Double parton interactions in photon+3 jet events in ppbar collisions sqrt{s}=1.96 TeV
aa r X i v : . [ h e p - e x ] F e b FERMILAB-PUB-09-644-E
Double parton interactions in γ +3 jet events in p ¯ p collisions at √ s = 1 .
96 TeV
V.M. Abazov , B. Abbott , M. Abolins , B.S. Acharya , M. Adams , T. Adams , E. Aguilo , G.D. Alexeev ,G. Alkhazov , A. Alton ,a , G. Alverson , G.A. Alves , L.S. Ancu , M. Aoki , Y. Arnoud , M. Arov ,A. Askew , B. ˚Asman , O. Atramentov , C. Avila , J. BackusMayes , F. Badaud , L. Bagby , B. Baldin ,D.V. Bandurin , S. Banerjee , E. Barberis , A.-F. Barfuss , P. Baringer , J. Barreto , J.F. Bartlett ,U. Bassler , D. Bauer , S. Beale , A. Bean , M. Begalli , M. Begel , C. Belanger-Champagne , L. Bellantoni ,J.A. Benitez , S.B. Beri , G. Bernardi , R. Bernhard , I. Bertram , M. Besan¸con , R. Beuselinck ,V.A. Bezzubov , P.C. Bhat , V. Bhatnagar , G. Blazey , S. Blessing , K. Bloom , A. Boehnlein ,D. Boline , T.A. Bolton , E.E. Boos , G. Borissov , T. Bose , A. Brandt , R. Brock , G. Brooijmans ,A. Bross , D. Brown , X.B. Bu , D. Buchholz , M. Buehler , V. Buescher , V. Bunichev , S. Burdin ,b ,T.H. Burnett , C.P. Buszello , P. Calfayan , B. Calpas , S. Calvet , E. Camacho-P´erez , J. Cammin ,M.A. Carrasco-Lizarraga , E. Carrera , B.C.K. Casey , H. Castilla-Valdez , S. Chakrabarti , D. Chakraborty ,K.M. Chan , A. Chandra , E. Cheu , S. Chevalier-Th´ery , D.K. Cho , S.W. Cho , S. Choi , B. Choudhary ,T. Christoudias , S. Cihangir , D. Claes , J. Clutter , M. Cooke , W.E. Cooper , M. Corcoran , F. Couderc ,M.-C. Cousinou , D. Cutts , M. ´Cwiok , A. Das , G. Davies , K. De , S.J. de Jong , E. De La Cruz-Burelo ,K. DeVaughan , F. D´eliot , M. Demarteau , R. Demina , D. Denisov , S.P. Denisov , S. Desai , H.T. Diehl ,M. Diesburg , A. Dominguez , T. Dorland , A. Dubey , L.V. Dudko , L. Duflot , D. Duggan , A. Duperrin ,S. Dutt , A. Dyshkant , M. Eads , D. Edmunds , J. Ellison , V.D. Elvira , Y. Enari , S. Eno , H. Evans ,A. Evdokimov , V.N. Evdokimov , G. Facini , A.V. Ferapontov , T. Ferbel , , F. Fiedler , F. Filthaut ,W. Fisher , H.E. Fisk , M. Fortner , H. Fox , S. Fuess , T. Gadfort , C.F. Galea , A. Garcia-Bellido ,V. Gavrilov , P. Gay , W. Geist , W. Geng , , D. Gerbaudo , C.E. Gerber , Y. Gershtein , D. Gillberg ,G. Ginther , , G. Golovanov , B. G´omez , A. Goussiou , P.D. Grannis , S. Greder , H. Greenlee ,Z.D. Greenwood , E.M. Gregores , G. Grenier , Ph. Gris , J.-F. Grivaz , A. Grohsjean , S. Gr¨unendahl ,M.W. Gr¨unewald , F. Guo , J. Guo , G. Gutierrez , P. Gutierrez , A. Haas ,c , P. Haefner , S. Hagopian ,J. Haley , I. Hall , L. Han , K. Harder , A. Harel , J.M. Hauptman , J. Hays , T. Hebbeker , D. Hedin ,J.G. Hegeman , A.P. Heinson , U. Heintz , C. Hensel , I. Heredia-De La Cruz , K. Herner , G. Hesketh ,M.D. Hildreth , R. Hirosky , T. Hoang , J.D. Hobbs , B. Hoeneisen , M. Hohlfeld , S. Hossain ,P. Houben , Y. Hu , Z. Hubacek , N. Huske , V. Hynek , I. Iashvili , R. Illingworth , A.S. Ito ,S. Jabeen , M. Jaffr´e , S. Jain , D. Jamin , R. Jesik , K. Johns , C. Johnson , M. Johnson , D. Johnston ,A. Jonckheere , P. Jonsson , A. Juste ,d , E. Kajfasz , D. Karmanov , P.A. Kasper , I. Katsanos ,V. Kaushik , R. Kehoe , S. Kermiche , N. Khalatyan , A. Khanov , A. Kharchilava , Y.N. Kharzheev ,D. Khatidze , M.H. Kirby , M. Kirsch , J.M. Kohli , A.V. Kozelov , J. Kraus , A. Kumar , A. Kupco ,T. Kurˇca , V.A. Kuzmin , J. Kvita , D. Lam , S. Lammers , G. Landsberg , P. Lebrun , H.S. Lee ,W.M. Lee , A. Leflat , J. Lellouch , L. Li , Q.Z. Li , S.M. Lietti , J.K. Lim , D. Lincoln , J. Linnemann ,V.V. Lipaev , R. Lipton , Y. Liu , Z. Liu , A. Lobodenko , M. Lokajicek , P. Love , H.J. Lubatti ,R. Luna-Garcia ,e , A.L. Lyon , A.K.A. Maciel , D. Mackin , P. M¨attig , R. Maga˜na-Villalba , P.K. Mal ,S. Malik , V.L. Malyshev , Y. Maravin , J. Mart´ınez-Ortega , R. McCarthy , C.L. McGivern , M.M. Meijer ,A. Melnitchouk , L. Mendoza , D. Menezes , P.G. Mercadante , M. Merkin , A. Meyer , J. Meyer ,N.K. Mondal , T. Moulik , G.S. Muanza , M. Mulhearn , O. Mundal , L. Mundim , E. Nagy ,M. Naimuddin , M. Narain , R. Nayyar , H.A. Neal , J.P. Negret , P. Neustroev , H. Nilsen , H. