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Published for SISSA by Springer

Received: December 4, 2014

Accepted: January 11, 2015

Published: March 18, 2015

V. Andreev,21 A. Baghdasaryan,33 K. Begzsuren,30 A. Belousov,21 V. Boudry,24G. Brandt,45 V. Brisson,23 D. Britzger,10 A. Buniatyan,2 A. Bylinkin,20,42L. Bystritskaya,20 A.J. Campbell,10 K.B. Cantun Avila,19 F. Ceccopieri,3 K. Cerny,27V. Chekelian,22 J.G. Contreras,19 J. Cvach,26 J.B. Dainton,16 K. Daum,32,37C. Diaconu,18 M. Dobre,4 V. Dodonov,10 G. Eckerlin,10 S. Egli,31 E. Elsen,10L. Favart,3 A. Fedotov,20 J. Feltesse,9 J. Ferencei,14 M. Fleischer,10 A. Fomenko,21E. Gabathuler,16 J. Gayler,10 S. Ghazaryan,10 A. Glazov,10 L. Goerlich,6N. Gogitidze,21 M. Gouzevitch,10,38 C. Grab,35 A. Grebenyuk,3 T. Greenshaw,16G. Grindhammer,22 D. Haidt,10 R.C.W. Henderson,15 M. Herbst,13 J. Hladk`y,26D. Ho mann,18 R. Horisberger,31 T. Hreus,3 F. Huber,12 M. Jacquet,23 X. Janssen,3H. Jung,10,3 M. Kapichine,8 C. Kiesling,22 M. Klein,16 C. Kleinwort,10 R. Kogler,11P. Kostka,16 J. Kretzschmar,16 K. Krger,10 M.P.J. Landon,17 W. Lange,34P. Laycock,16 A. Lebedev,21 S. Levonian,10 K. Lipka,10,41 B. List,10 J. List,10B. Lobodzinski,22 E. Malinovski,21 H.-U. Martyn,1 S.J. Maxeld,16 A. Mehta,16 A.B. Meyer,10 H. Meyer,32 J. Meyer,10 S. Mikocki,6 A. Morozov,8 K. Mller,36 Th. Naumann,34 P.R. Newman,2 C. Niebuhr,10 G. Nowak,6 J.E. Olsson,10D. Ozerov,10 P. Pahl,10 C. Pascaud,23 G.D. Patel,16 E. Perez,9,39 A. Petrukhin,10I. Picuric,25 H. Pirumov,10 D. Pitzl,10 R. Plaakyte,10,41 B. Pokorny,27 R. Polifka,27,43V. Radescu,10,41 N. Raicevic,25 T. Ravdandorj,30 P. Reimer,26 E. Rizvi,17P. Robmann,36 R. Roosen,3 A. Rostovtsev,20 M. Rotaru,4 S. Rusakov,21 D.lek,27 D.P.C. Sankey,5 M. Sauter,12 E. Sauvan,18,44 S. Schmitt,10 L. Schoe el,9A. Schning,12 H.-C. Schultz-Coulon,13 F. Sefkow,10 S. Shushkevich,10Y. Soloviev,10,21 P. Sopicki,6 D. South,10 V. Spaskov,8 A. Specka,24 M. Steder,10B. Stella,28 U. Straumann,36 T. Sykora,3,27 P.D. Thompson,2 D. Traynor,17 P. Trul,36I. Tsakov,29 B. Tseepeldorj,30,40 J. Turnau,6 A. Valkrov,27 C. Valle,18P. Van Mechelen,3 Y. Vazdik,21 D. Wegener,7 E. Wnsch,10 J.ek,27 Z. Zhang,23R.lebk,27 H. Zohrabyan33 and F. Zomer23

1I. Physikalisches Institut der RWTH, Aachen, Germany

Open Access, c

[circlecopyrt] The Authors.

Article funded by SCOAP3. doi:http://dx.doi.org/10.1007/JHEP03(2015)092

Web End =10.1007/JHEP03(2015)092

Measurement of dijet production in di ractive deep-inelastic ep scattering at HERA

JHEP03(2015)092

H1 collaboration

2School of Physics and Astronomy, University of Birmingham, Birmingham, U.K.a

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

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

5STFC, Rutherford Appleton Laboratory, Didcot, Oxfordshire, U.K.a

6Institute for Nuclear Physics, Cracow, Polandd

7Institut fr Physik, TU Dortmund, Dortmund, Germanye

8Joint Institute for Nuclear Research, Dubna, Russia

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

10DESY, Hamburg, Germany

11Institut fr Experimentalphysik, Universitat Hamburg, Hamburg, Germanye

12Physikalisches Institut, Universitat Heidelberg, Heidelberg, Germanye

13Kirchho -Institut fr Physik, Universitat Heidelberg, Heidelberg, Germanye

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

15Department of Physics, University of Lancaster, Lancaster, U.K.a

16Department of Physics, University of Liverpool, Liverpool, U.K.a

17School of Physics and Astronomy, Queen Mary, University of London, London, U.K.a

18Aix Marseille Universit, CNRS/IN2P3, CPPM UMR 7346, 13288 Marseille, France

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

20Institute for Theoretical and Experimental Physics, Moscow, Russiah

21Lebedev Physical Institute, Moscow, Russia

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

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

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

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

26Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republicj

27Faculty of Mathematics and Physics, Charles University, Praha, Czech Republicj

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

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

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

31Paul Scherrer Institut, Villigen, Switzerland

aSupported by the U.K. Science and Technology Facilities Council, and formerly by the U.K. Particle Physics and Astronomy Research Council.

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

cSupported by the Romanian National Authority for Scientic Research under the contract PN 09370101.

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

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

fSupported by VEGA SR grant no. 2/7062/ 27.

gSupported by CONACYT, Mxico, grant 48778-F.

hRussian Foundation for Basic Research (RFBR), grant no 1329.2008.2 and Rosatom.

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

jSupported by the Ministry of Education of the Czech Republic under the projects LC527, INGOLA09042 and MSM0021620859.

JHEP03(2015)092

32Fachbereich C, Universitat Wuppertal, Wuppertal, Germany

33Yerevan Physics Institute, Yerevan, Armenia

34DESY, Zeuthen, Germany

35Institut fr Teilchenphysik, ETH, Zrich, Switzerlandk

36Physik-Institut der Universitat Zrich, Zrich, Switzerlandk

37Also at Rechenzentrum, Universitat Wuppertal, Wuppertal, Germany.

38Also at IPNL, Universit Claude Bernard Lyon 1, CNRS/IN2P3, Villeurbanne, France.

39Also at CERN, Geneva, Switzerland.

40Also at Ulaanbaatar University, Ulaanbaatar, Mongolia.

41Supported by the Initiative and Networking Fund of the Helmholtz Association (HGF) under the contract VH-NG-401 and S0-072.

42Also at Moscow Institute of Physics and Technology, Moscow, Russia.

43Also at Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7.

44Also at LAPP, Universit de Savoie, CNRS/IN2P3, Annecy-le-Vieux, France.

45Department of Physics, Oxford University, Oxford, U.K.aE-mail: mailto:[email protected]

Web End [email protected]

Abstract: A measurement is presented of single- and double-di erential dijet cross sections in di ractive deep-inelastic ep scattering at HERA using data collected by the H1 experiment corresponding to an integrated luminosity of 290 pb1. The investigated phase space is spanned by the photon virtuality in the range of 4 < Q2 < 100 GeV2 and by the fractional proton longitudinal momentum loss xIP < 0.03. The resulting cross sections are compared with next-to-leading order QCD predictions based on di ractive parton distribution functions and the value of the strong coupling constant is extracted.

Keywords: Lepton-Nucleon Scattering, Di raction, Jet physics

ArXiv ePrint: 1412.0928v2

JHEP03(2015)092

kSupported by the Swiss National Science Foundation.

Contents

1 Introduction 1

2 Kinematics 2

3 Monte Carlo models and xed order QCD calculations 3

4 Experimental technique 54.1 H1 detector 54.2 Reconstruction of observables 64.3 Event selection 74.4 Corrections to the data 84.5 Systematic uncertainties 9

5 Results 10

6 Conclusions 12

1 Introduction

In deep-inelastic scattering (DIS), di ractive reactions of the type ep eXY , where

X is a high-mass hadronic nal state and Y is either the elastically scattered proton or its low-mass excitation, represent about 10% of the events at HERA and provide rich experimental input for testing quantum chromodynamics (QCD) in the di ractive regime. These processes can be understood as probing by a virtual photon emitted from the beam lepton a net colour singlet carrying vacuum quantum numbers (a pomeron) [1, 2]. Due to the colourless exchange the systems X and Y are separated by a rapidity interval free of hadronic activities. In these processes at least one hard scale is involved such that perturbative QCD (pQCD) can be applied.

According to the QCD collinear factorisation theorem [3], calculations of di ractive cross sections factorise into process dependent hard scattering coe cient functions and a set of process independent di ractive parton distribution functions (DPDFs). While the hard scattering coe cient functions are calculable in pQCD, the DPDFs have to be determined from QCD ts to the measured inclusive di ractive cross sections. In such QCD ts [4], DGLAP evolution [57] of the DPDFs is assumed. The QCD factorisation theorem is proven to hold for inclusive and dijet di ractive processes [8], assuming high enough photon virtuality such that higher twist e ects can be neglected. The DPDFs are experimentally determined by assuming an additional factorisation of the DPDFs dependence on the scattered proton momentum from the dependence on the other variables, ascribed to the structure of the colourless exchange. This assumption is known as proton vertex

JHEP03(2015)092

factorisation. A pomeron ux in the proton is introduced and universal parton densities are attributed to the di ractively exchanged object. Many measurements of di raction in DIS suggest the validity of the proton vertex factorisation assumption in DIS [4, 911].

In leading order the inclusive di ractive cross section in ep scattering is proportional to the charge-squared weighted sum of the quark distribution functions in the pomeron, while its gluon content can be determined only indirectly via scaling violations. As events with two jets (dijets) are readily produced in gluon-induced processes, measurements of di ractive dijet cross sections are sensitive to the value of the strong coupling s and to the gluon content of the pomeron. The production of dijets in di ractive DIS has previously been studied at HERA using either the large rapidity gap (LRG) method [1214] or by direct detection of the outgoing proton [15].

In this paper cross section measurements of dijet production in di ractive ep scattering are presented, based on data collected in the years 2005-2007 with the H1 detector at HERA. Di ractive events are selected by means of the LRG method, requiring a clear separation in rapidity of the nal state systems X and Y . The measured cross sections are compared to next-to-leading order (NLO) QCD predictions evaluated with input DPDFs determined in previous inclusive di ractive measurements by the H1 collaboration [4].

The present analysis is based on the full HERA-II data sample resulting in signicantly increased statistics with respect to previous analyses. Furthermore, the cross sections are determined using a regularised unfolding procedure which fully accounts for e ciencies, migrations and correlations among the measurements. The measured dijet cross sections are used to extract the strong coupling constant s in di ractive DIS processes for the rst time.

2 Kinematics

A leading order (LO) diagram of boson-gluon fusion, which is the dominant process for the production of two jets in di ractive DIS, is depicted in gure 1. The incoming electron1 of four-momentum k interacts with the incoming proton of four-momentum p via the exchange of a virtual photon of four-momentum q = k k. The outgoing proton or its

low-mass dissociation state carries four-momentum p. The DIS kinematics is described by the following set of variables:

Q2 = q2 = (k k)2, x =

Q2 2p q

JHEP03(2015)092

, y = p q

p k

, (2.1)

where Q2, x and y denote the photon virtuality, the Bjorken-x variable and the inelasticity of the process, respectively. Conservation laws stipulate the relation Q2 = xys, where s stands for the ep centre-of-mass energy squared.

The kinematics of the di ractive exchange is described in terms of the additional quantities

xIP = q (p p) q p

, t = (p p)2 (2.2)

1In this paper the term electron is used generically to refer to both electrons and positrons.

e(k)

* (q)

g(v)

Figure 1: Leading order diagram for the production of dijets in di ractive DIS.

with xIP and t being the longitudinal momentum fraction of the incoming proton carried by the pomeron and the squared four-momentum transfer at the proton vertex, respectively. The fractional longitudinal momentum of the pomeron transferred to the dijet system is given by

xIP , (2.3)

where v is the four-momentum of the parton entering the hard interaction.

3 Monte Carlo models and xed order QCD calculations

The RAPGAP event generator [16] allows for the simulation of processes ep eXY

including both leading (pomeron) and sub-leading (reggeon) exchanges. Assuming the proton vertex factorisation, the parton densities obtained in the previous QCD analysis of inclusive di ractive data (H12006 Fit-B) [4] are convoluted with leading order QCD matrix elements. Higher order QCD radiation e ects are modelled via initial and nal state parton showers in the leading-log approximation [17]. Hadronisation is accounted for by making use of the Lund string model [18] as implemented in PYTHIA [19].

Within the di ractive selection based on the LRG method, the system Y may also be a low mass dissociative system. Proton dissociation events are simulated in the the range of MY < 20 GeV using the RAPGAP event generator, where MY is the mass of the system

Y . Resonant contributions together with the continuum part of the MY distribution are modelled similarly to the DIFFVM event generator [20]. A small admixture of resolved p scattering is included in xed LO mode of jet production in the low Q2 region [21]. The resolved photon contribution is simulated with the RAPGAP event generator using the SaS-G PDF set [22] as the input PDF of the photon. QED radiation e ects are simulated with the HERACLES [23] program interfaced to RAPGAP. Besides the Born level contribution, the simulated cross sections include contributions from initial and nal

IP remnant

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p(p)

Y(p)

zIP = q vq (p p)

= x

state emission of real photons from the electron, from vertex corrections as well as from self energy diagrams. As the H12006 Fit-B DPDF set has previously been observed to underestimate the data in the low Q2 region, a weighting is applied for Q2 < 7 GeV2, parametrised as the ratio of the data in [4] to the Monte Carlo expectation based on the H12006 Fit-B DPDF set.

Background arising from non-di ractive DIS processes is also simulated with the RAPGAP event generator using its inclusive mode together with the CTEQ6L PDF set [24].

The MC simulation is used to correct the data for detector e ects. The generated events undergo the full GEANT [25] simulation of the H1 detector and are analysed in the same way as the real data. In order to describe the measured distributions, the di ractive MC is reweighted in several variables as discussed in 4.4.

QCD predictions of the dijet cross sections at the parton level are evaluated at NLO using the NLOJET++ program [26, 27]. The NLO pQCD predictions are calculated in the MS-scheme with ve active avors. The two-loop approximation of the renormalisation group equation is used for the running of the strong coupling constant with a coupling strength of s(MZ) = 0.118. The cross sections are evaluated in intervals of xIP , e ectively replacing the beam proton by a pomeron (slicing method). The H12006 Fit-B DPDF set is used in the calculation. The renormalisation and factorisation scales r and f are provided by the photon virtuality and the average transverse momentum of the leading and sub-leading jet, hpTi, in the -p centre-of-mass frame and are de

ned as r = f =

[radicalbig]hpTi2 + Q2. The uncertainty on the prediction due to missing

higher orders is estimated by simultaneous variation of the renormalisation and factorisation scales by factors of 0.5 or 2. An uncertainty on the NLO prediction from the experimental uncertainties on the DPDF set is obtained using the eigenvector decomposition of the uncertainties of the H12006 Fit-B DPDF set. This uncertainty is propagated to the NLO prediction using the sign-improved formulae for error propagation [28]. A signicant contribution to the uncertainty of the H12006 Fit-B set originates from the restriction of the input data to zIP < 0.8 and the extrapolation of the DPDF to zIP > 0.8.

Whereas the measured cross sections are compared to the predictions obtained by the slicing method, an alternative method of adapting the NLO calculations for di ractive DIS is used in the s extraction. In order to provide theory predictions with di erent values of s(MZ), the fastNLO method [2931] is used. Cross section predictions are obtained by folding tabulated matrix elements obtained from NLOJET++ [26, 27] with the DPDF parametrisation. The matrix elements are determined as a function of the observable of interest, the factorisation scale F and the convolution variable x. The relation x = xIP zIP is used when folding with the DPDF. This way predictions can be obtained for di erent choices of DPDFs, of s and of the renormalisation and the factorisation scales without having to calculate the matrix elements all over again. Settings identical to the slicing method are used for parameters such as renormalisation and factorisation scales or DPDF set and very good numerical agreement with the slicing method is found. The uncertainty on the prediction due to missing higher orders is estimated by varying the scales by a factor f, where 0.5 < f < 2.

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Since the measured cross sections are given at the level of stable hadrons, the QCD predicted cross sections have to be corrected for e ects of initial and nal state parton showers, hadronisation and fragmentation. These corrections are determined for each of the measured cross sections as the ratio of hadron to parton level cross sections, predicted with the RAPGAP event generator. Two distinct models of parton showers, the leading-log approximation and the colour dipole model as implemented in the ARIADNE program [32], are used in this calculation. In each measurement interval the resulting correction is taken as the average of the values predicted by the two models and the uncertainties on the correction factors are taken as half the di erence of the two predictions. The hadron level cross sections are on average about 5% higher than the parton level cross sections. The total uncertainty on the NLO QCD predictions is obtained as the quadratic sum of the uncertainties from scale variation, DPDF t and hadronisation uncertainties.

4 Experimental technique

4.1 H1 detector

A detailed description of the detector can be found elsewhere [33]. Here only those detector components relevant for the present analysis are briey described. A right-handed coordinate system with the origin at the nominal interaction point and with the z-axis pointing in the proton beam direction is conventionally chosen as the laboratory frame. The polar angle is measured with respect to the z-axis, while the direction in the x-y plane is dened by the azimuthal angle . The pseudorapidity is dened as = ln tan(/2).

The liquid argon (LAr) sampling calorimeter [34] is located inside a 1.15 T solenoidal eld and covers the polar angular range 4 < < 154. The energy resolutions for electromagnetic and hadronic showers as determined in test beam measurements [35, 36] are (E)/E 11%/[radicalbig]E/GeV 1% and (E)/E 50%/[radicalbig]E/GeV 2%, respectively. The

energy and scattering angle of the scattered electron is measured in a scintillating bre calorimeter SpaCal [37, 38] with a resolution of (E)/E 7%/[radicalbig]E/GeV 1%. The

precision of the energy scale is 1% covering the polar angular range 154 < e < 174.

The measurement of the polar angle of the scattered electron e is improved by means of a backward proportional chamber (BPC). The precision of the polar angle measurement is 1 mrad.

Trajectories of charged particles are measured with the central tracking detector (CTD) located inside the LAr calorimeter with a transverse momentum resolution of pT /pT

0.2 % pT /GeV 1.5% in the polar angular range of 15 < <165.

The information from CTD and LAr is used for the reconstruction of the system X. The interaction vertex position is determined event-by-event using the particle trajectories measured in CTD.

The following H1 forward detectors are used in the LRG selection of di ractive events. The forward muon detector (FMD) consists of six proportional chambers which are grouped into two three-layer sections separated by a toroidal magnet. Although the nominal coverage of FMD is 1.9 < < 3.7, particles with pseudorapidity up to 6.5 can be detected

indirectly through their interactions with the beam transport system and detector support

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structures. The lead-scintillator Plug calorimeter is located at z = 4.9 m and covers the range 3.5 < < 5.5. The very forward region is covered by the forward tagging system (FTS) comprising scintillators surrounding the beam pipe. Only one station of FTS, situated at z = 28 m and covering the range 6.0 < < 7.5, is included in the present analysis.

The instantaneous luminosity is monitored based on the rate of the Bethe-Heitler process ep ep. The nal state photon is detected by a photon detector located close to

the beam pipe at z = 103 m. The precision of the integrated luminosity measurement is

improved in a dedicated analysis of the QED Compton process [39].

4.2 Reconstruction of observables

The DIS observables Q2, x and y are reconstructed using the electron- method [40]. Within this method, the photon virtuality Q2 is reconstructed based on the measured four-momentum of the scattered electron, while the inelasticity y and Bjorken-x are determined making use of combined information from the hadronic nal state (HFS) and the scattered electron.

The four-momenta of the particles attributed to HFS are reconstructed using an algorithm which combines information provided by the tracking system and the LAr calorimeter by avoiding double counting of hadronic energy [41, 42]. The calibration of the HFS energy scale derived in [43] is applied. The performance of the calibration was studied by comparing the transverse momentum balance in data and MC in the kinematic domain of this analysis.

Jets are reconstructed in the -p centre-of-mass frame using the inclusive kT jet algorithm [44] with the pT recombination scheme as implemented in the FastJet program [45]. The jet distance parameter is set to R = 1.0. The transverse momenta and pseudorapidi-ties of the leading and sub-leading jets are denoted as pT,1, 1 and pT,2, 2, respectively.2

The invariant mass of the nal state system X is reconstructed as:

MX = c(max)

qP 2X, (4.1)

where PX is the four-momentum of the system X obtained as a vector sum of all particles contained in the HFS. The MC simulation is used in order to derive the average correction for detector losses c(max), where max is the pseudorapidity of the most forward energy deposition above 800 MeV in the LAr calorimeter. The momentum fractions xIP and zIP are reconstructed as:

and

where M12 is the invariant mass of the dijet system.

Cross sections for dijet production in di ractive DIS are measured di erentially with respect to the variables Q2, y, xIP , zIP , pT,1, pT,2, hpTi = (pT,1+pT,2)/2 and = |12|.

2Observables in the -p centre-of-mass frame are labelled with an asterisk.

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xIP = Q2 + M2X

ys (4.2)

zIP = Q2 + M212

Q2 + M2X

, (4.3)

4.3 Event selection

The measurement is based on the H1 data collected in the years 2005 to 2007 with a total integrated luminosity of 290 pb1. The nominal beam energies of the protons and electrons are Ep = 920 GeV and Ee = 27.6 GeV, respectively.

The longitudinal position of the reconstructed event vertex is restricted to the range

35 < zvtx < 35 cm. DIS events are selected by the identication of the scattered electron in the backward calorimeter SpaCal. The isolated energy deposit of electromagnetic structure with the highest transverse momentum is identied as scattered electron and has to have a measured energy of at least 9.5 GeV.

Only events accepted by a trigger combining signals induced by the scattered electron in the SpaCal with minimum track information of the CTD are used in the analysis. The trigger e ciency related to the CTD condition is found to be 98%-99%, depending on the detector conguration and is reproduced by the MC simulation within 2%. The trigger e ciency related to the SPACAL condition is better than 99%.

Residual non-DIS background is dominated by photoproduction processes, where a hadron is misidentied as the scattered electron, whereas the true scattered electron escapes detection due to its small scattering angle. This background is reduced to a negligible level by demanding 35 <

Pi(E pz)i < 75 GeV, where the sum runs over all HFS particles and

the scattered electron candidate. Elastic QED Compton scattering ep ep introduces

another background contribution which is suppressed by rejecting congurations with two

back-to-back clusters in SpaCal.

Di ractive events are identied with the LRG method which requires an empty interval in rapidity between the systems X and Y . The low-mass system Y is produced at very large pseudorapidities and escapes detection. The di ractive signature is thus dened by the systems X (in the main detector) and Y (undetected). The energy of any cluster in the forward region of the LAr calorimeter is required to be below the noise level of 800 MeV, which is ensured by demanding max < 3.2. The variable max corresponds to the LAr cluster above the noise threshold which has the largest pseudorapidity. Information provided by the forward detectors FMD, FTS and the Plug calorimeter is used in order to extend the gap to rapidities beyond the LAr acceptance and in order to suppress the proton dissociation contribution. These detectors are required to show no signal above noise level [46]. At high momentum fractions xIP , the system X tends to extend into the direction of the outgoing system Y and the experimental separation of the systems X and Y is not possible. The LRG selection method is thus applicable only in the region of xIP [lessorsimilar] 0.03. The sample of DIS events satisfying the LRG criteria is dominated by the di ractive exchange, as the system X is isolated in the main part of the H1 detector, while the system Y escapes undetected down the beam pipe. The signal is dominated by proton-elastic processes, ep eXp, however, a small fraction of proton dissociation events is also

accepted by the LRG selection. The LRG requirements impose restrictions on the mass and scattering angle of the hadronic system Y . These correspond approximately to the requirements MY < 1.6 GeV and |t| < 1 GeV2. Migrations in these variables are modelled

using MC simulations.

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Extended Analysis Phase Space Measurement Cross section Phase Space

DIS 3 < Q2 < 100 GeV2 4 < Q2 < 100 GeV2

y < 0.7 0.1 < y < 0.7

Di raction

pT,1 > 3.0 GeV pT,1 > 5.5 GeV pT,2 > 3.0 GeV pT,2 > 4.0 GeV

2 < lab1,2 < 2 1 < lab1,2 < 2

Table 1: Summary of the extended analysis phase space and the phase space for the dijet cross sections measurements.

Events are selected in a phase space which is extended compared to the measurement phase space in order to improve the precision of the measurement by accounting for migrations at the phase space boundaries. Events within the DIS phase space of y < 0.7 and 3 < Q2 < 100 GeV2 are selected. The events are required to have at least two jets in the pseudorapidity range 2 < lab1,2 < 2 and transverse momenta greater than 3 GeV in the

-p centre-of-mass frame.

The measurement phase is dened by the DIS requirements of 0.1 < y < 0.7 and 4 < Q2 < 100 GeV2. The pseudorapidity of jets is restricted in the laboratory frame to

1 < lab1,2 < 2 to ensure the jets to be contained well within the central detector. The transverse momenta of the leading and sub-leading jets are required to be larger than 5.5 GeV and 4.0 GeV, respectively. The extended phase space and the measurement phase space denitions are summarised in table 1. The total number of events accepted by the LRG selection criteria together with the DIS and jet requirements is 50000 and 15000

for the extended and measurement phase space, respectively.

4.4 Corrections to the data

Cross sections at the level of stable hadrons are obtained from the measured event rates in data by applying corrections determined using the MC simulation. In gure 2 kinematic distributions of the observables Q2, pT,1, xIP and zIP as observed in the detector are shown in comparison to the expectations from the reweighted MC simulation. The overall good description of the data is achieved after applying a dedicated weighting of the MC simulation in the variables zIP , xIP and xdijet =

P1,2(Ejet pjetz)i/ [summationtext]HFS(E pz)i. Weights are obtained from the reconstructed kinematic distributions and are applied at the hadron level. This procedure is iterated until a good description of the shapes of the observables is achieved.

The data are corrected for detector ine ciencies, acceptance and nite resolution using the regularised unfolding procedure as implemented in TUnfold [47]. A detector response matrix A, with elements aij expressing the probability for an observable originating in the generated MC sample from an interval i to be measured in an interval j, is determined using

xIP < 0.04 xIP < 0.03

LRG requirements |t| < 1 GeV2

MY < 1.6 GeV

Dijets

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the MC simulation. Migrations from outside the measurement phase space are included by additional rows of the detector response matrix. The domains of jets with 3.0 < pT,1 < 5.5 GeV and of events with 0.03 < xIP < 0.04 are found to be the dominating sources of these migrations. The MC simulation is reweighted in order to describe the data also in these regions beyond the nominal phase space.

Two sources of background are considered in this analysis and are subtracted from the data using Monte Carlo simulations prior to unfolding: di ractive dijet events with MY > 1.6 GeV and |t| < 1 GeV2 and background from non-di ractive DIS.

For a background subtracted measurement yj, the corresponding number of events in the truth bin i, xi, is found by solving a minimisation problem for a 2 function

2 = (y Ax)T V 1yy(y Ax) + 2x2, (4.4)

where x and y are vectors dened by yj and xi, respectively, Vyy is the covariance matrix accounting for the statistical uncertainties of yj and is a regularisation parameter introduced in order to damp statistical uctuations of the solution. The regularisation parameter is determined using the L-Curve scan [47].

The cross section in each measurement interval i is given by

i(ep epX) =

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(1 + i,rad), (4.5)

where L is the integrated luminosity of the data sample and (1 + i,rad) is the correction for QED radiation e ects in the interval i. These corrections are calculated as a ratio of

RAPGAP predictions with and without QED radiation simulated. The di erential cross section is determined by dividing i by the area of the corresponding interval.

4.5 Systematic uncertainties

The systematic uncertainties induced by experimental e ects and by the process modelling are propagated to each measurement interval in the unfolding procedure (eq. (4.4)). A dedicated detector response matrix is constructed for each variation related to particular sources of uncertainties:

The energy of the scattered electron is varied by 1% with a resulting uncertainty

on the integrated dijet cross section of 1%.

The polar angle of the scattered electron is varied by 1 mrad with a resulting un

certainty on the integrated dijet cross section of 1%.

The energy of each particle contained in HFS is varied by 1% [43] which translates

into an uncertainty on the integrated dijet cross section of 4%.

Uncertainties related to the model dependent corrections of the data are accounted

for by varying the shape of the kinematic distributions in Q2, xIP , , pT,1, zIP , xdijet and in the MC such that the data are still described within the statisti

cal uncertainties. For this purpose, the multiplicative weights (log Q2)0.2, x0.05IP,

0.01(10.01), p0.04T,1, z0.15IP, x0.15dijet and (1.5+ )0.5 are applied, respectively.

The largest resulting uncertainty of 3% arises from the variation of the shape in pT,1. The shape of the distribution in t is varied within the experimental uncertainty on the t-slope [48] by applying a weight of et in MC, which translates into an uncertainty on the integrated dijet cross section of 1 %. The integrated cross section uncertainty due to the model dependence of the measurement is of the order of 5 %.

The following uncertainties on the global normalisation are considered:

The luminosity of the data is measured with a precision 2.7 % [39].

The trigger e ciency related to the tracking and SpaCal condition induces an uncer

tainty of 2% and 1%, respectively.

The uncertainty accounting for the LRG selection e ciency is 7% [49].

The normalisation of the non-di ractive DIS background modelled by RAPGAP is

varied by 50 % and the normalisation of the di ractive background is varied by 100 %, yielding a resulting uncertainty on the integrated dijet cross section below 1% in both cases.

The total systematic uncertainty is obtained by adding the individual contributions in quadrature.

5 Results

The integrated cross section in the measurement phase space specied in table 1 is found to be

dijetmeas(ep eXY ) = 73 2 (stat.) 7 (syst.) pb . (5.1) The NLO QCD prediction of the total di ractive dijet cross section is

dijettheo(ep eXY ) = 77 +2520 (scale) +414 (DPDF) 3 (had) pb , (5.2)

in very good agreement with the measurement. The uncertainty on the NLO prediction is found to be signicantly larger than the experimental uncertainty.

Single di erential cross sections are given in tables 2 and 3 and are shown in gures 36. The statistical correlations between measurements in di erent bins are given in tables 6 and 7. The di erential cross sections as a function of the DIS variables Q2 and y are shown in gure 3, as a function of the momentum fractions xIP and zIP are shown in gure 4 and as a function of the jet variables pT,1, pT,2, hpT i and are shown in gure 5 and 6.

For the majority of the measurements, the data precision is limited by systematic e ects. The statistical correlations are small for the inclusive kinematic variables Q2 and y and moderate (|| < 0.6) for the other variables. The gures also include the NLO QCD

predictions which describe within their large uncertainties the data well.

The dynamics of dijet production is further studied in terms of double di erential cross sections in bins of zIP and of the QCD scale dening observables Q2 and pT,1. The

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double di erential cross sections are listed in tables 45 and are shown in gures 710. The corresponding statistical correlations between measurements in di erent bins are given in tables 89. Figure 7 shows the double di erential cross section measured in bins of zIP and

Q2. The ratio of the data to the theory prediction is shown in gure 8. The data are well described by the NLO prediction in most of the phase space. The double di erential cross section measured in bins of pT,1 and Q2 is shown in gure 9 and the corresponding ratios of the measurements to the NLO predictions are shown in gure 10.

The present measurement is based on a six times increased luminosity as compared to the previous H1 measurement of dijet production with LRG [13] and is using a more sophisticated data correction method. A direct comparison of the present data to other measurements of dijet production in di ractive DIS is not possible because of di erent phase space denitions. Measurements based on the direct detection of a forward proton [15] are limited in statistical precision due to the restricted geometrical acceptance of the proton taggers.

The experimental uncertainties on both single- and double-di erential cross sections are in general smaller than the theory uncertainties. The data thus have the power to constrain QCD in di ractive DIS. Here, the double-di erential dijet cross sections as a function of Q2 and pT,1 are used to determine the value of the strong coupling constant s(MZ) at the scale of the mass of the Z-boson, MZ. The value of s(MZ) is determined by an iterative 2-minimisation procedure using NLO calculations, corrected for hadronisation e ects following the method [50]. In the t, the uncertainties on the HFS energy scale are treated as 50% correlated and 50% uncorrelated. All other experimental uncertainties are treated as correlated. Scale uncertainties, hadronisation uncertainties and DPDF uncertainties of the NLO calculation are propagated to the t result as described in [50].

The t yields a value of 2/ndof = 16.7/14, with ndof being the number of degrees of

freedom, thus indicating good agreement of theory to data. The nuisance parameters of the correlated systematic uncertainties are equally distributed around zero with absolute values below one. The value of s(MZ) determined in the t to the dijet cross sections is

s(MZ) = 0.1190.004 (exp)0.002 (had)0.005 (DPDF)0.010 (r)0.004 (f)

= 0.119 0.004 (exp) 0.012 (DPDF, theo)

(5.3)

The largest uncertainties arise from the estimate of the contributions from orders beyond NLO and from the poor knowledge of the DPDF. The largest contribution to the experimental uncertainty of 0.003 arises from the global normalisation uncertainty.

The result for s(MZ) is consistent within the uncertainties with the world average [51, 52] and with values from other jet data in DIS and photoproduction [50, 53, 54] as well as values of s(MZ) determined from jet data at the Tevatron [55, 56] and at the LHC [57, 58].

Although the uncertainty of this s(MZ) extraction is not competitive with measurements in other processes the agreement with the other measurements supports the underlying concept of treating dijet production in di ractive DIS with perturbative QCD calculations.

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6 Conclusions

Integrated, single- and double-di erential cross sections of di ractive DIS dijet production are measured with the H1 experiment in ep collisions at HERA and compared with NLO QCD predictions.

The integrated di ractive dijet cross section is found to be well described by the NLO QCD prediction using the H12006 Fit-B DPDF set. Both shapes and normalisation of the single-di erential cross sections are reproduced by the theory within the experimental and theory uncertainties, conrming at improved precision the conclusions from previous H1 measurements. Good agreement of the theory with the measurement is also found for the shapes and normalisation of the double di erential cross sections. The cross section measurements presented here show experimental uncertainties signicantly smaller than the uncertainties of the theory predictions. From a t of the NLO prediction to the double di erential cross sections in Q2 and pT,1, the strong coupling constant has been determined to be s(MZ) = 0.119 (4)exp (12)theo.

Acknowledgments

We are grateful to the HERA machine group whose outstanding e orts 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 sta for continual assistance and the DESY directorate 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.

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Q2 d/dQ2 tot stat sys E HFS Q2 xIP p T,1 zIP xdijet t bgr 1 + had 1 + rad [GeV2] [pb/GeV2] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%]

4 6 8.20 13.2 5.7 11.9 1.0 4.5 3.9 2.1 1.1 2.8 5.0 1.9 0.7 1.2 0.9 0.1 1.05 0.05 1.056 10 4.23 11.8 4.0 11.0 2.6 1.7 5.0 0.5 0.5 0.5 3.1 3.2 1.6 1.6 1.5 0.3 1.05 0.04 1.03 10 18 1.92 11.4 4.0 10.7 1.0 1.9 4.6 0.9 0.6 0.8 3.1 3.1 1.5 1.7 0.9 0.4 1.05 0.04 1.03 18 34 0.797 11.6 4.8 10.5 1.1 2.1 5.1 0.1 0.6 0.1 2.9 2.5 1.3 1.4 0.6 0.2 1.06 0.04 1.03 34 100 0.164 12.3 6.2 10.6 0.9 2.3 5.0 0.2 0.5 0.6 2.7 2.9 1.5 1.6 0.8 0.1 1.06 0.04 1.03y d/dy tot stat sys E HFS Q2 xIP p T,1 zIP xdijet t bgr 1 + had 1 + rad

[pb] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%]0.10 0.22 113 18.4 6.5 17.2 2.1 0.2 8.7 3.6 0.2 4.2 3.5 8.9 3.6 3.9 1.5 0.6 1.01 0.06 1.07 0.22 0.34 163 12.7 4.5 11.9 2.0 1.1 5.9 2.0 0.5 1.5 3.2 4.1 2.1 1.4 0.9 0.6 1.02 0.04 1.05 0.34 0.46 144 11.2 4.3 10.4 1.6 2.8 4.2 0.4 0.8 0.1 3.1 2.3 1.3 1.0 1.1 0.3 1.06 0.04 1.04 0.46 0.58 106 11.2 5.0 10.0 1.2 3.2 3.2 0.7 0.8 0.9 3.1 1.0 0.6 1.9 0.3 0.4 1.13 0.03 1.02 0.58 0.70 76.5 12.4 7.0 10.2 0.7 4.3 2.3 1.0 0.6 1.6 3.3 0.3 0.4 1.2 1.5 0.2 1.17 0.02 0.97 xIP d/dxIP tot stat sys E HFS Q2 xIP p T,1 zIP xdijet t bgr 1 + had 1 + rad

[pb] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%]2.30 2.10 14.2 42.0 36.2 21.1 1.8 3.9 9.3 2.7 4.0 3.7 5.8 11.4 4.7 7.6 1.2 0.7 1.17 0.13 1.06 2.10 1.90 53.5 14.7 8.9 11.7 1.6 2.4 5.6 0.6 1.2 0.8 3.2 3.7 1.8 2.3 1.4 0.0 1.10 0.08 1.04 1.90 1.70 111 11.6 5.5 10.2 1.5 1.3 4.5 1.1 0.1 0.2 3.5 1.5 1.0 1.4 1.1 0.0 1.06 0.04 1.04 1.70 1.52 196 10.9 4.9 9.8 1.3 2.5 3.6 1.0 0.5 0.5 3.4 0.0 0.3 0.5 0.5 0.8 1.03 0.03 1.03 zIP d/dzIP tot stat sys E HFS Q2 xIP p T,1 zIP xdijet t bgr 1 + had 1 + rad

[pb] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%]0.00 0.22 70.4 20.3 9.3 18.0 1.4 3.4 4.0 1.2 0.5 4.6 2.4 12.0 4.1 6.5 0.5 0.8 1.10 0.03 1.06 0.22 0.40 132 11.9 6.3 10.1 1.5 3.0 1.2 0.9 0.3 0.1 3.9 2.3 2.2 1.0 0.9 0.4 1.07 0.02 1.04 0.40 0.60 89.7 14.9 6.8 13.3 1.2 1.6 9.1 1.3 0.8 1.2 2.8 3.9 1.4 0.5 0.6 0.3 1.10 0.03 1.02 0.60 0.80 54.8 14.9 7.5 12.9 2.5 1.9 7.6 1.4 0.9 1.2 3.2 4.2 1.4 0.2 2.0 0.1 1.10 0.10 1.02 0.80 1.00 19.9 45.0 11.4 43.5 0.8 0.6 42.1 1.9 1.3 2.4 2.5 5.1 2.0 3.0 1.5 0.6 0.57 0.10 1.00

Table 2: Di ractive DIS dijet cross section measured di erentially as a function of Q2, y, log xIP and zIP . The statistical stat and systematic sys uncertainties are given together with the total uncertainty tot. The next 12 columns represent +1 shifts for the systematic error contributions from: electron polar angle measurement , electron energy scale E, HFS energy scale HFS, model uncertainties Q2 , xIP , , p T,1, zIP , xdijet , and t and the background normalisation uncertainty bgr. The global normalisation uncertainty of 7.8% is not listed explicitly but is included in the total systematic uncertainty sys. The last two column show the

correction factors for hadronisation and QED radiation, respectively.

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p T,1 d/dp T,1 tot stat sys E HFS Q2 xIP p T,1 zIP xdijet t bgr 1 + had 1 + rad [GeV ] [pb/GeV] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%]

5.50 7.00 30.8 9.6 3.2 9.0 1.4 1.4 3.1 0.9 0.5 0.6 1.3 1.7 0.9 0.6 0.8 0.1 1.05 0.05 1.03 7.00 9.00 10.5 11.8 6.1 10.0 1.3 3.0 4.6 0.6 0.8 0.4 1.4 1.5 0.9 1.2 1.0 0.7 1.06 0.04 1.04 9.00 15.00 1.07 19.6 12.7 14.9 1.3 2.3 9.8 0.1 1.0 0.1 4.2 2.7 1.1 5.3 1.5 0.7 1.04 0.03 1.06 p T,2 d/dp T,2 tot stat sys E HFS Q2 xIP p T,1 zIP xdijet t bgr 1 + had 1 + rad [GeV ] [pb/GeV] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%]

4.00 6.50 22.3 10.4 3.7 9.7 1.5 2.3 3.8 1.0 0.7 0.8 1.2 2.0 1.2 1.2 0.8 0.1 1.10 0.06 1.03 6.50 9.00 5.67 12.2 6.9 10.1 1.2 2.0 4.9 0.6 0.6 0.2 2.6 1.3 0.5 1.2 1.0 0.6 0.97 0.02 1.04 9.00 15.00 0.539 18.2 12.3 13.4 1.1 1.5 7.8 0.5 0.6 0.8 6.2 2.4 0.9 2.8 1.3 0.1 0.97 0.02 1.06 hp T i d/dhp T i tot stat sys E HFS Q2 xIP p T,1 zIP xdijet t bgr 1 + had 1 + rad [GeV ] [pb/GeV] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%]

4.75 6.50 27.6 9.9 3.5 9.3 1.5 2.0 3.3 1.1 0.5 0.8 1.0 1.9 1.0 0.8 0.8 0.1 1.09 0.06 1.03 6.50 9.00 8.52 11.3 5.2 10.0 1.4 2.4 5.0 0.4 0.8 0.1 1.7 0.8 0.4 1.5 1.1 0.5 1.01 0.03 1.04 9.00 15.00 0.701 19.7 13.4 14.4 0.7 1.2 9.2 0.3 0.7 0.2 5.4 3.5 1.3 3.8 0.9 0.5 1.01 0.03 1.06

d/d tot stat sys E HFS Q2 xIP p T,1 zIP xdijet t bgr 1 + had 1 + rad

[pb] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%]0.00 0.15 51.6 17.9 9.5 15.1 1.6 2.8 4.4 1.0 1.0 0.8 3.8 2.3 1.4 10.6 1.2 0.1 1.04 0.03 1.03 0.15 0.40 57.8 14.1 7.3 12.1 1.2 1.0 5.1 0.9 0.9 0.7 3.0 2.1 1.5 6.2 1.1 0.2 1.05 0.03 1.04 0.40 0.80 45.1 12.5 5.7 11.1 1.9 2.5 4.3 0.9 0.8 0.5 3.8 2.2 1.2 3.2 1.3 0.5 1.06 0.04 1.04 0.80 1.30 33.9 12.3 5.5 10.9 1.7 2.4 4.7 1.0 0.5 0.3 3.7 2.4 1.0 2.5 0.6 0.3 1.07 0.05 1.03 1.30 3.00 9.29 15.0 6.7 13.4 1.2 3.4 5.3 1.0 0.2 0.0 2.8 3.4 1.2 7.4 1.1 0.3 1.04 0.06 1.03

Table 3: Di ractive DIS dijet cross section measured di erentially as a function of p T,1, p T,2, hp T i and . The statistical stat and systematic sys uncertainties are given together with the total uncertainty tot. Further details are given in table 2.

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2dzIP dQ2 tot stat sys E HFS Q2 xIP p T,1 zIP xdijet t bgr 1 + had 1 + rad

[GeV2] [pb/GeV2] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%]0.0 0.3 4 10 7.67 14.8 7.7 12.7 2.0 3.5 1.0 1.6 0.3 3.4 3.3 6.5 2.2 3.1 1.3 0.5 1.08 0.03 1.05

10 20 2.40 15.6 10.0 12.1 0.7 2.9 2.1 2.0 0.2 1.1 3.2 5.7 1.5 4.6 0.4 0.7 1.08 0.02 1.05 20 40 0.544 27.6 20.8 18.2 2.2 4.7 3.3 0.9 0.2 4.7 3.5 11.6 2.8 7.3 0.4 0.2 1.09 0.02 1.05 40 100 0.0994 41.6 35.7 21.3 1.2 7.3 3.3 0.4 0.1 4.1 4.1 12.9 3.1 10.0 3.7 2.0 1.09 0.02 1.06 0.3 0.5 4 10 8.80 18.4 9.3 15.9 2.0 3.1 8.6 0.7 1.2 1.0 5.3 7.4 3.9 0.6 1.5 0.1 1.08 0.02 1.03

10 20 2.31 19.9 13.6 14.5 2.0 2.4 6.9 0.4 0.7 1.5 3.3 7.7 4.1 0.0 0.4 1.0 1.08 0.02 1.03 20 40 1.12 17.0 12.6 11.4 0.4 3.2 3.7 0.2 0.5 0.7 3.0 5.3 2.8 0.3 0.0 0.2 1.08 0.03 1.02 40 100 0.264 20.1 17.1 10.6 0.7 2.6 4.4 0.2 0.4 0.9 2.1 3.4 2.1 1.4 1.3 0.2 1.07 0.03 1.03 0.5 0.7 4 10 4.50 17.8 13.3 11.8 3.3 1.9 6.5 1.4 1.1 0.7 3.1 2.8 0.4 0.9 0.7 0.2 1.14 0.06 1.03

10 20 1.86 15.2 11.8 9.6 0.8 1.0 3.1 0.5 0.5 0.4 3.1 2.6 0.6 0.2 1.8 0.1 1.12 0.06 1.02 20 40 0.703 16.2 13.5 8.9 2.0 0.8 0.2 0.7 0.5 0.6 2.2 2.3 0.7 0.2 1.6 0.2 1.12 0.06 1.02 40 100 0.109 31.9 29.7 11.4 2.2 0.8 3.2 0.8 0.1 1.3 1.4 4.0 1.0 1.6 5.6 0.1 1.12 0.06 1.01 0.7 1.0 4 10 1.99 27.8 11.7 25.2 2.2 2.9 21.9 1.6 1.8 1.9 3.8 6.5 2.6 1.7 2.9 0.3 0.79 0.11 1.02

10 20 0.639 26.9 11.2 24.5 1.4 0.4 22.1 0.4 1.1 1.6 1.7 5.2 2.0 2.4 1.8 0.3 0.81 0.11 1.01 20 40 0.248 22.4 13.0 18.2 0.9 1.6 15.3 0.3 0.9 1.1 2.6 4.3 1.6 1.1 0.3 0.0 0.85 0.11 1.00 40 100 0.0968 18.5 13.3 13.0 0.3 2.1 9.0 0.5 0.4 1.1 2.2 3.4 1.5 1.3 0.4 0.5 0.89 0.10 1.01

Table 4: Di ractive DIS dijet cross section measured di erentially as a function of zIP and Q2. The statistical stat and systematic sys uncertainties are given together with the total uncertainty tot. Further details are given in table 2.

