19 5 % energy not in jets , corr.

y > 0.19 20 % corr.

Trigger efciency high y 0.32%

nominal 0.3 %

Electron track and vertex efciency high y 1 %

nominal 0.21%

Electron charge ID efciency high y 0.5 %

Electron ID efciency high y zimp < 20 (> 20) cm 0.5 % (1 %)

nominal zimp < 20 (> 20) cm 0.2 % (1 %)

Extra background suppression E e < 10 GeV Dele > 0.80 0.04 corr.

High y background subtraction high y 1.03 0.08 corr.

QED radiative corrections x < 0.1 , 0.1 x < 0.3 , x 0.3 0.3 % , 1.0 %, 2.0 %

high y: y < 0.8 (y > 0.8) 1 % (1.5 %)

Acceptance corrections high y 0.5 %

nominal 0.2 %

Luminosity 4 % corr.

the Q2 x plane are chosen to be the same in the overlapping

region for Ep = 460, 575 and 920 GeV for 35 Q2

800 GeV2.

4.5 Systematic uncertainties

The uncertainties on the measurement lead to systematic errors on the cross sections, which can be split into bin-to-bin correlated and uncorrelated parts. All the correlated systematic errors are found to be symmetric to a good approximation and are assumed so in the following. The total systematic error is formed by adding the individual errors in quadrature.

The size of each systematic uncertainty source and its region of applicability are given in Table 2. Further details can be found elsewhere [49,5254,64] in which several of the sources of uncertainty have been investigated using the Ep = 920 GeV LAr data. The results of similar studies

performed using the Ep = 460 GeV and 575 GeV LAr

data are compared to these earlier analyses to determine the systematic uncertainties. The inuence of the systematic uncertainties on the cross section measurements are given in Tables 3, 4, and their origin and method of estimation are discussed below.

Electron energy: Uncertainties arise from the particular choice of calibration samples, and the linearity correction uncertainty. These uncertainties are taken from the analysis of the 920 GeV data [5]. The uncertainty varies as a function of zimp [5], the z position of the scattered electron in the calorimeter, as given in Table 2. The correlated part of the uncertainty of 0.3 % accounts for a possible bias in the ED A reconstruction used as a reference scale in the energy calibration procedure. This results in a systematic uncertainty which is up to 2 3 % at low y.

Hadronic Calibration: An uncorrelated uncertainty of 1 % is used for the hadronic energy measurement. The uncertainty is determined by quantifying the agreement between data and simulation in the mean of the PT,h/PT,e distribution in different kinematic regions. The correlated part of the uncertainty accounts for a possible bias in the ED A reconstruction used as a reference scale in the energy calibration. It is determined to be 0.3 % and results in a correlated systematic error on the cross section which is up to 23 % at low y. The resulting correlated system

atic error is typically below 1 % for the cross sections. Polar angle: A correlated 1 mrad uncertainty on the determination of the electron polar angle is considered.

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Table 3 The NC e+ p reduced cross section

NC(x, Q2) for Ep = 460 GeV and Pe = 0 with total (tot), statistical (stat), total uncorrelated

systematic (unc) errors and two of its contributions from the electron energy error (Eunc) and the hadronic energy error (hunc). The effect of the other uncorrelated systematic errors is included in unc. In addition the correlated systematic (cor) and its contributions from a positive variation of one standard deviation of the electron energy error (E+cor), of the polar electron angle error (+cor), of the hadronic energy error (h+cor), of the error due to noise subtraction (N+cor), of the error due to background subtraction charge asymmetry (S+cor) and of the error due to variation of the cut value on the electron discriminator Dele (D+cor) are given. The overall normalisation uncertainty of 4 % is not included in the errors

Q2 (GeV2) x y

NC tot

(%)

35 8.10 104 0.850 1.343 6.5 4.5 3.8 0.6 2.8 2.8 0.3 0.4 0.2 0.7 2.3 1.2 45 1.04 103 0.850 1.173 6.3 4.7 3.4 0.4 2.4 2.4 0.1 0.5 0.1 0.6 2.1 1.0 45 1.18 103 0.750 1.187 5.7 5.1 2.2 0.6 0.8 1.3 0.2 0.5 0.0 0.3 0.6 1.0 60 1.39 103 0.850 1.190 6.2 5.0 3.0 0.2 2.0 2.0 0.1 0.3 0.1 0.5 1.7 0.8 60 1.58 103 0.750 1.117 4.7 4.0 2.0 0.5 0.6 1.4 0.2 0.6 0.0 0.2 0.6 1.0 90 2.09 103 0.850 1.269 6.3 5.3 2.9 0.3 1.8 1.8 0.2 0.4 0.1 0.5 1.4 0.9 90 2.36 103 0.750 1.193 4.6 4.1 1.9 0.3 0.5 1.1 0.2 0.5 0.1 0.2 0.3 0.9 90 2.73 103 0.650 1.156 4.2 3.8 1.8 0.4 0.2 0.8 0.2 0.6 0.0 0.2 0.3 0.4 120 2.78 103 0.850 1.249 6.8 6.1 2.7 0.1 1.5 1.6 0.0 0.4 0.1 0.4 0.9 1.2 120 3.15 103 0.750 1.099 5.3 4.8 1.9 0.4 0.4 0.9 0.2 0.4 0.0 0.2 0.4 0.6 120 3.63 103 0.650 1.052 4.7 4.3 1.9 0.6 0.2 0.6 0.2 0.4 0.0 0.2 0.2 0.2 120 4.82 103 0.490 1.041 3.3 2.7 1.8 0.6 0.1 0.8 0.3 0.7 0.0 0.2 0.1 0.0 150 3.47 103 0.850 1.230 7.8 7.1 2.6 0.4 1.4 1.9 0.2 0.3 0.1 0.4 0.8 1.6 150 3.94 103 0.750 1.024 6.1 5.8 1.9 0.4 0.3 0.8 0.2 0.4 0.0 0.2 0.2 0.6 150 4.54 103 0.650 1.010 5.4 5.0 2.0 0.9 0.1 0.5 0.2 0.4 0.0 0.2 0.2 0.1 150 6.03 103 0.490 1.060 3.2 2.5 1.8 0.5 0.1 0.7 0.3 0.6 0.0 0.2 0.1 0.0 150 8.00 103 0.369 0.9774 3.0 2.6 1.4 0.6 0.0 0.9 0.4 0.8 0.0 0.1 0.0 0.0 150 1.30 102 0.227 0.8384 3.8 3.3 1.5 1.2 0.0 1.1 0.8 0.7 0.0 0.0 0.0 0.0 150 2.00 102 0.148 0.7006 5.2 4.5 2.2 1.7 1.0 1.7 1.0 1.0 0.4 0.8 0.0 0.0 200 4.63 103 0.850 1.117 9.6 9.1 2.5 0.3 1.1 2.1 0.1 0.4 0.0 0.3 0.6 1.9 200 5.25 103 0.750 1.011 8.1 7.7 1.9 0.3 0.3 1.1 0.2 0.4 0.0 0.2 0.1 1.0 200 6.06 103 0.650 0.9997 6.8 6.5 2.0 0.9 0.2 0.6 0.1 0.5 0.1 0.2 0.2 0.0 200 8.04 103 0.490 0.9567 3.8 3.4 1.7 0.3 0.1 0.6 0.3 0.6 0.0 0.2 0.1 0.0 200 1.30 102 0.303 0.8430 3.4 3.1 1.0 0.6 0.0 0.8 0.4 0.7 0.0 0.0 0.0 0.0 200 2.00 102 0.197 0.6517 4.1 3.5 1.8 1.6 0.0 1.2 1.0 0.7 0.0 0.0 0.0 0.0 200 3.20 102 0.123 0.5275 4.2 4.0 0.9 0.1 0.1 0.6 0.1 0.5 0.1 0.3 0.0 0.0 200 5.00 102 0.079 0.5297 4.3 4.1 1.2 0.9 0.2 0.7 0.5 0.4 0.1 0.2 0.0 0.0 200 8.00 102 0.049 0.4587 5.0 4.7 1.3 0.9 0.3 1.0 0.6 0.7 0.2 0.2 0.0 0.0 200 1.30 101 0.030 0.3610 5.6 5.1 1.9 1.5 0.1 1.6 0.9 0.7 0.1 1.0 0.0 0.0 200 1.80 101 0.022 0.3201 6.8 5.8 2.3 1.1 1.4 2.6 0.7 0.9 0.4 2.3 0.0 0.0 200 4.00 101 0.010 0.1694 13.1 8.2 4.5 0.3 4.0 9.2 0.2 1.1 0.6 9.1 0.0 0.0 250 5.79 103 0.850 1.049 10.9 10.4 2.5 0.3 0.9 2.2 0.1 0.2 0.0 0.3 0.6 2.0 250 6.56 103 0.750 1.036 9.1 8.8 1.9 0.2 0.3 1.3 0.2 0.4 0.1 0.2 0.2 1.1 250 7.57 103 0.650 0.9480 8.0 7.7 2.0 0.9 0.1 0.5 0.2 0.4 0.0 0.2 0.2 0.0 250 1.00 102 0.490 0.8829 4.3 3.9 1.7 0.3 0.1 0.6 0.3 0.5 0.0 0.2 0.1 0.0 250 1.30 102 0.379 0.8281 4.0 3.7 1.3 0.4 0.0 0.6 0.4 0.5 0.0 0.1 0.0 0.0 250 2.00 102 0.246 0.6799 4.0 3.8 1.0 0.6 0.0 0.8 0.5 0.7 0.0 0.0 0.0 0.0 250 3.20 102 0.154 0.5817 4.4 4.1 1.3 1.0 0.2 0.9 0.4 0.6 0.1 0.6 0.0 0.0 250 5.00 102 0.098 0.5025 4.4 4.1 1.3 0.9 0.1 0.9 0.3 0.6 0.0 0.7 0.0 0.0 250 8.00 102 0.062 0.4429 4.7 4.4 1.3 1.0 0.1 1.0 0.5 0.6 0.1 0.7 0.0 0.0 250 1.30 101 0.038 0.3750 4.9 4.4 1.4 0.8 0.1 1.6 0.3 0.5 0.1 1.5 0.0 0.0

stat (%)

unc (%)

Eunc (%)

hunc (%)

cor (%)

E+cor (%)

+cor (%)

h+cor (%)

N+cor (%)

S+cor (%)

D+cor (%)

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Table 3 continued

Q2 (GeV2) x y

NC tot

(%)

250 1.80 101 0.027 0.3582 5.1 4.5 2.1 1.3 0.9 1.3 0.6 0.7 0.3 0.8 0.0 0.0 250 4.00 101 0.012 0.1675 12.6 6.6 4.9 2.7 3.6 9.5 1.6 1.0 0.6 9.3 0.0 0.0 300 6.95 103 0.850 0.8700 13.8 13.3 2.4 0.2 0.8 2.5 0.2 0.2 0.0 0.3 0.8 2.3 300 7.88 103 0.750 0.8274 11.1 10.9 2.0 0.2 0.3 1.0 0.2 0.3 0.0 0.2 0.3 0.9 300 9.09 103 0.650 0.8411 9.8 9.6 1.9 0.3 0.1 0.5 0.1 0.4 0.0 0.2 0.2 0.0 300 1.21 102 0.490 0.9058 4.8 4.5 1.7 0.3 0.1 0.5 0.3 0.4 0.0 0.1 0.0 0.0 300 2.00 102 0.295 0.7296 4.4 4.2 1.0 0.6 0.0 0.8 0.6 0.5 0.0 0.0 0.0 0.0 300 3.20 102 0.185 0.6231 4.7 4.5 0.9 0.3 0.2 0.7 0.3 0.3 0.1 0.5 0.0 0.0 300 5.00 102 0.118 0.5210 4.9 4.7 1.1 0.6 0.2 0.9 0.4 0.5 0.1 0.6 0.0 0.0 300 8.00 102 0.074 0.4584 5.2 4.9 1.4 1.0 0.2 1.0 0.6 0.6 0.1 0.5 0.0 0.0 300 1.30 101 0.045 0.3695 5.5 5.1 1.5 1.0 0.2 1.6 0.5 0.6 0.0 1.4 0.0 0.0 300 1.80 101 0.033 0.3330 5.8 5.2 2.2 1.5 0.9 1.2 0.9 0.8 0.3 0.3 0.0 0.0 300 4.00 101 0.015 0.1567 13.0 7.7 5.2 3.1 3.6 9.1 2.1 1.3 0.6 8.8 0.0 0.0 400 9.27 103 0.850 1.025 13.8 13.3 2.4 0.6 0.6 2.5 0.2 0.3 0.0 0.2 0.6 2.4 400 1.05 102 0.750 1.074 10.4 10.1 2.2 1.0 0.3 0.7 0.2 0.3 0.1 0.2 0.1 0.6 400 1.21 102 0.650 0.9263 10.0 9.8 1.9 0.2 0.1 0.4 0.2 0.3 0.0 0.2 0.2 0.0 400 1.61 102 0.490 0.8145 5.7 5.4 1.7 0.2 0.0 0.5 0.2 0.5 0.0 0.1 0.0 0.0 400 3.20 102 0.246 0.6305 5.2 5.0 1.0 0.6 0.0 0.8 0.6 0.6 0.0 0.0 0.0 0.0 400 5.00 102 0.157 0.5686 5.4 5.2 1.0 0.6 0.2 0.9 0.5 0.5 0.1 0.4 0.0 0.0 400 8.00 102 0.098 0.4493 5.8 5.7 1.0 0.4 0.1 0.7 0.4 0.4 0.1 0.5 0.0 0.0 400 1.30 101 0.061 0.4300 5.6 5.3 1.2 0.4 0.1 1.2 0.4 0.4 0.1 1.1 0.0 0.0 400 1.80 101 0.044 0.3375 6.2 5.8 1.7 0.8 0.7 0.9 0.7 0.6 0.2 0.2 0.0 0.0 400 4.00 101 0.020 0.1494 13.1 8.7 4.6 1.9 3.7 8.6 1.9 0.9 0.7 8.3 0.0 0.0 500 1.16 102 0.850 1.002 15.0 14.6 2.4 0.1 0.4 2.2 0.2 0.2 0.0 0.2 0.0 2.2 500 1.31 102 0.750 0.7577 13.8 13.6 2.1 0.6 0.2 0.5 0.3 0.3 0.0 0.2 0.1 0.1 500 1.51 102 0.650 0.6938 12.4 12.2 1.9 0.3 0.1 0.4 0.2 0.4 0.1 0.2 0.0 0.0 500 2.01 102 0.490 0.7395 6.7 6.5 1.7 0.1 0.0 0.4 0.1 0.4 0.0 0.1 0.0 0.0 500 3.20 102 0.308 0.6559 6.1 6.0 1.0 0.3 0.0 0.6 0.3 0.5 0.0 0.0 0.0 0.0 500 5.00 102 0.197 0.6106 6.1 5.9 1.3 0.9 0.0 1.1 0.9 0.6 0.0 0.0 0.0 0.0 500 8.00 102 0.123 0.4712 6.5 6.3 1.0 0.5 0.0 0.8 0.5 0.4 0.0 0.4 0.0 0.0 500 1.30 101 0.076 0.4112 7.7 7.5 1.4 0.6 0.1 1.2 0.6 0.5 0.0 0.9 0.0 0.0 500 1.80 101 0.055 0.3045 8.7 8.4 1.5 0.6 0.1 1.4 0.6 0.4 0.1 1.1 0.0 0.0 500 2.50 101 0.039 0.2759 8.5 8.3 1.9 0.9 0.8 1.2 0.9 0.6 0.2 0.3 0.0 0.0 500 4.00 101 0.025 0.1311 13.7 11.8 4.1 1.9 3.1 5.8 1.8 0.7 0.7 5.3 0.0 0.0 500 6.50 101 0.015 0.01698 27.9 23.0 7.0 2.8 5.9 14.3 2.8 1.4 1.0 13.9 0.0 0.0 650 1.51 102 0.850 0.8058 19.6 19.4 2.7 0.5 0.5 1.1 0.1 0.2 0.1 0.3 0.7 0.7 650 1.71 102 0.750 0.9192 14.0 13.9 2.0 0.1 0.2 0.4 0.1 0.3 0.0 0.2 0.2 0.0 650 1.97 102 0.650 0.9125 12.1 12.0 1.9 0.0 0.1 0.4 0.1 0.4 0.0 0.1 0.1 0.0 650 2.61 102 0.490 0.6085 8.0 7.8 1.8 0.5 0.0 0.5 0.2 0.4 0.0 0.1 0.0 0.0 650 5.00 102 0.256 0.4952 7.9 7.8 1.1 0.6 0.0 0.8 0.6 0.6 0.0 0.0 0.0 0.0 650 8.00 102 0.160 0.4515 7.9 7.8 1.0 0.4 0.2 0.8 0.5 0.4 0.1 0.5 0.0 0.0 650 1.30 101 0.098 0.3732 9.5 9.3 1.4 0.6 0.2 0.8 0.6 0.4 0.1 0.3 0.0 0.0 650 1.80 101 0.071 0.3397 9.7 9.5 1.5 0.5 0.2 1.1 0.6 0.5 0.0 0.9 0.0 0.0 650 2.50 101 0.051 0.2520 10.3 10.1 1.7 0.7 0.5 0.9 0.7 0.3 0.1 0.5 0.0 0.0

stat (%)

unc (%)

Eunc (%)

hunc (%)

cor (%)

E+cor (%)

+cor (%)

h+cor (%)

N+cor (%)

S+cor (%)

D+cor (%)

123

Eur. Phys. J. C (2014) 74:2814 Page 13 of 26 2814

Table 3 continued

Q2 (GeV2) x y

NC tot

(%)

stat (%)

unc (%)

Eunc (%)

hunc (%)

cor (%)

E+cor (%)

+cor (%)

h+cor (%)

N+cor (%)

S+cor (%)

D+cor (%)

650 4.00 101 0.032 0.1915 12.8 11.2 3.9 1.9 2.7 4.8 1.9 0.8 0.7 4.3 0.0 0.0 650 6.50 101 0.020 0.02382 27.6 22.4 7.8 3.7 6.4 14.0 3.5 1.1 1.2 13.5 0.0 0.0 800 1.85 102 0.850 0.2872 37.1 36.9 3.9 1.1 0.4 0.5 0.2 0.3 0.0 0.2 0.3 0.1 800 2.10 102 0.750 0.6634 19.2 19.0 2.3 0.2 0.2 0.3 0.1 0.2 0.1 0.2 0.0 0.0 800 2.42 102 0.650 0.6620 16.0 15.9 2.1 0.4 0.1 0.4 0.3 0.2 0.0 0.1 0.0 0.0 800 3.21 102 0.490 0.6172 8.8 8.6 1.8 0.6 0.0 0.4 0.3 0.3 0.0 0.1 0.0 0.0 800 5.00 102 0.315 0.4847 9.1 9.0 1.2 0.7 0.0 0.6 0.5 0.3 0.0 0.0 0.0 0.0 800 8.00 102 0.197 0.4527 9.3 9.1 1.3 0.8 0.0 0.7 0.5 0.6 0.0 0.0 0.0 0.0 800 1.30 101 0.121 0.3868 10.8 10.6 1.4 0.5 0.3 0.9 0.7 0.4 0.2 0.4 0.0 0.0 800 1.80 101 0.087 0.3642 11.0 10.9 1.5 0.2 0.1 0.8 0.4 0.3 0.0 0.6 0.0 0.0 800 2.50 101 0.063 0.2749 11.7 11.6 1.7 0.6 0.6 1.0 0.8 0.4 0.2 0.5 0.0 0.0 800 4.00 101 0.039 0.1262 16.7 15.8 3.5 1.5 2.3 3.9 1.5 0.4 0.6 3.5 0.0 0.0 800 6.50 101 0.024 0.01953 31.8 28.9 7.1 2.9 5.9 11.4 2.8 0.7 1.0 11.0 0.0 0.0

This contribution leads to a typical uncertainty on the reduced cross sections of less than 1 %.

Noise subtraction: Energy classied as noise in the LAr calorimeter is excluded from the HFS. For y < 0.19 the calorimetric energy not contained within hadronic jets is classied as noise. The uncertainty on the subtracted noise is estimated to be 5 % of the noise contribution as determined from the analysis of the HERAII Ep = 920

GeV data [5]. For y > 0.19 the noise contribution is restricted to the sum of isolated low energy calorimetric depositions. Here the residual noise contribution is assigned an uncertainty of 20 %, to accomodate differences between data and simulation.

Nominal trigger efciency: The uncertainty on the trigger efciency in the nominal analysis is determined separately for both Ep = 460 and 575 GeV data taking peri

ods. Three trigger requirements are employed: the global timing, the event timing and the calorimeter energy. The inefciency of global timing criteria to suppress out of time beam related background was continuously monitored with high precision and found to be 0.3 % and is corrected for. Finally the event timing trigger requirements were also continuously monitored in the data. After rejection of local inefcient regions the overall trigger efciency is close to 100 % and an uncertainty of 0.3 % is assigned.

High y trigger efciency: At low E e the LAr electron trigger is supplemented by the SpaCal trigger and by the

Level 3 electron trigger based on the LAr Jet Trigger and the Fast Track Trigger. The same global timing conditions as mentioned above are used in the high y triggers.The SpaCal trigger and the LAr electron trigger together with the L3 electron trigger are independent since the

SpaCal trigger is red by the backward going hadronic nal state particles. The efciency of each of these two groups of triggers is determined using events triggered by the other group as a monitor sample. In the analysis events from both groups of triggers are used. The combined efciency is calculated and is found to vary between 91 % and 97 % at E e = 3 GeV. The statistical uncertainty of

the combined efciency together with a 0.3 % uncertainty arising from the global timing conditions is adopted as uncorrelated trigger uncertainty. It varies from 0.3 % at high electron energies to 2 % at E e = 3 GeV.

Electron track-vertex efciency: The efciencies for reconstructing a track associated to the scattered lepton and for reconstructing the interaction vertex are determined simultaneously. The efciency measurement follows the procedure used in the analysis of the HERAII Ep = 920 GeV data and checked on the Ep = 460 and

575 GeV data. Three algorithms are used to determine the interaction vertex. The data and MC efciencies are compared for each contributing algorithm. The combined efciency in the nominal analysis is found to be larger than 99.5 % in the data. The residual differences between data and simulation after correction of simulation by 0.3 % dene the uncorrelated systematic uncertainty which is 0.2 % and is considered to be uncorrelated. In the high y analysis a more stringent requirement on the quality of the track associated to the scattered lepton is applied. The efciency was measured using electrons in the region of E e > 18 GeV and checked at low E e using a sample of QED Compton events. It is found to be 96 % in data with a difference of 1 % between data and simulation. This difference was corrected for and a 1 % uncorrelated uncertainty is adopted.

123

2814 Page 14 of 26 Eur. Phys. J. C (2014) 74:2814

Table 4 The NC e+ p reduced cross section

NC(x, Q2) for Ep = 575 GeV and Pe = 0 with total (tot), statistical (stat), total uncorrelated

systematic (unc) errors and two of its contributions from the electron energy error (Eunc) and the hadronic energy error (hunc). The effect of the other uncorrelated systematic errors is included in unc. In addition the correlated systematic (cor) and its contributions from a positive variation of one standard deviation of the electron energy error (E+cor), of the polar electron angle error (+cor), of the hadronic energy error (h+cor), of the error due to noise subtraction (N+cor), of the error due to background subtraction charge asymmetry (S+cor) and of the error due to variation of the cut value on the electron discriminator Dele (D+cor) are given. The overall normalisation uncertainty of 4 % is not included in the errors

Q2 (GeV2) x y

NC tot

(%)

35 6.50 104 0.848 1.303 8.6 7.1 3.8 0.5 2.7 3.1 0.2 0.5 0.2 0.6 2.7 1.2 45 8.40 104 0.848 1.413 7.2 6.0 3.4 0.4 2.2 2.0 0.2 0.4 0.1 0.5 1.6 1.1 45 9.30 104 0.760 1.235 8.2 7.7 2.6 0.5 0.7 1.4 0.2 0.6 0.1 0.3 0.7 0.9 60 1.11 103 0.848 1.259 8.0 7.1 3.2 0.3 2.0 1.8 0.1 0.4 0.1 0.5 1.5 0.8 60 1.24 103 0.760 1.411 6.4 5.8 2.3 0.7 0.6 1.3 0.4 0.5 0.0 0.2 0.6 1.0 60 1.39 103 0.680 1.268 7.5 7.2 2.0 0.5 0.2 1.1 0.2 0.6 0.0 0.2 0.5 0.7 90 1.67 103 0.848 1.310 8.6 7.9 2.9 0.3 1.7 1.7 0.2 0.4 0.1 0.4 1.4 0.8 90 1.86 103 0.760 1.326 6.9 6.5 2.1 0.3 0.5 1.1 0.1 0.5 0.0 0.3 0.3 0.9 90 2.09 103 0.680 1.316 6.2 5.8 1.9 0.5 0.2 1.0 0.2 0.6 0.0 0.2 0.2 0.7 90 2.36 103 0.600 1.342 6.4 6.0 2.0 0.8 0.1 0.8 0.2 0.8 0.0 0.2 0.1 0.0 120 2.23 103 0.848 1.374 9.0 8.4 2.7 0.3 1.5 1.4 0.2 0.4 0.1 0.4 0.6 1.1 120 2.49 103 0.760 1.173 8.0 7.7 2.0 0.6 0.4 0.8 0.3 0.3 0.0 0.2 0.3 0.6 120 2.78 103 0.680 1.161 7.2 6.9 1.9 0.4 0.2 0.6 0.1 0.4 0.0 0.2 0.2 0.3 120 3.15 103 0.600 1.115 6.8 6.5 1.8 0.4 0.1 0.7 0.3 0.6 0.0 0.2 0.3 0.0 120 3.63 103 0.520 1.185 6.0 5.7 1.8 0.5 0.1 0.8 0.4 0.7 0.0 0.2 0.1 0.0 120 4.82 103 0.392 1.074 5.5 5.1 1.6 0.5 0.0 1.0 0.3 0.9 0.0 0.2 0.0 0.0 150 2.79 103 0.848 1.291 10.8 10.3 2.6 0.3 1.2 1.8 0.1 0.3 0.1 0.4 0.8 1.5 150 3.11 103 0.760 1.171 9.8 9.5 2.0 0.3 0.4 1.0 0.2 0.5 0.1 0.3 0.5 0.6 150 3.47 103 0.680 1.324 7.9 7.6 2.3 1.3 0.2 0.6 0.1 0.5 0.0 0.2 0.3 0.2 150 3.94 103 0.600 1.244 7.2 6.9 1.8 0.2 0.1 0.6 0.2 0.5 0.0 0.1 0.2 0.0 150 4.54 103 0.520 1.041 7.1 6.8 1.8 0.3 0.1 0.7 0.3 0.6 0.0 0.2 0.2 0.0 150 6.03 103 0.392 1.020 4.0 3.6 1.4 0.7 0.0 0.8 0.5 0.6 0.0 0.1 0.0 0.0 150 8.00 103 0.295 0.9700 4.2 3.9 1.1 0.8 0.0 0.9 0.5 0.8 0.0 0.0 0.0 0.0 150 1.30 102 0.182 0.8609 5.7 5.2 1.8 1.4 0.9 1.2 0.9 0.6 0.2 0.5 0.0 0.0 150 2.00 102 0.118 0.7980 7.8 6.9 2.8 2.5 1.0 2.0 1.6 1.0 0.3 0.8 0.0 0.0 200 3.72 103 0.848 1.296 13.3 12.9 2.6 0.1 1.2 2.0 0.2 0.3 0.1 0.3 0.9 1.7 200 4.15 103 0.760 1.288 11.8 11.5 2.1 0.2 0.3 1.2 0.2 0.5 0.0 0.2 0.1 1.0 200 4.63 103 0.680 1.051 11.3 11.1 2.2 1.1 0.2 0.5 0.2 0.3 0.0 0.2 0.3 0.2 200 5.25 103 0.600 1.169 9.1 8.9 1.8 0.2 0.1 0.5 0.2 0.4 0.0 0.2 0.1 0.0 200 6.06 103 0.520 1.110 8.3 8.1 1.8 0.2 0.1 0.5 0.2 0.4 0.0 0.2 0.1 0.0 200 8.04 103 0.392 0.9625 4.8 4.6 1.3 0.4 0.0 0.8 0.3 0.7 0.0 0.1 0.1 0.0 200 1.30 102 0.242 0.8743 4.7 4.4 1.3 1.0 0.0 1.0 0.6 0.7 0.0 0.0 0.0 0.0 200 2.00 102 0.157 0.7573 5.1 4.9 0.9 0.3 0.0 0.8 0.2 0.6 0.1 0.5 0.0 0.0 200 3.20 102 0.098 0.6151 5.6 5.5 1.0 0.5 0.0 0.6 0.3 0.5 0.1 0.3 0.0 0.0 200 5.00 102 0.063 0.5041 6.5 6.4 1.2 0.6 0.5 0.8 0.4 0.6 0.2 0.1 0.0 0.0 200 8.00 102 0.039 0.4211 7.7 7.3 1.7 1.4 0.2 1.5 0.9 0.6 0.1 1.1 0.0 0.0 200 1.30 101 0.024 0.3857 7.6 7.2 1.9 1.5 0.2 1.5 0.7 0.9 0.2 0.9 0.0 0.0 200 1.80 101 0.018 0.3034 10.4 9.3 2.6 0.6 2.1 3.7 0.5 0.8 0.3 3.6 0.0 0.0 200 4.00 101 0.008 0.1910 13.2 11.0 3.7 0.7 3.1 6.3 0.5 1.2 0.4 6.1 0.0 0.0 250 4.64 103 0.848 0.8545 19.8 19.5 2.5 0.2 1.0 2.5 0.1 0.3 0.1 0.3 1.4 2.0 250 5.18 103 0.760 1.080 14.3 14.1 2.2 0.2 0.3 1.5 0.1 0.4 0.1 0.2 0.0 1.4

stat (%)

unc (%)

Eunc (%)

hunc (%)

cor (%)

E+cor (%)

+cor (%)

h+cor (%)

N+cor (%)

S+cor (%)

D+cor (%)

123

Eur. Phys. J. C (2014) 74:2814 Page 15 of 26 2814

Table 4 continued

Q2 (GeV2) x y

NC tot

(%)

250 5.79 103 0.680 0.9481 13.9 13.7 2.3 1.2 0.1 0.5 0.2 0.3 0.0 0.2 0.2 0.0 250 6.56 103 0.600 0.9475 11.6 11.5 1.8 0.2 0.1 0.5 0.1 0.4 0.0 0.2 0.1 0.0 250 7.57 103 0.520 1.018 9.8 9.6 1.8 0.2 0.1 0.6 0.2 0.5 0.0 0.2 0.1 0.0 250 1.00 102 0.392 0.9523 5.3 5.1 1.2 0.4 0.0 0.6 0.3 0.5 0.0 0.1 0.0 0.0 250 1.30 102 0.303 0.8513 5.3 5.1 1.1 0.6 0.0 0.8 0.6 0.5 0.0 0.0 0.0 0.0 250 2.00 102 0.197 0.7707 5.5 5.2 1.5 1.2 0.0 1.1 0.9 0.6 0.0 0.0 0.0 0.0 250 3.20 102 0.123 0.6210 5.9 5.7 1.4 1.0 0.3 1.0 0.4 0.6 0.0 0.6 0.0 0.0 250 5.00 102 0.079 0.5412 6.1 5.9 1.4 1.0 0.1 0.9 0.5 0.6 0.0 0.6 0.0 0.0 250 8.00 102 0.049 0.4602 6.7 6.4 1.3 0.9 0.1 1.3 0.3 0.5 0.1 1.2 0.0 0.0 250 1.30 101 0.030 0.3906 6.6 6.2 1.4 0.7 0.2 1.8 0.3 0.5 0.0 1.8 0.0 0.0 250 1.80 101 0.022 0.3514 7.8 6.9 2.5 1.5 1.5 2.5 0.7 0.6 0.4 2.3 0.0 0.0 250 4.00 101 0.010 0.1556 13.0 10.1 4.2 2.5 2.7 7.1 1.5 1.0 0.5 6.8 0.0 0.0 300 5.57 103 0.848 1.208 16.0 15.7 2.5 0.6 0.8 2.1 0.3 0.3 0.1 0.3 0.2 2.1 300 6.22 103 0.760 0.8707 18.1 18.0 2.1 0.2 0.3 1.3 0.2 0.4 0.1 0.2 0.4 1.1 300 6.95 103 0.680 0.9694 15.0 14.8 2.1 0.8 0.1 0.5 0.1 0.5 0.0 0.2 0.0 0.0 300 7.88 103 0.600 1.035 12.9 12.7 1.9 0.1 0.1 0.5 0.1 0.5 0.0 0.2 0.0 0.0 300 9.09 103 0.520 0.8632 12.1 12.0 1.8 0.3 0.1 0.6 0.3 0.5 0.0 0.1 0.0 0.0 300 1.21 102 0.392 0.9079 6.2 6.0 1.3 0.4 0.0 0.6 0.4 0.5 0.0 0.1 0.0 0.0 300 2.00 102 0.236 0.6653 6.5 6.3 1.0 0.6 0.0 0.9 0.6 0.7 0.0 0.0 0.0 0.0 300 3.20 102 0.148 0.6171 6.7 6.6 1.0 0.5 0.1 0.8 0.3 0.4 0.0 0.6 0.0 0.0 300 5.00 102 0.094 0.5364 6.9 6.8 1.2 0.8 0.0 0.9 0.5 0.6 0.1 0.5 0.0 0.0 300 8.00 102 0.059 0.4802 7.4 7.2 1.3 0.9 0.0 1.2 0.5 0.6 0.1 0.9 0.0 0.0 300 1.30 101 0.036 0.3762 7.6 7.2 1.5 1.0 0.1 1.9 0.4 0.6 0.1 1.7 0.0 0.0 300 1.80 101 0.026 0.3190 8.7 8.1 2.5 1.8 1.1 2.0 1.1 0.9 0.3 1.4 0.0 0.0 300 4.00 101 0.012 0.1469 15.5 12.0 4.8 2.8 3.4 8.6 1.7 1.1 0.6 8.4 0.0 0.0 400 7.43 103 0.848 0.8123 23.1 22.9 2.6 0.3 0.7 2.3 0.3 0.3 0.1 0.3 0.6 2.2 400 8.29 103 0.760 0.5949 23.1 23.0 2.3 0.6 0.2 0.8 0.1 0.3 0.0 0.2 0.0 0.8 400 9.27 103 0.680 1.013 16.1 16.0 2.0 0.4 0.2 0.4 0.2 0.2 0.0 0.2 0.2 0.0 400 1.05 102 0.600 0.8806 15.6 15.5 1.9 0.3 0.1 0.5 0.2 0.4 0.0 0.2 0.0 0.0 400 1.21 102 0.520 0.9991 13.0 12.9 1.9 0.1 0.1 0.5 0.2 0.4 0.0 0.1 0.0 0.0 400 1.61 102 0.392 0.8791 7.1 7.0 1.2 0.3 0.0 0.6 0.3 0.5 0.0 0.1 0.0 0.0 400 3.20 102 0.197 0.6501 7.3 7.2 1.1 0.8 0.0 1.0 0.8 0.6 0.0 0.0 0.0 0.0 400 5.00 102 0.126 0.5099 8.0 7.9 1.1 0.6 0.1 1.0 0.6 0.6 0.0 0.5 0.0 0.0 400 8.00 102 0.079 0.4452 8.6 8.5 1.1 0.6 0.1 1.1 0.6 0.6 0.1 0.7 0.0 0.0 400 1.30 101 0.049 0.3769 8.5 8.2 1.3 0.4 0.2 1.7 0.4 0.4 0.0 1.6 0.0 0.0 400 1.80 101 0.035 0.3421 8.9 8.6 2.0 1.0 1.1 1.6 0.9 0.6 0.3 1.1 0.0 0.0 400 4.00 101 0.016 0.1488 16.6 13.4 4.6 2.0 3.5 8.6 1.9 0.9 0.7 8.4 0.0 0.0 500 9.29 103 0.848 0.7285 27.8 27.6 2.7 0.3 0.5 2.1 0.0 0.1 0.1 0.2 0.4 2.1 500 1.04 102 0.760 0.7348 22.8 22.7 2.3 1.0 0.3 0.5 0.2 0.4 0.1 0.2 0.0 0.1 500 1.16 102 0.680 1.177 16.2 16.1 2.0 0.1 0.1 0.4 0.1 0.3 0.0 0.2 0.0 0.0 500 1.31 102 0.600 0.8538 17.7 17.6 1.9 0.2 0.1 0.5 0.2 0.4 0.0 0.1 0.2 0.0 500 1.51 102 0.520 1.040 14.2 14.1 1.9 0.4 0.1 0.4 0.3 0.3 0.0 0.1 0.0 0.0 500 2.01 102 0.392 0.7340 9.1 9.0 1.3 0.4 0.0 0.6 0.4 0.4 0.0 0.1 0.0 0.0 500 3.20 102 0.246 0.6891 8.4 8.3 1.1 0.7 0.0 0.8 0.7 0.4 0.0 0.0 0.0 0.0 500 5.00 102 0.157 0.5602 8.9 8.8 1.0 0.3 0.4 0.8 0.3 0.3 0.1 0.7 0.0 0.0

stat (%)

unc (%)

Eunc (%)

hunc (%)

cor (%)

E+cor (%)

+cor (%)

h+cor (%)

N+cor (%)

S+cor (%)

D+cor (%)

123

2814 Page 16 of 26 Eur. Phys. J. C (2014) 74:2814

Table 4 continued

Q2 (GeV2) x y

NC tot

(%)

stat (%)

unc (%)

Eunc (%)

hunc (%)

cor (%)

E+cor (%)

+cor (%)

h+cor (%)

N+cor (%)

S+cor (%)

D+cor (%)

500 8.00 102 0.098 0.4454 9.8 9.7 1.0 0.5 0.2 0.7 0.5 0.3 0.1 0.3 0.0 0.0 500 1.30 101 0.061 0.3831 11.5 11.4 1.3 0.5 0.2 1.4 0.5 0.4 0.1 1.3 0.0 0.0 500 1.80 101 0.044 0.3467 11.6 11.3 1.5 0.6 0.1 1.6 0.6 0.5 0.1 1.4 0.0 0.0 500 2.50 101 0.032 0.2290 13.8 13.5 2.0 0.8 1.2 1.7 0.8 0.4 0.3 1.4 0.0 0.0 500 4.00 101 0.020 0.1687 18.1 16.3 4.2 1.8 3.2 6.7 1.8 0.6 0.7 6.3 0.0 0.0 500 6.50 101 0.012 0.02022 31.5 28.9 5.5 2.3 4.3 11.2 2.3 0.9 0.7 10.9 0.0 0.0 650 1.21 102 0.848 0.4914 38.7 38.5 3.0 0.4 0.4 1.0 0.2 0.0 0.0 0.2 0.5 0.8 650 1.35 102 0.760 0.6986 28.3 28.2 2.2 0.3 0.2 0.6 0.2 0.2 0.1 0.2 0.4 0.0 650 1.51 102 0.680 0.6789 25.2 25.1 2.1 0.2 0.1 0.5 0.1 0.3 0.0 0.2 0.3 0.0 650 1.71 102 0.600 0.6957 21.4 21.3 2.0 0.3 0.1 0.5 0.2 0.4 0.0 0.1 0.0 0.0 650 1.97 102 0.520 0.4817 22.7 22.6 2.0 0.6 0.1 0.6 0.4 0.4 0.0 0.1 0.0 0.0 650 2.61 102 0.392 0.6348 10.8 10.7 1.3 0.4 0.0 0.5 0.2 0.5 0.0 0.1 0.0 0.0 650 5.00 102 0.205 0.4685 11.7 11.6 1.3 0.9 0.0 1.0 0.8 0.6 0.0 0.0 0.0 0.0 650 8.00 102 0.128 0.4525 11.4 11.3 1.1 0.5 0.0 0.9 0.6 0.4 0.1 0.5 0.0 0.0 650 1.30 101 0.079 0.3975 13.4 13.3 1.4 0.6 0.0 1.2 0.6 0.5 0.0 0.9 0.0 0.0 650 1.80 101 0.057 0.3285 14.0 13.9 1.4 0.3 0.2 1.4 0.4 0.2 0.0 1.4 0.0 0.0 650 2.50 101 0.041 0.2401 15.5 15.3 2.0 1.0 0.9 1.3 1.0 0.6 0.3 0.6 0.0 0.0 650 4.00 101 0.026 0.1563 20.4 18.9 4.5 2.1 3.3 6.2 2.2 0.9 0.9 5.7 0.0 0.0 650 6.50 101 0.016 0.02266 35.8 33.3 6.0 2.3 4.9 11.4 2.2 0.9 0.8 11.1 0.0 0.0 800 1.49 102 0.848 0.6679 31.9 31.8 3.1 0.9 0.4 0.5 0.4 0.2 0.1 0.2 0.0 0.1 800 1.66 102 0.760 0.4843 38.5 38.4 2.7 0.6 0.2 0.7 0.6 0.3 0.1 0.3 0.0 0.0 800 1.85 102 0.680 0.6761 27.1 27.0 2.2 0.2 0.1 0.4 0.2 0.3 0.0 0.1 0.0 0.0 800 2.10 102 0.600 0.6604 24.5 24.4 2.1 0.1 0.1 0.5 0.1 0.5 0.0 0.1 0.0 0.0 800 2.42 102 0.520 0.6435 21.9 21.8 1.9 0.1 0.0 0.6 0.0 0.6 0.0 0.1 0.0 0.0 800 3.21 102 0.392 0.4923 13.6 13.5 1.4 0.5 0.0 0.4 0.3 0.3 0.0 0.1 0.0 0.0 800 5.00 102 0.252 0.5837 12.0 11.9 1.2 0.7 0.0 0.8 0.6 0.6 0.0 0.0 0.0 0.0 800 8.00 102 0.157 0.5522 12.0 12.0 1.1 0.4 0.1 0.8 0.6 0.4 0.1 0.3 0.0 0.0 800 1.30 101 0.097 0.2926 18.3 18.3 1.3 0.1 0.1 0.7 0.4 0.2 0.1 0.6 0.0 0.0 800 1.80 101 0.070 0.2636 18.7 18.6 1.5 0.5 0.1 1.5 0.7 0.5 0.0 1.2 0.0 0.0 800 2.50 101 0.050 0.1811 20.5 20.4 1.9 0.8 0.8 1.3 1.1 0.5 0.2 0.5 0.0 0.0 800 4.00 101 0.032 0.1614 22.2 21.3 3.8 1.5 2.7 4.9 1.5 0.4 0.5 4.6 0.0 0.0 800 6.50 101 0.019 0.02134 43.1 40.8 6.7 2.6 5.4 12.1 2.7 0.6 1.1 11.8 0.0 0.0

Electron charge identication efciency: In the high y analysis the efciency for correct charge identication of the scattered lepton is measured in the region E e > 18 GeV which is free from photoproduction background. The simulation describes the efciency of the data with an overall difference of 0.5 %, and no signi-cant time dependence is observed. This is validated using ISR events in which the incoming beam positron has reduced energy due to QED radiation, yielding a sample of events which is free from photoproduction background but has E e below 12 GeV. The measured cross section is corrected for the overall difference by increas-

ing the measured values by 20.5 % with an uncertainty

of 20.25 %. The factor of two accounts for the fact that

charge misidentication has a dual inuence on the measurement by causing both a loss of signal events and an increase of the subtracted background [53].

Electron identication: A calorimetric algorithm based on longitudinal and transverse shower shape quantities is used to identify electrons in the Ep = 460 and 575 GeV

data sample. The efciency of this selection can be estimated using a simple track based electron nder which searches for an isolated high pT track associated to an electromagnetic energy deposition. The efciency is

123

Eur. Phys. J. C (2014) 74:2814 Page 17 of 26 2814

well described by the simulation and the uncertainty of 0.2 % (0.5 %) is assigned in the nominal (high y) analysis at zimp < 20 cm. For zimp > 20 cm the uncertainty is taken to be 1 % due to the lack of statistics in this region selected by the track based algorithm.

Extra background suppression: The uncertainty on the efciency of the Dele requirement has been studied with

J/ ee decays in data and is well described by the

simulation. A variation of 0.04 around the nominal Dele

cut value accommodates any residual difference between data and simulation. This variation leads to a cross section uncertainty of up to 2 % at highest y.

High y background subtraction: In the high y analysis the photoproduction background asymmetry is measured in the Ep = 460 and 575 GeV data, and found to be con

sistent with the determination using the Ep = 920 GeV

data [5,53], albeit with reduced precision. Therefore the asymmetry is taken from the analysis of the HERAII data at Ep = 920 GeV and the associated uncertainty is

increased to 0.08. The resulting uncertainty on the measured cross sections is at most 2.7 % at y = 0.85 and

Q2 = 35 GeV2.

QED radiative corrections: An error on the cross sections originating from the QED radiative corrections is taken into account. This is determined by comparing the predicted radiative corrections from the programs Hera-cles (as implemented in Djangoh), Hector, and Eprc.The radiative corrections due to the exchange of two or more photons between the lepton and the quark lines, which are not included in Djangoh, vary with the polarity of the lepton beam. This variation, estimated using Eprc, is found to be small compared to the quoted errors and is neglected [53].

Model uncertainty of acceptance correction: The MC simulation is used to determine the acceptance correction to the data and relies on a specic choice of PDFs. The assigned uncertainty is listed in Table 2.

Luminosity: The integrated luminosity is measured using the Bethe-Heitler process ep ep with an

uncertainty of 4 %, of which 0.5 % is from the uncertainty in the theoretical calculation of this QED process.

5 Results

5.1 Double differential cross sections

The reduced cross sections

[bracketleftBig][parenleftbig]

F2,i f (yi)FL,i[parenrightbig][summationtext]

j i,j bj i[bracketrightBig]2 2i +[summationdisplay]

j

b2j,

(6)

where f (y) = y2/(1 + (1 y)2) and i is the mea

sured reduced cross section at an x, Q2 point i with a combined statistical and uncorrelated systematic uncertainty

i = [radicalbigg][parenleftBig]

2i,stat + 2i,syst[parenrightBig]

NC(x, Q2) for Pe = 0 are mea

sured in the kinematic range 35 Q2 800 GeV2 and

0.00065 x 0.65 at two different centre-of-mass ener

gies and are referred to as the LAr data. The data are presented in Tables 3, 4 and shown in Fig. 4. The gure also includes previously published H1 data [3] in the Q2 range of the new

data reported here, and are referred to as the SpaCal data. The published 920 GeV e+ p LAr data [5] are scaled by a normal-isation factor of 1.018 [33]. This correction factor arises from an error in the Compton generator used in the determination of the integrated luminosity of the HERA-II 920 GeV data set. The new LAr data provide additional low x measurements for Q2 35 GeV2 (from the Ep = 460 and 575 GeV

data sets). The data are compared to the H1PDF2012 t [5] which provides a good description of the data.

5.2 Measurement of FFFLLL

According to Eq. 1 it is straightforward to determine FL by a linear t as a function of y2/(1+(1y)2) to the reduced cross

section measured at given values of x and Q2 but at different centre-of-mass energies. An example of this procedure is shown in Fig. 5 for six different values of x at Q2 = 60 GeV2.

This method however does not optimally account for correlations across all measurements, and therefore an alternative procedure is applied.

The structure functions FL and F2 are simultaneously determined from the cross section measurements at Ep =

460, 575 and 920 GeV using a 2 minimisation technique as employed in [3]. In this approach the values of FL and F2 at each measured x, Q2 point are free parameters of the t. For Q2 800 GeV2 the inuence of the x F3 structure func

tion is predicted to be small and is neglected. In addition, a set of nuisance parameters bj for each correlated systematic error source j is introduced. The minimisation is performed using the new measurements presented here as well as previously published data from H1 [3,5]. The 2 function for the minimisation is

2 FL,i, F2,i, bj

[parenrightbig]

= [summationdisplay]

i

. The effect of correlated error

sources j on the cross section measurements is given by the systematic error matrix i,j . The correlations of systematic uncertainties between the SpaCal data sets at different energies are taken from [3]. The systematic uncertainties of the LAr measurements are taken to be 100 % correlated among the 460, 575 and 920 GeV data sets. There is no correlation between LAr and SpaCal measurements except for a common integrated luminosity normalisation of the LAr and SpaCal data at Ep = 460 and 575 GeV. For low y 0.35,

123

2814 Page 18 of 26 Eur. Phys. J. C (2014) 74:2814

Fig. 4 The reduced cross section

NC(x, Q2) + 0.3i

measured at three proton beam energies Ep = 460 GeV

(diamonds, i = 0), 575 GeV

(squares, i = 1) and 920 GeV

(circles, i = 2). The previously

published H1 SpaCal data are shown by the open symbols. The solid symbols are the H1 LAr data. The new measurements reported here correspond to the lled diamonds and squares.The inner error bars represent the statistical errors, the full error bars include the statistical and systematic uncertainties added in quadrature, excluding the normalisation uncertainty.The curves represent the prediction from the H1PDF2012 NLO QCD t

H1 Collaboration

2 = 35 GeV

Q

2

2 = 45 GeV

Q

2

2 = 60 GeV

Q

2

2 = 90 GeV

Q

2

2

0

1.5

1

0.5

0

2

1.5

1

0.5

+ 0.3 i

NC

2 = 300 GeV

Q

2

2 = 400 GeV

Q

2

2 = 500 GeV

Q

2

2 = 650 GeV

Q

2

2

1.5

1

0.5

0

2 = 800 GeV

Q

2

-3 10 -1

10

-3 10 -1

10

-3 10 -1

10

2

x x x

1.5

E = 575 GeV (i=1)

p

E = 920 GeV (i=2)

p

E

p

= 460 GeV (i=0)

1

+ p, LAr

H1 NC e

+ p, SpaCal

H1 NC e

H1PDF 2012

0.5

+ p, LAr

H1 NC e

+ p, SpaCal

H1 NC e

H1PDF 2012

+ p, LAr

H1 NC e

+ p, SpaCal

H1 NC e

H1PDF 2012

0 -3 10 -1

10

x

H1 Collaboration

Fig. 5 The reduced cross section

NC(x, Q2) as a function of y2/(1 + (1 y)2)

for six values of x atQ2 = 60 GeV2, measured for

proton beam energies ofEp = 920, 575 and 460 GeV.

The inner error bars denote the statistical error, the outer error bars show statistical and systematic uncertainties added in quadrature. The luminosity uncertainty is not included in the error bars. The negative slopes of the linear ts (solid line) which were performed using total errors, illustrate the non-vanishing values of the structure function FL(x, Q2)

1.7

Q2= 60 GeV2, x=0.00111

Q2= 60 GeV2, x=0.00124

Q2= 60 GeV2, x=0.00139

1.6

1.5

1.4

1.3

1.2

1.1

1

NC

0.9

~ 1.7

Q2= 60 GeV2, x=0.00158

Ep = 920 GeV H1, SpaCal

Q2= 60 GeV2, x=0.00182

Ep = 575 GeV

H1, LAr H1, SpaCal

1.5

Q2= 60 GeV2, x=0.00242

Ep = 460 GeV

H1, LAr H1, SpaCal

Linear fit

1.6

1.4

1.3

1.2

1.1

1

0.9

0 0.5 0 0.5 0 0.5 1

y2/(1+(1-y)2)

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Eur. Phys. J. C (2014) 74:2814 Page 19 of 26 2814

Table 5 The proton structure functions FL and F2 measured at the given values of Q2 and x without model assumptions. stat FL, uncor FL, cor FL and tot FL are the statistical, uncorrelated systematic, correlated systematic, and total uncertainty onFL respectively. stat F2, uncor F2, cor F2 and tot F2 are the statistical, uncorrelated systematic and total uncertainty on F2, respectively. The correlation coefcient between the FL and F2 values, , is also given

Q2 (GeV2) x FL stat FL uncor FL cor FL tot FL F2 stat F2 uncor F2 cor F2 tot F2

1.5 0.279 104 0.088 0.113 0.186 0.053 0.224 0.732 0.066 0.096 0.028 0.120 0.882 2.0 0.372 104 0.110 0.069 0.131 0.062 0.160 0.843 0.028 0.051 0.032 0.066 0.855 2.0 0.415 104 0.437 0.110 0.181 0.071 0.223 0.904 0.039 0.060 0.030 0.078 0.852 2.0 0.464 104 0.043 0.052 0.104 0.033 0.121 0.740 0.033 0.052 0.009 0.062 0.822 2.5 0.465 104 0.013 0.057 0.120 0.046 0.141 0.846 0.022 0.045 0.016 0.053 0.856 2.5 0.519 104 0.103 0.062 0.129 0.042 0.149 0.897 0.023 0.045 0.016 0.053 0.860 2.5 0.580 104 0.174 0.047 0.090 0.058 0.117 0.889 0.021 0.034 0.028 0.049 0.821 2.5 0.658 104 0.169 0.043 0.099 0.063 0.125 0.865 0.019 0.035 0.031 0.050 0.840 2.5 0.759 104 0.413 0.096 0.155 0.079 0.198 0.877 0.024 0.035 0.026 0.050 0.783 3.5 0.651 104 0.130 0.065 0.135 0.052 0.158 0.973 0.025 0.050 0.022 0.060 0.846 3.5 0.727 104 0.199 0.061 0.133 0.044 0.152 0.989 0.024 0.047 0.021 0.057 0.850 3.5 0.812 104 0.253 0.044 0.094 0.041 0.112 0.981 0.019 0.036 0.016 0.044 0.811 3.5 0.921 104 0.230 0.037 0.099 0.037 0.112 0.968 0.015 0.033 0.014 0.039 0.816 3.5 0.106 103 0.155 0.049 0.123 0.046 0.141 0.934 0.015 0.032 0.010 0.037 0.797 3.5 0.141 103 0.665 0.112 0.221 0.123 0.276 0.937 0.011 0.028 0.012 0.032 0.735 5.0 0.931 104 0.411 0.081 0.162 0.068 0.193 1.149 0.031 0.060 0.031 0.075 0.846 5.0 0.104 103 0.344 0.065 0.142 0.044 0.163 1.072 0.027 0.052 0.024 0.063 0.859 5.0 0.116 103 0.258 0.048 0.108 0.049 0.128 1.127 0.021 0.042 0.018 0.050 0.828 5.0 0.131 103 0.306 0.037 0.109 0.041 0.122 1.082 0.016 0.037 0.017 0.044 0.830 5.0 0.152 103 0.224 0.044 0.134 0.045 0.148 1.060 0.014 0.034 0.015 0.040 0.834 5.0 0.201 103 0.533 0.057 0.203 0.084 0.227 1.018 0.008 0.028 0.012 0.032 0.809 6.5 0.121 103 0.435 0.096 0.179 0.077 0.218 1.215 0.037 0.066 0.027 0.080 0.853 6.5 0.135 103 0.199 0.071 0.151 0.042 0.172 1.103 0.030 0.055 0.020 0.066 0.862 6.5 0.151 103 0.137 0.051 0.114 0.054 0.136 1.135 0.023 0.044 0.023 0.055 0.844 6.5 0.171 103 0.357 0.040 0.119 0.044 0.133 1.158 0.017 0.041 0.020 0.048 0.844 6.5 0.197 103 0.318 0.044 0.145 0.053 0.161 1.147 0.014 0.038 0.019 0.044 0.855 6.5 0.262 103 0.188 0.046 0.205 0.090 0.229 1.044 0.007 0.029 0.017 0.034 0.842 8.5 0.158 103 0.499 0.109 0.195 0.095 0.243 1.352 0.044 0.074 0.033 0.092 0.845 8.5 0.177 103 0.489 0.089 0.184 0.051 0.210 1.335 0.038 0.067 0.022 0.080 0.862 8.5 0.197 103 0.271 0.057 0.123 0.058 0.147 1.196 0.027 0.048 0.021 0.059 0.841 8.5 0.224 103 0.242 0.045 0.125 0.042 0.139 1.158 0.019 0.043 0.017 0.050 0.849 8.5 0.258 103 0.123 0.045 0.140 0.051 0.156 1.038 0.015 0.036 0.016 0.042 0.853 8.5 0.342 103 0.167 0.045 0.216 0.089 0.238 1.095 0.007 0.030 0.017 0.035 0.846 12 0.223 103 0.094 0.101 0.159 0.084 0.206 1.314 0.039 0.041 0.044 0.072 0.855 12 0.249 103 0.544 0.098 0.155 0.058 0.193 1.389 0.035 0.035 0.028 0.057 0.835 12 0.278 103 0.281 0.059 0.098 0.047 0.124 1.310 0.024 0.024 0.019 0.039 0.757 12 0.316 103 0.248 0.050 0.100 0.038 0.118 1.258 0.019 0.022 0.015 0.033 0.733 12 0.364 103 0.435 0.055 0.121 0.041 0.139 1.268 0.016 0.022 0.013 0.030 0.728 12 0.483 103 0.414 0.050 0.162 0.064 0.181 1.189 0.007 0.016 0.012 0.021 0.651 15 0.279 103 0.510 0.109 0.183 0.085 0.230 1.485 0.040 0.047 0.049 0.079 0.854 15 0.312 103 0.148 0.088 0.150 0.052 0.181 1.370 0.032 0.035 0.027 0.054 0.834 15 0.348 103 0.188 0.061 0.099 0.039 0.122 1.329 0.023 0.023 0.017 0.036 0.748 15 0.395 103 0.419 0.051 0.100 0.036 0.118 1.321 0.017 0.021 0.015 0.031 0.710 15 0.455 103 0.257 0.062 0.117 0.045 0.140 1.269 0.015 0.018 0.013 0.027 0.693

123

2814 Page 20 of 26 Eur. Phys. J. C (2014) 74:2814

Table 5 continued

Q2 (GeV2) x FL stat FL uncor FL cor FL tot FL F2 stat F2 uncor F2 cor F2 tot F2

15 0.604 103 0.066 0.054 0.157 0.066 0.179 1.180 0.007 0.014 0.012 0.019 0.620 20 0.372 103 0.216 0.116 0.197 0.065 0.238 1.452 0.041 0.051 0.033 0.073 0.877 20 0.415 103 0.322 0.092 0.158 0.044 0.188 1.424 0.032 0.037 0.021 0.054 0.837 20 0.464 103 0.412 0.070 0.108 0.037 0.134 1.396 0.024 0.025 0.015 0.037 0.752 20 0.526 103 0.358 0.052 0.103 0.037 0.121 1.354 0.018 0.021 0.015 0.032 0.708 20 0.607 103 0.304 0.062 0.119 0.041 0.140 1.295 0.015 0.019 0.013 0.027 0.693 20 0.805 103 0.212 0.060 0.163 0.068 0.186 1.222 0.007 0.014 0.012 0.019 0.608 25 0.493 103 0.363 0.072 0.157 0.043 0.178 1.484 0.022 0.040 0.024 0.052 0.851 25 0.616 103 0.284 0.043 0.089 0.031 0.103 1.382 0.013 0.021 0.014 0.028 0.698 25 0.759 103 0.296 0.065 0.124 0.042 0.146 1.330 0.015 0.020 0.013 0.028 0.700 25 0.101 102 0.168 0.064 0.167 0.068 0.191 1.236 0.007 0.014 0.012 0.020 0.616 35 0.651 103 0.453 0.124 0.214 0.091 0.264 1.612 0.043 0.058 0.030 0.078 0.889 35 0.727 103 0.041 0.144 0.232 0.065 0.281 1.419 0.038 0.048 0.020 0.065 0.884 35 0.812 103 0.106 0.075 0.107 0.054 0.142 1.411 0.026 0.027 0.019 0.042 0.753 35 0.921 103 0.436 0.080 0.125 0.040 0.153 1.405 0.022 0.024 0.014 0.035 0.727 35 0.106 102 0.196 0.072 0.130 0.042 0.155 1.325 0.017 0.021 0.012 0.030 0.698 35 0.141 102 0.057 0.067 0.170 0.065 0.194 1.226 0.008 0.015 0.011 0.021 0.639 45 0.837 103 0.179 0.117 0.188 0.061 0.230 1.518 0.042 0.054 0.022 0.072 0.875 45 0.934 103 0.516 0.167 0.238 0.058 0.296 1.517 0.043 0.052 0.022 0.071 0.869 45 0.104 102 0.366 0.084 0.107 0.054 0.146 1.430 0.029 0.027 0.016 0.042 0.731 45 0.118 102 0.396 0.108 0.118 0.042 0.165 1.395 0.025 0.025 0.014 0.038 0.732 45 0.137 102 0.255 0.100 0.151 0.047 0.187 1.350 0.021 0.023 0.013 0.034 0.729 45 0.181 102 0.099 0.075 0.175 0.065 0.202 1.210 0.009 0.016 0.011 0.021 0.659 60 0.112 102 0.282 0.146 0.179 0.051 0.237 1.446 0.058 0.058 0.021 0.084 0.851 60 0.125 102 0.279 0.165 0.198 0.055 0.263 1.548 0.048 0.050 0.018 0.072 0.844 60 0.139 102 0.383 0.095 0.105 0.049 0.150 1.450 0.033 0.030 0.016 0.047 0.731 60 0.158 102 0.464 0.102 0.101 0.047 0.151 1.369 0.027 0.024 0.014 0.039 0.711 60 0.182 102 0.159 0.230 0.320 0.047 0.397 1.288 0.028 0.033 0.012 0.045 0.818 60 0.242 102 0.044 0.094 0.185 0.069 0.218 1.186 0.011 0.016 0.011 0.023 0.683 90 0.187 102 0.041 0.222 0.207 0.045 0.307 1.330 0.095 0.077 0.017 0.123 0.862 90 0.209 102 0.060 0.109 0.119 0.041 0.166 1.313 0.051 0.045 0.014 0.069 0.801 90 0.237 102 0.007 0.109 0.101 0.040 0.154 1.218 0.037 0.029 0.012 0.048 0.769 90 0.273 102 0.447 0.143 0.135 0.048 0.202 1.325 0.031 0.027 0.013 0.043 0.717 90 0.362 102 0.163 0.167 0.233 0.058 0.293 1.145 0.015 0.017 0.011 0.025 0.699 120 0.220 102 0.070 0.067 0.241 0.041 0.253 1.400 0.019 0.060 0.027 0.069 0.908 120 0.250 102 0.450 0.096 0.252 0.037 0.272 1.414 0.022 0.051 0.025 0.061 0.875 120 0.280 102 0.136 0.094 0.103 0.036 0.144 1.299 0.022 0.025 0.021 0.039 0.711 120 0.320 102 0.073 0.175 0.342 0.032 0.385 1.129 0.103 0.146 0.018 0.179 0.963 120 0.360 102 0.480 0.178 0.234 0.039 0.296 1.245 0.062 0.063 0.012 0.089 0.886 120 0.480 102 0.152 0.166 0.212 0.071 0.278 1.069 0.024 0.024 0.010 0.035 0.762 150 0.280 102 0.123 0.083 0.270 0.046 0.286 1.357 0.024 0.065 0.025 0.074 0.931 150 0.310 102 0.306 0.099 0.290 0.035 0.308 1.330 0.022 0.056 0.023 0.065 0.904 150 0.350 102 0.038 0.085 0.127 0.038 0.157 1.274 0.017 0.027 0.021 0.038 0.728 150 0.390 102 0.401 0.095 0.124 0.029 0.159 1.266 0.015 0.022 0.020 0.033 0.675 150 0.450 102 0.554 0.114 0.153 0.038 0.195 1.209 0.014 0.023 0.020 0.034 0.668 150 0.600 102 0.137 0.118 0.194 0.060 0.235 1.069 0.009 0.020 0.018 0.028 0.677

