Combined inclusive diffractive cross sections measured with forward proton spectrometers in deep inelastic ep scattering at HERA H 1 and ZEUS Collaborations

A combination of the inclusive diffractive cross section measurements made b y the H1 and ZEUS Collaborations at HERA is presented. The analysis uses samples of diffractive deep inelasticep scattering data at a centre-of-mass energy √ s = 318 GeV where leading protons are detected by dedicated spectrometers. Correlations of systema tic uncertainties are taken into account, resulting in an improved precision of the cross sectio n measurement which reaches 6% for the most precise points. The combined data cove r the range 2.5 < Q2 < 200 GeV2 in photon virtuality,0.00035 < xIP < 0.09 in proton fractional momentum loss, 0.09 < |t| < 0.55 GeV2 in squared four-momentum transfer at the proton vertex and0.0018 < β < 0.816 in β = x/xIP , wherex is the Bjorken scaling variable. Submitted toEur. Phys. J.C F.D. Aaron, H. Abramowicz, I. Abt, L. Adamczyk, M. Adamus, R. Aggarwal , C. Alexa, V. Andreev, S. Antonelli , P. Antonioli, A. Antonov, M. Arneodo, O. Arslan, V. Aushev, Y. Aushev, , O. Bachynska , S. Backovic, A. Baghdasaryan , S. Baghdasaryan , A. Bamberger , A.N. Barakbaev , G. Barbagli , G. Bari, F. Barreiro, E. Barrelet , W. Bartel, N. Bartosik, D. Bartsch, M. Basile, K. Begzsuren , O. Behnke, J. Behr , U. Behrens, L. Bellagamba, A. Belousov, P. Belov, A. Bertolin, S. Bhadra, M. Bindi, J.C. Bizot , C. Blohm, V. Bokhonov, K. Bondarenko, E.G. Boos, K. Borras, D. Boscherini , D. Bot, V. Boudry, I. Bozovic-Jelisavcic , T. Bołd, N. Brümmer, J. Bracinik, G. Brandt , M. Brinkmann, V. Brisson, D. Britzger, I. Brock, E. Brownson, R. Brugnera, D. Bruncko, A. Bruni, G. Bruni, B. Brzozowska, A. Bunyatyan, P.J. Bussey , A. Bylinkin, B. Bylsma, L. Bystritskaya, A. Caldwell, A.J. Campbell , K.B. Cantun Avila, M. Capua, R. Carlin, C.D. Catterall , F. Ceccopieri , K. Cerny, V. Cerny, S. Chekanov , V. Chekelian, J. Chwastowski , J. Ciborowski , R. Ciesielski , L. Cifarelli, F. Cindolo, A. Contin, J.G. Contreras , A.M. Cooper-Sarkar , N. Coppola, M. Corradi, F. Corriveau, M. Costa, J.A. Coughlan, J. Cvach, G. D’Agostini, J.B. Dainton, F. Dal Corso, K. Daum, B. Delcourt, J. Delvax, R.K. Dementiev , M. Derrick, R.C.E. Devenish , S. De Pasquale , E.A. De Wolf, J. del Peso , C. Diaconu, M. Dobre, D. Dobur, V. Dodonov, B.A. Dolgoshein, G. Dolinska, A. Dossanov , A.T. Doyle, V. Drugakov, A. Dubak, L.S. Durkin, S. Dusini , G. Eckerlin, S. Egli, Y. Eisenberg, A. Eliseev, E. Elsen, P.F. Ermolov, A. Eskreys, S. Fang, L. Favart, S. Fazio, A. Fedotov, R. Felst , J. Feltesse , J. Ferencei , J. Ferrando , M.I. Ferrero, J. Figiel , D.-J. Fischer , M. Fleischer , A. Fomenko, M. Forrest , B. Foster , E. Gabathuler , G. Gach, A. Galas, E. Gallo, A. Garfagnini , J. Gayler , A. Geiser , S. Ghazaryan , I. Gialas, A. Gizhko, L.K. Gladilin, D. Gladkov, C. Glasman , A. Glazov, L. Goerlich, N. Gogitidze, O. Gogota, Yu.A. Golubkov, P. G̈ottlicher, M. Gouzevitch, C. Grab, I. Grabowska-Bołd , A. Grebenyuk, J. Grebenyuk , T. Greenshaw, I. Gregor, G. Grigorescu, G. Grindhammer , G. Grzelak, O. Gueta, M. Guzik, C. Gwenlan, A. Hüttmann, T. Haas, S. Habib, D. Haidt, W. Hain, R. Hamatsu , J.C. Hart , H. Hartmann, G. Hartner , R.C.W. Henderson , E. Hennekemper , H. Henschel , M. Herbst , G. Herrera, M. Hildebrandt , E. Hilger, K.H. Hiller, J. Hladḱy, D. Hochman, D. Hoffmann, R. Hori, R. Horisberger , T. Hreus, F. Huber , Z.A. Ibrahim, Y. Iga, R. Ingbir, M. Ishitsuka, M. Jacquet , H.-P. Jakob, X. Janssen , F. Januschek , T.W. Jones , L. Jönsson, M. Jüngst , H. Jung, I. Kadenko, B. Kahle, S. Kananov , T. Kanno, M. Kapichine, U. Karshon, F. Karstens , I.I. Katkov, P. Kaur, M. Kaur, I.R. Kenyon, A. Keramidas, L.A. Khein, C. Kiesling, J.Y. Kim, D. Kisielewska, S. Kitamura, R. Klanner , M. Klein, U. Klein, C. Kleinwort, E. Koffeman, R. Kogler, N. Kondrashova , O. Kononenko, P. Kooijman, Ie. Korol, I.A. Korzhavina, P. Kostka, A. Kotański, U. Kötz, H. Kowalski, M. Krämer, J. Kretzschmar , K. Krüger, O. Kuprash, M. Kuze, M.P.J. Landon , W. Lange, G. Lǎstovǐcka-Medin, P. Laycock, A. Lebedev, A. Lee, V. Lendermann, B.B. Levchenko, S. Levonian, A. Levy, V. Libov, S. Limentani , T.Y. Ling, K. Lipka, M. Lisovyi, B. List, J. List, E. Lobodzinska , B. Lobodzinski , W. Lohmann, B. Löhr, E. Lohrmann, K.R. Long, A. Longhin, D. Lontkovskyi ,