zIP Q2 d

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p T,1 Q2

d2dp T,1dQ2 tot stat sys E HFS Q

2 xIP p T,1 zIP xdijet t bgr 1 + had 1 + rad

[GeV2] [GeV] [pb/GeV3] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%] [%]5.5 7.0 4 6 3.35 15.6 9.1 12.7 0.4 5.9 1.2 2.7 1.1 3.4 1.3 5.8 2.9 0.6 1.0 0.1 1.05 0.05 1.04

6 10 1.84 12.7 7.1 10.5 3.0 0.8 4.7 1.5 0.3 1.0 1.8 2.9 1.3 0.7 1.6 0.1 1.05 0.05 1.02 10 18 0.834 12.3 7.2 9.9 1.2 0.9 3.2 1.1 0.5 1.4 1.6 3.9 1.7 0.6 1.1 0.2 1.05 0.05 1.02 18 34 0.344 13.3 8.6 10.1 1.5 0.4 5.1 0.3 0.5 0.4 1.4 2.6 1.7 1.1 0.0 0.0 1.06 0.05 1.03 34 100 0.0613 15.8 11.7 10.6 1.5 0.7 5.0 0.4 0.5 1.1 1.7 3.4 2.0 0.9 1.6 0.1 1.07 0.04 1.02 7.0 9.0 4 6 1.23 18.6 15.1 10.9 0.1 3.0 6.1 1.3 1.2 1.5 2.5 0.1 0.7 0.0 0.3 0.5 1.06 0.04 1.05

6 10 0.578 16.4 12.9 10.1 1.9 3.3 3.9 1.1 0.8 0.0 0.6 2.1 1.3 1.5 0.8 0.4 1.06 0.04 1.05 10 18 0.287 16.6 12.6 10.7 0.4 3.1 6.0 0.3 0.7 0.1 1.3 0.3 0.4 2.3 0.7 0.6 1.06 0.05 1.04 18 34 0.100 20.4 17.6 10.3 0.3 5.2 3.5 0.2 0.8 0.2 0.5 1.0 0.4 0.0 1.5 0.7 1.07 0.04 1.04 34 100 0.0276 19.9 17.4 9.6 0.6 3.7 3.1 0.6 0.5 1.0 0.6 1.6 0.4 1.0 1.5 0.6 1.06 0.06 1.04 9.0 15.0 4 6 0.122 30.1 26.6 14.2 7.8 0.5 5.5 0.1 0.7 0.3 5.5 1.2 0.5 3.3 2.2 0.8 1.04 0.03 1.06

6 10 0.0511 30.4 24.7 17.8 1.9 1.1 12.4 0.6 1.3 0.0 6.3 2.8 0.9 6.1 3.0 0.4 1.03 0.03 1.05 10 18 0.0207 35.5 30.0 19.0 1.4 1.7 11.6 1.1 1.0 1.4 6.5 6.4 2.9 5.6 6.0 0.5 1.03 0.02 1.05 18 34 0.0160 24.5 20.1 14.0 1.6 1.8 8.2 0.0 0.6 0.1 4.6 2.6 0.6 5.2 2.5 0.4 1.04 0.04 1.06 34 100 0.0034 31.9 27.8 15.7 3.6 0.3 9.0 1.8 0.7 1.0 3.5 3.1 1.5 6.0 4.9 1.0 1.05 0.03 1.07

Table 5: Di ractive DIS dijet cross section measured di erentially as a function of p T,1 and Q2. The statistical stat and systematic sys uncertainties are given together with the total uncertainty tot.. Further details are given in table 2.

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Q2 [GeV] #Bin 1 2 3 4 54 6 1 100 5 5

6 10 2 100 1 1

10 18 3 100 2 1

18 34 4 100 8

34 100 5 100

y #Bin 1 2 3 4 5 0.1 0.2 1 100 7 8 5 4

0.2 0.3 2 100 6 8 4

0.3 0.5 3 100 4 7

0.5 0.6 4 100 10

0.6 0.7 5 100

xIP #Bin 1 2 3 4

2.30 2.10 1 100 55 17 2 2.10 1.90 2 100 41 11 1.90 1.70 3 100 31 1.70 1.52 4 100

zIP #Bin 1 2 3 4 5 0.0 0.2 1 100 24 8 1

0.2 0.4 2 100 31 10 2

0.4 0.6 3 100 45 17

0.6 0.8 4 100 52

0.8 1.0 5 100Table 6: Correlation coe cients between data points for the single-di erential measurements in Q2, y, xIP and zIP . The values are given in per cent.

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pT,1 [GeV] #Bin 1 2 3

5.5 7.0 1 100 26 1

7.0 9.0 2 100 54

9.0 15.0 3 100

pT,2 [GeV] #Bin 1 2 3

4.0 6.5 1 100 36 13

6.5 9.0 2 100 46

9.0 15.0 3 100 hpTi [GeV] #Bin 1 2 3

4.75 6.50 1 100 33 12

6.50 9.00 2 100 49

9.00 15.00 3 100

#Bin 1 2 3 4 5 0.00 0.15 1 100 49 13 1 2

0.15 0.40 2 100 29 9 1

0.40 0.80 3 100 19 7

0.80 1.30 4 100 20

1.30 3.00 5 100Table 7: Correlation coe cients between data points for the single-di erential measurements in pT,1, pT,2, hpTi and . The values are given in per cent.

zIP Q2 [GeV2] #Bin 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.0 0.3 4 10 1 100 1 32 3 11 3

10 20 2 100 2 1 3 41 2 19 520 40 3 100 4 2 37 4 20 1 4 1 40 100 4 100 3 37 1 22 1 5 0.3 0.5 4 10 5 100 3 46 2 15

10 20 6 100 3 3 53 2 1920 40 7 100 3 2 51 2 1 1740 100 8 100 2 51 21 0.5 0.7 4 10 9 100 5 47 2

10 20 10 100 3 1 46 120 40 11 100 2 2 44 1 40 100 12 100 1 51 0.7 1.0 4 10 13 100 4

10 20 14 100 520 40 15 100 2 40 100 16 100

Table 8: Correlation coe cients between data points for the double-di erential measurement in zIP and Q2. The values are given in per cent.

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pT,1 [GeV] Q2 [GeV2] #Bin 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 5.5 7.0 4 6 1 100 7 1 44 2 13 1 1 1

6 10 2 100 3 3 57 3 1 17 1 1 1 10 18 3 100 2 1 1 3 59 1 1 2 1 22 1 1 18 34 4 100 3 1 58 1 2 1 2 25 2 34 100 5 100 1 56 1 2 27 7.0 9.0 4 6 6 100 7 3 3 1 60 2 5 6 3

6 10 7 100 4 2 1 3 57 3 2 10 18 8 100 2 6 60 4 4 18 34 9 100 1 7 3 6 62 3 34 100 10 100 4 2 5 5 64 9.0 15.0 4 6 11 100 5 13 14 7

6 10 12 100 6 3 10 18 13 100 10 9 18 34 14 100 8 34 100 15 100

Table 9: Correlation coe cients between data points for the double-di erential measurement in pT,1 and Q2. The values are given in per cent.

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#Entries

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H1 Data

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0 0.005 0.01 0.015 0.02 0.025 0.03

0 0.2 0.4 0.6 0.8 1

Figure 2: Distributions of the kinematic quantities Q2, pT,1, xIP and zIP . The data are shown as black points compared to the sum of MC simulation estimates. The lled area shows the contribution of non-di ractive DIS, the dotted line shows the di ractive contribution with the elastically scattered proton added to the non-di ractive DIS and the dashed line displays the proton dissociation contribution added to the di ractive contribution with the elastically scattered proton and the non-di ractive DIS contribution. The sum of all contributions including the resolved photon processes is given by the full line. The MC is reweighted to the data. The ratio of data to the MC prediction is shown in the lower part of of the individual gures.