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Eur. Phys. J. C (2014) 74:2814 Page 21 of 26 2814

Table 5 continued

Q2 (GeV2) x FL stat FL uncor FL cor FL tot FL F2 stat F2 uncor F2 cor F2 tot F2

200 0.370 102 0.039 0.110 0.305 0.044 0.327 1.231 0.033 0.072 0.023 0.083 0.944 200 0.410 102 0.157 0.141 0.321 0.033 0.352 1.160 0.032 0.059 0.020 0.070 0.929 200 0.460 102 0.146 0.115 0.131 0.038 0.179 1.188 0.023 0.025 0.019 0.039 0.758 200 0.520 102 0.184 0.126 0.138 0.033 0.189 1.136 0.019 0.022 0.019 0.035 0.719 200 0.610 102 0.253 0.141 0.169 0.033 0.223 1.107 0.016 0.021 0.018 0.032 0.690 200 0.800 102 0.228 0.126 0.203 0.057 0.246 0.995 0.008 0.018 0.017 0.026 0.654 250 0.460 102 0.620 0.136 0.365 0.052 0.393 1.340 0.041 0.086 0.025 0.099 0.950 250 0.520 102 0.214 0.159 0.349 0.039 0.385 1.186 0.037 0.065 0.020 0.077 0.931 250 0.580 102 0.243 0.130 0.142 0.038 0.196 1.176 0.026 0.027 0.019 0.041 0.770 250 0.660 102 0.163 0.145 0.146 0.030 0.208 1.087 0.022 0.022 0.016 0.035 0.742 250 0.760 102 0.117 0.159 0.173 0.031 0.237 0.998 0.018 0.020 0.016 0.032 0.714 250 0.100 101 0.105 0.139 0.197 0.050 0.246 0.914 0.008 0.015 0.015 0.023 0.650 250 0.130 101 0.140 0.228 0.280 0.095 0.374 0.842 0.008 0.014 0.014 0.021 0.650 300 0.560 102 0.038 0.161 0.316 0.041 0.357 1.138 0.048 0.075 0.021 0.091 0.942 300 0.690 102 0.345 0.151 0.149 0.039 0.216 1.118 0.030 0.028 0.019 0.045 0.781 300 0.790 102 0.377 0.168 0.148 0.027 0.225 1.058 0.025 0.022 0.016 0.037 0.752 300 0.910 102 0.349 0.193 0.176 0.028 0.263 0.967 0.021 0.019 0.015 0.033 0.734 300 0.121 101 0.324 0.157 0.200 0.047 0.258 0.839 0.009 0.014 0.014 0.022 0.663 400 0.930 102 0.093 0.164 0.135 0.033 0.215 0.950 0.033 0.025 0.015 0.044 0.790 400 0.105 101 0.199 0.180 0.131 0.020 0.223 0.923 0.028 0.019 0.014 0.037 0.760 400 0.121 101 0.051 0.207 0.179 0.027 0.275 0.913 0.023 0.021 0.015 0.034 0.736 400 0.161 101 0.180 0.182 0.202 0.043 0.276 0.788 0.011 0.013 0.012 0.021 0.680 500 0.116 101 0.255 0.184 0.119 0.028 0.221 0.868 0.037 0.022 0.014 0.046 0.790 500 0.131 101 0.340 0.207 0.143 0.019 0.252 0.946 0.033 0.022 0.015 0.042 0.755 500 0.152 101 0.279 0.244 0.149 0.021 0.287 0.860 0.028 0.017 0.012 0.035 0.742 500 0.201 101 0.192 0.214 0.211 0.043 0.304 0.770 0.013 0.014 0.013 0.023 0.691 650 0.151 101 0.229 0.219 0.145 0.018 0.263 0.917 0.043 0.026 0.013 0.052 0.804 650 0.171 101 0.229 0.209 0.132 0.016 0.248 0.743 0.033 0.021 0.012 0.041 0.769 650 0.197 101 0.204 0.254 0.148 0.019 0.294 0.735 0.030 0.017 0.011 0.036 0.750 650 0.261 101 0.651 0.244 0.201 0.036 0.318 0.739 0.016 0.014 0.012 0.024 0.698 800 0.185 101 0.625 0.228 0.158 0.014 0.278 0.821 0.045 0.028 0.013 0.054 0.812 800 0.210 101 0.205 0.230 0.167 0.015 0.285 0.762 0.036 0.026 0.012 0.046 0.774 800 0.242 101 0.123 0.281 0.148 0.016 0.318 0.698 0.033 0.017 0.010 0.039 0.753 800 0.322 101 0.276 0.253 0.202 0.031 0.325 0.642 0.016 0.014 0.010 0.023 0.714

the coefcient f (y) is small compared to unity and thus FL can not be accurately measured. To avoid unphysical values for FL in this kinematic region the 2 function is modied by adding an extra prior [3]. The minimisation of the 2 function with respect to these variables leads to a system of linear equations which is solved analytically. This technique is identical to the linear t discussed above when considering a single x, Q2 bin and neglecting correlations between the cross section measurements.

The 2 per degree of freedom is found to be 184/210. The systematic sources include normalisation uncertainties

for the SpaCal and LAr data sets for Ep = 460, 575 and

920 GeV data which are all shifted in the minimisation procedure by less than one standard deviation with the exception of the LAr 920 GeV data which are re-normalised by +3.4 %,

or 1.2 standard deviations. All other sources of uncertainty including those related to calibration scales, noise subtractions, background estimates and polar angle measurements are shifted by typically less than 0.3 and never more than 0.8 standard deviations.

The measured structure functions are given in Table 5 over the full range in Q2 from 1.5 to 800 GeV2. Only

123

2814 Page 22 of 26 Eur. Phys. J. C (2014) 74:2814

measurements of FL with a total uncertainty less than 0.3 for Q2 25 GeV2, or total uncertainty less than 0.4 for

Q2 35 GeV2 are considered. The table also includes

the correlation coefcient between the F2 and FL values. In Figs. 6 and 7 the measured structure functions F2 and FL are shown in the regions 2 Q2 25 GeV2 and

Q2 35 GeV2 respectively. The new data reported here, in

which the scattered electron is recorded in the LAr calorimeter, provide small additional constraints on the FL measurement for 1.5 Q2 25 GeV2 by means of correlations

in the systematic uncertainties. The SpaCal and LAr data are used together for 35 Q2 90 GeV2 . For Q2 120 GeV2

FL is determined exclusively from the LAr cross section measurements. Therefore these data supersede the previous measurements of F2 and FL in [2,3]. For precision analyses of

H1 data it is recommended to use the published tables of the reduced differential cross sections given in Tables 3, 4 and the full breakdown of systematic uncertainties instead of the derived quantities F2 or FL.

This measurement of FL and F2 at high y constitutes a model independent method with no assumptions made on the values of the structure functions. Within uncertainties the FL structure function is observed to be positive everywhere and approximately equal to 20 % of F2. Also shown are the FL and F2 measurements from the ZEUS collaboration [4] which agree with the H1 data. The ZEUS data are moved to the Q2 values of the H1 measurements using the H1PDF2012 NLO QCD t. This QCD t is able to provide a

good description of both measurements of FL and F2 across the full Q2 range.

In order to reduce the experimental uncertainties the FL measurements are combined at each Q2 value. Furthermore the highest Q2 bins are also averaged to achieve an approximately uniform experimental precision over the full kinematic range of the measurement. The Q2 averaging is performed for Q2 = 300 and 400 GeV2, and for the Q2 =

500, 600 and 800 GeV2 values. The resulting data are given in Table 6 and shown in Fig. 8 where the average x for each Q2 is provided on the upper scale of the gure. The data are compared to a suite of QCD predictions at NNLO: HERAPDF1.5 [65], CT10 [66], ABM11 [67], MSTW2008 [68], JR09 [69,70] and NNPDF2.3 [71,72]. In all cases the perturbative calculations provide a reasonable description of the data.

A similar average of FL measurements over x has already been performed in [3] for Q2 < 45 GeV2. A small problem in [3] has been identied in the averaging procedure which lead to underestimated correlated systematic uncertainties which has been corrected in the measurements reported here. Therefore the data presented in Table 6 supersedes the corresponding Table from [3].