a16 Supported by the Polish National Science Centre, project No. DEC-2011/01/BST2/03643 a17 Now at Rockefeller University, New York, NY 10065, USA a18  from processes in which a photon exchanged between the electron and the proton probes a 5 colour-singlet combination of partons with vacuum quantum numbers emitted by the proton.

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The negative four-momentum squared of the virtual photon, Q 2 , supplies a hard scale, which 7 allows the application of perturbative quantum chromodynamics (QCD). Diffractive reactions 8 in DIS are a tool to investigate low-momentum partons in the proton, notably through the study 9 of diffractive parton distribution functions (DPDFs), determined by a QCD analysis of the data.

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In diffractive ep scattering the virtual photon dissociates at a photon-proton centre-of-mass 11 energy W and squared four-momentum transfer t at the proton vertex (figure 1), producing a 12 hadronic system X with mass M X . The fractional longitudinal momentum loss of the proton 13 is denoted as x IP , while the fraction of this momentum taking part in the interaction with the 14 photon is denoted as β. These variables are related to Bjorken x by The variable x IP is given by  Similarly to inclusive DIS, diffractive cross section measurements are conventionally expressed in terms of the reduced diffractive cross section, σ D(4) r , which is related to the measured ep cross section by The reduced cross section σ D(3) r (β, Q 2 , x IP ) is obtained by integrating σ D(4) r (β, Q 2 , x IP , t) over t. The diffractive reduced cross section is related to the diffractive structure functions by: (2) Experimentally, diffractive ep scattering is characterised by the presence of a leading proton optics. The results from both methods are found to be consistent [1,2,4,6,7].

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Combining measurements can provide more precise and kinematically extended data than 33 the individual measurements. In this paper, a combination of the
of the data samples are listed in table 2. In the restricted t range, these uncertainties are in gen-

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In the H1 case the measurements are extracted at fixed β, whereas for ZEUS the cross section 89 is measured at fixed M X ; also the Q 2 and x IP central values differ. Therefore, prior to the 90 combination, the H1 and ZEUS data are transformed to a common grid of (β, Q 2 , x IP ) points.

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The grid points are based on the original binning scheme of the 'FPS HERA II' data. The

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(Q 2 , x IP ) grid points at the lowest Q 2 value of 2.5 GeV 2 and at the lowest and highest x IP values, 93 which are beyond the 'FPS HERA II' data grid, are taken from the 'LPS 2' measurement.

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The transformation of a measurement from the original i th point (β i , Q 2 i , x IP i ) to the nearest 95 grid point (β grid , Q 2 grid , x IP grid ) is performed by multiplying the measured cross section by the The cross sections from all the data sets are shown in figure 2 after correcting to 0.09 < 102 |t| < 0.55 GeV 2 and transforming to the common grid.

Combination method 104
The combination is based on the χ 2 minimisation method described in [8] and used for previous 105 combined HERA results [10]. The averaging procedure is based on the assumption that at a 106 given kinematic point the H1 and ZEUS experiments are measuring the same cross section.

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The correlated systematic uncertainties are floated coherently. The procedure allows a model 108 independent check of the data consistency and leads to a significant reduction of the correlated 109 uncertainties.

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For an individual data set, the χ 2 function is defined as: Here µ i is the measured cross section value at a point i (β i , Q 2 i , x IP i ), and γ i j , δ i,stat and δ i,uncor which is determined by the expected cross section, corrected for the biases due to the correlated 120 systematic uncertainties. This is taken into account by the If several analyses provide measurements at the same (β, 122 from the sum of the χ 2 exp of each data set, assuming the individual data sets to be statistically

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For each combined data point the difference between the average obtained by considering 208 each of the procedural effects and the nominal average is calculated and summed in quadrature.

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The effect of the procedural uncertainties is 2.9% on average and 9.3% at most. We are grateful to the HERA machine group whose outstanding efforts have made these exper-   (β, Q 2 , x IP ) for diffractive ep scattering, ep → eXp. The values indicated by δ stat , δ uncor , δ cor , δ exp , δ proc and δ tot represent the statistical, uncorrelated systematic, correlated systematic, experimental, procedural and total uncertainties, respectively.      (β, Q 2 , x IP ) for 0.09 < |t| < 0.55 GeV 2 as a function of Q 2 for different values of β at x IP = 0.05. The HERA combined data are compared to the H1 and ZEUS data inputs to the averaging procedure. The error bars indicate the statistical and systematic uncertainties added in quadrature for the input measurements and the statistical, systematic and procedural uncertainties added in quadrature for the combined points. Normalisation uncertainties are not included in the error bars of the individual measurements, whereas they are included in the error bars of the combined points. (β, Q 2 , x IP ) for 0.09 < |t| < 0.55 GeV 2 as a function of x IP for different values of β and Q 2 . The error bars indicate the statistical, systematic and procedural uncertainties added in quadrature. The normalisation uncertainty is included.