H1 Data

NLO

H12006 Fit-B

(1+

)

had

)

had

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(1+

)

had

)

had

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]

[pb/GeV

/dy [pb] s d

[pb/GeV

250

200

/dQ s d

150

100

-1

Data/NLO

10 2

0.2 0.4 0.6

2 [GeV

]

Figure 3: Di ractive dijet di erential cross section as a function of Q2 and y. The inner error bars on the data points represent the statistical uncertainties, while the outer error bars include the systematic uncertainties added in quadrature. The NLO QCD prediction based on the H12006 Fit-B DPDF set is displayed as a white line. The light shaded band indicates the uncertainty arising from hadronisation and the DPDF t added in quadrature. The outer dark band shows the full theory uncertainty including the QCD scale uncertainty added in quadrature. The ratio of the single-di erential cross section to the NLO prediction is shown in the lower part of the individual gures.

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H1 Data

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H12006 Fit-B

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)

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)

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/dz s d

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200

100

Data/NLO

0 -2.2 -2 -1.8 -1.6

0 0 0.2 0.4 0.6 0.8 1

log

Figure 4: Di ractive dijet di erential cross section as a function of log xIP and zIP . The inner error bars on the data points represent the statistical uncertainties, while the outer error bars include the systematic uncertainties added in quadrature. Further details are given in gure 3.

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H1 Data

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)

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T,1

T,2

/p* s d

/dp* s d

-1

Data/NLO

0 6 8 10 12 14

0 5 10 15

[GeV]

T,1

T,2

Figure 5: Di ractive dijet di erential cross section as a function of pT,1 and pT,2. The inner error bars on the data points represent the statistical uncertainties, while the outer error bars include the systematic uncertainties added in quadrature. Further details are given in gure 3.

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H1 Data

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H12006 Fit-B

(1+

)

had

)

had

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(1+

)

had

)

had

100

[pb/GeV]

* [pb] h D /d s d

/d s d

-1

Data/NLO

0 5 10 15

0 0 1 2 3

[GeV]

Figure 6: Di ractive dijet di erential cross section as a function of hpTi and . The

inner error bars on the data points represent the statistical uncertainties, while the outer error bars include the systematic uncertainties added in quadrature. Further details are given in gure 3.

H1 Data

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H12006 Fit-B

(1+

)

had

]

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4 < Q

[pb/GeV

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2 < 20 GeV

10 < Q

/dz s d

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20 < Q

2 < 40 GeV

20 < Q

2 < 100 GeV

40 < Q

2 < 100 GeV

40 < Q

0.4

0.2

0 0 0.2 0.4 0.6 0.8 1

Figure 7: Double-di erential cross section as a function of zIP and Q2. The inner error bars on the data points represent the statistical uncertainties, while the outer error bars include the systematic uncertainties added in quadrature. Further details are given in gure 3.

H1 Data

NLO

H12006 Fit-B

(1+

)

had

2 H1

2 < 10 GeV

4 < Q

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4 < Q

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10 < Q

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2 < 40 GeV

20 < Q

2 < 40 GeV

20 < Q

2 < 100 GeV

40 < Q

2 < 100 GeV

40 < Q

0 0 0.2 0.4 0.6 0.8 1

Figure 8: Ratio of the double-di erential cross section to the NLO prediction as a function of zIP and Q2. The inner error bars on the data points represent the statistical uncertainties, while the outer error bars include the systematic uncertainties added in quadrature. Further details are given in gure 3.

2 < 6 GeV

4 < Q

2 < 6 GeV

4 < Q

]

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H1 Data

-2

NLO

H12006 Fit-B

(1+

)

had

-3

6 8 10 12 14

[GeV]

T,1

Figure 9: Double-di erential cross section as a function of pT,1 and Q2. The inner error bars on the data points represent the statistical uncertainties, while the outer error bars include the systematic uncertainties added in quadrature. Further details are given in gure 3.

Data/NLO

2 < 6 GeV

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[GeV]

T,1

1.5

H1 Data

NLO

H12006 Fit-B

(1+

)

had

0.5

6 8 10 12 14

[GeV]

T,1

Figure 10: Ratio of the double-di erential cross section to the NLO prediction as a function of pT,1 and Q2. The inner error bars on the data points represent the statistical uncertainties, while the outer error bars include the systematic uncertainties added in quadrature. Further details are given in gure 3.

Open Access. This article is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/

Web End =CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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JHEP03(2015)092

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SISSA, Trieste, Italy 2015

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A measurement is presented of single- and double-differential dijet cross sections in diffractive deep-inelastic ep scattering at HERA using data collected by the H1 experiment corresponding to an integrated luminosity of 290 pb^sup -1^. The investigated phase space is spanned by the photon virtuality in the range of 4 < Q ^sup 2^ < 100 GeV^sup 2^ and by the fractional proton longitudinal momentum loss x ^sub ^ < 0.03. The resulting cross sections are compared with next-to-leading order QCD predictions based on diffractive parton distribution functions and the value of the strong coupling constant is extracted.

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Title

Measurement of dijet production in diffractive deep-inelastic ep scattering at HERA

Author

Andreev, V; Baghdasaryan, A; Begzsuren, K; Belousov, A; Boudry, V; Brandt, G; Brisson, V; Britzger, D; Buniatyan, A; Bylinkin, A; Bystritskaya, L; Campbell, A J; Cantun Avila, K B; Ceccopieri, F; Cerny, K; Chekelian, V; Contreras, J G; Cvach, J; Dainton, J B; Daum, K; Diaconu, C; Dobre, M; Dodonov, V; Eckerlin, G; Egli, S; Elsen, E; Favart, L; Fedotov, A; Feltesse, J; Ferencei, J; Fleischer, M; Fomenko, A; Gabathuler, E; Gayler, J; Ghazaryan, S; Glazov, A; Goerlich, L; Gogitidze, N; Gouzevitch, M; Grab, C; Grebenyuk, A; Greenshaw, T; Grindhammer, G; Haidt, D; Henderson, R C; W; Herbst, M; Hladky, J; Hoffmann, D; Horisberger, R; Hreus, T; Huber, F; Jacquet, M; Janssen, X; Jung, H; Kapichine, M; Kiesling, C; Klein, M; Kleinwort, C; Kogler, R; Kostka, P; Kretzschmar, J; Krüger, K; Landon, M P; J; Lange, W; Laycock, P; Lebedev, A; Levonian, S; Lipka, K; List, B; List, J; Lobodzinski, B; Malinovski, E; Martyn, H-u; Maxfield, S J; Mehta, A; Meyer, A B; Meyer, H; Meyer, J; Mikocki, S; Morozov, A; Müller, K; Naumann, Th; Newman, P R; Niebuhr, C; Nowak, G; Olsson, J E; Ozerov, D; Pahl, P; Pascaud, C; Patel, G D; Perez, E; Petrukhin, A; Picuric, I; Pirumov, H; Pitzl, D; Placakyt, R; Pokorny, B; Polifka, R; Radescu, V; Raicevic, N; Ravdandorj, T; Reimer, P; Rizvi, E; Robmann, P; Roosen, R; Rostovtsev, A; Rotaru, M; Rusakov, S; Sálek, D; Sankey, D P; C; Sauter, M; Sauvan, E; Schmitt, S; Schoeffel, L; Schöning, A; Schultz-coulon, H-c; Sefkow, F; Shushkevich, S; Soloviev, Y; Sopicki, P; South, D; Spaskov, V; Specka, A; Steder, M; Stella, B; Straumann, U; Sykora, T; Thompson, P D; Traynor, D; Truöl, P; Tsakov, I; Tseepeldorj, B; Turnau, J; Valkárová, A; Vallée, C; Van Mechelen, P; Vazdik, Y; Wegener, D; Wünsch, E; ácek, J; Zhang, Z; Lebcík, R; Zohrabyan, H; Zomer, F

Pages

1-35

Publication year

2015

Publication date

Mar 2015

Publisher

Springer Nature B.V.

e-ISSN

10298479

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.1007/JHEP03(2015)092

ProQuest document ID

1668120852

SISSA, Trieste, Italy 2015

Measurement of dijet production in diffractive deep-inelastic ep scattering at HERA

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