The cross section ratio R of longitudinally to transversely polarised virtual photons is related to the structure functions F2 and FL as

R =

LT =

FL F2 FL

. (7)

Fig. 6 The proton structure functions FL(x, Q2) (solid symbols) and F2(x, Q2) (open symbols) measured by H1 (circles) and ZEUS (diamonds) in the region 2 Q2 25 GeV2. Only the F2(x, Q2)

measurements obtained in the determinations of FL by H1 and

ZEUS are shown. The inner error bars represent the statistical uncertainties, the full error bars include the statistical and systematic uncertainties added in quadrature, including all correlated and uncorrelated uncertainties. The curves represent the prediction from the H1PDF2012 NLO QCD t

H1 Collaboration

2 = 2.0 GeV

Q

2

2 = 2.5 GeV

Q

2

2 = 3.5 GeV

Q

2

2 = 5.0 GeV

Q

2

1.5

1

0.5

0

2 = 6.5 GeV

Q

2

2 = 8.5 GeV

Q

2

2 = 12 GeV

Q

2

2 = 15 GeV

Q

2

1.5

L

, F

2

F

1

0.5

0

2 = 20 GeV

Q

2

2 = 25 GeV

Q

2

-4

-3

10 -4

10

-3

10

1.5

10 x x

1

F

H1

H1

F

ZEUS

ZEUS

F

H1PDF 2012

H1PDF 2012

2

2

2

0.5

F

F

F

L

L

L

0

-4

-3

10 -4

10

10

-3

10 x x

123

Eur. Phys. J. C (2014) 74:2814 Page 23 of 26 2814

Fig. 7 The proton structure functions FL(x, Q2) (solid symbols) and F2(x, Q2) (open symbols) measured by H1 (circles) and ZEUS (diamonds) in the region 35 Q2

800 GeV2. Only the F2(x, Q2) measurements obtained in the determinations of FL by H1 and

ZEUS are shown. The inner error bars represent the statistical uncertainties, the full error bars include the statistical and systematic uncertainties added in quadrature, including all correlated and uncorrelated uncertainties. The curves represent the prediction from the H1PDF2012 NLO QCD t

H1 Collaboration

2 = 35 GeV

Q

2

2 = 45 GeV

Q

2

2 = 60 GeV

Q

2

2 = 90 GeV

Q

2

1.5

0

1

0.5

0

2 = 120 GeV

Q

2

2 = 150 GeV

Q

2

2 = 200 GeV

Q

2

2 = 250 GeV

Q

2

1.5

1

0.5

L

, F

2

F

2 = 300 GeV

Q

2

2 = 400 GeV

Q

2

2 = 500 GeV

Q

2

2 = 650 GeV

Q

2

1.5

0

1

0.5

0

2 = 800 GeV

Q

2

-3

10 -2

10

-3

10 -2

10

-3

10 -2

10

1.5

x x x

1

F

H1

H1

F

ZEUS

ZEUS

F

H1PDF 2012

H1PDF 2012

2

2

2

0.5

F

F

F

L

L

L

-3

10 -2

10

x

This ratio has previously been observed to be approximately constant for 3.5 Q2 45 GeV2 [3].

The values of R as a function of Q2 are determined by minimising the 2 function of Eq. 6 in which FL is replaced by

FL =

R1 + R

F2

assuming the value of R is constant as a function of x for a given Q2. The minimum is found numerically in this case, using the MINUIT package [73]. The asymmetric uncertainties are determined using a MC method in which the mean squared deviation from the measured value of R is used to dene the asymmetric uncertainties. The resulting value of R(Q2) is shown in Fig. 9. The measurements are compared to the prediction of the HERAPDF1.5 NNLO for s = 225 GeV and y = 0.7. The expected small variation

of R in the region of x in which the data are sensitive to this quantity is also shown.

The data are found to be consistent with a constant value across the entire Q2 range shown. The t is repeated by assuming that R is constant over the full Q2 range. This yields a value of R = 0.23 0.04 with 2/ndf =314/367

which agrees well with the value obtained previously [3]

using only data up to Q2 = 45 GeV2, and with the ZEUS

data [4].

In NLO and NNLO QCD analyses of precision DIS data on F2 and the reduced NC cross sections the gluon density is constrained indirectly via scaling violations. The Altarelli-Martinelli relation [6], however, would allow for a direct extraction of the gluon density from measurements of FL.

This relation cannot be solved analytically for the gluon density, but approximate solutions at order s have been proposed [7477]

xg(x, Q2) 1.77

32S(Q2) FL(ax, Q2), (8)

where a is a numerical factor and is here set to unity. This relation can be used to demonstrate sensitivity of the direct measurement of FL to the gluon density by comparing the gluon obtained from the FL measurements to the predicted gluon density obtained from a NLO QCD t to DIS data. In Fig. 10 the gluon density extracted according to Eq. 8 is compared to the prediction from the gluon density determined in the NLO HERAPDF1.5 QCD t. In order to judge on the goodness of the approximation, the gluon density as obtained by applying Eq. 8 to the FL prediction based on

123

2814 Page 24 of 26 Eur. Phys. J. C (2014) 74:2814

Table 6 The proton structure function FL(x, Q2) obtained by averaging FL data from Table 5 at the given values of Q2 and x. stat, uncor, cor and tot are the statistical, uncorrelated systematic, correlated systematic, and total uncertainty on FL, respectively

Q2 (GeV2) x FL stat uncor cor tot

1.5 0.279 104 0.088 0.113 0.186 0.053 0.224 2.0 0.427 104 0.127 0.039 0.074 0.044 0.095 2.5 0.588 104 0.156 0.025 0.050 0.053 0.077 3.5 0.877 104 0.227 0.021 0.049 0.040 0.067 5.0 0.129 103 0.314 0.022 0.055 0.045 0.074 6.5 0.169 103 0.264 0.023 0.058 0.050 0.080 8.5 0.224 103 0.216 0.025 0.062 0.051 0.084 12 0.319 103 0.324 0.026 0.051 0.044 0.072 15 0.402 103 0.266 0.027 0.051 0.042 0.071 20 0.540 103 0.327 0.029 0.053 0.040 0.072 25 0.687 103 0.282 0.029 0.061 0.037 0.077 35 0.958 103 0.213 0.035 0.059 0.040 0.080 45 0.121 102 0.303 0.043 0.060 0.044 0.086 60 0.157 102 0.315 0.051 0.060 0.044 0.090 90 0.243 102 0.125 0.061 0.062 0.039 0.095 120 0.303 102 0.198 0.054 0.077 0.029 0.098 150 0.402 102 0.264 0.044 0.068 0.035 0.088 200 0.541 102 0.150 0.056 0.073 0.034 0.099 250 0.736 102 0.196 0.061 0.075 0.033 0.102 346 0.986 102 0.039 0.059 0.057 0.029 0.087 636 0.184 101 0.152 0.066 0.045 0.020 0.082

10

x

0.28

0.43

0.59

0.88

1.29

1.69

2.24

3.19

4.02

5.40

6.87

9.58

12.1

15.7

24.3

30.3

40.2

54.1

73.6

98.6

184

1 10 100 1000

H1 Collaboration

0.5

R

0

1 10 100 1000

Q

Fig. 9 The ratio R(Q2) averaged over x in the region 1.5 Q2

800 GeV2 (solid points). The error bars represent the full errors as obtained by the Monte Carlo procedure described in the text. The ZEUS data are also shown (open symbols). The ZEUS data point at Q2 =

45 GeV2 is slightly shifted for better visibility of the erros. The solid curve represents the prediction from the HERAPDF1.5 NNLO QCD t and its uncertainty for s = 225 Gev2 and y = 0.7. The additional

dashed and dotted curves show the variations of R in the region of x where the data are sensitive to this quantity

2 [GeV

2

]

H1 Collaboration

10

x

0.28

0.43

0.59

0.88

1.29

1.69

2.24

3.19

4.02

5.40

6.87

9.58

12.1

15.7

24.3

30.3

40.2

54.1

73.6

98.6

184

20

xg

10

H1 Collaboration

0.4

0

L 0.2

1 10 100 1000

Q

2 [GeV

2

]

0

Q

Fig. 8 The proton structure function FL averaged over x at different Q2 (solid points). The average value of x for each Q2 is given above each data point. The inner error bars represent the statistical uncertainties, the full error bars include the statistical and systematic uncertainties added in quadrature, including all correlated and uncorrelated uncertainties. The FL measurements by ZEUS are also shown (open points).

The data are compared to NNLO predictions from a selection of PDF sets as indicated

the NLO HERAPDF1.5 QCD t is also shown. A reasonable agreement between the gluon density as extracted from the direct measurement of FL based on the approximate relation

Fig. 10 The gluon density xg(x, Q2) averaged over x in the region 1.5 Q2 800 GeV2 (solid points). The average value of x for each

Q2 is given above each data point. The inner error bars represent the statistical uncertainties, the full error bars include the statistical and systematic uncertainties added in quadrature, including all correlated and uncorrelated uncertainties. The shaded regions represent the prediction from the HERAPDF1.5 NLO QCD t. The dashed line corresponds to xg as obtained by applying Eq. 8 to the FL prediction based on the

HERAPDF1.5 NLO QCD t

with the gluon derived indirectly from scaling violations is observed.

6 Conclusions

The unpolarised neutral current inclusive DIS cross section for ep interactions are measured at two centre-of-mass ener-

2 [GeV

2

]

123

Eur. Phys. J. C (2014) 74:2814 Page 25 of 26 2814

gies of s = 225 and 252 GeV in the region of 35 < Q2 <

800 GeV2, with integrated luminosities of 11.8 pb1 and 5.4 pb1 respectively. The measurements are performed up to the highest accessible inelasticity of y = 0.85 where the

contribution of the FL structure function to the reduced cross section is sizeable. The data are used together with previously published measurements at s = 319 GeV (Ep = 920 GeV)

to simultaneously extract the FL and F2 structure functions in a model independent way. The new data extend previous measurements of FL up to Q2 = 800 GeV2 and supersede

previous H1 data. Predictions of different perturbative QCD calculations at NNLO are compared to data. Good agreement is observed between the measurements and the theoretical calculations. The ratio R of the longitudinally to transversely polarised virtual photon cross section is consistent with being constant over the kinematic range of the data, and is determined to be 0.23 0.04. The FL measurements are

used to perform a gluon density extraction based on a NLO approximation which is found to agree reasonably well with the gluon determined from scaling violations.

Acknowledgments We are grateful to the HERA machine group whose outstanding efforts have made this experiment possible. We thank the engineers and technicians for their work in constructing and maintaining the H1 detector, our funding agencies for nancial support, the DESY technical staff for continual assistance and the DESY directorate for support and for the hospitality which they extend to the non DESY members of the collaboration. We would like to give credit to all partners contributing to the EGI computing infrastructure for their support for the H1 Collaboration. We would also like to thank the members of the MSTW, CT, ABM, JR, NNPDF and HERAPDF collaborations for their help in producing theoretical predictions of FL shown in Fig. 8.

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Funded by SCOAP3 / License Version CC BY 4.0.

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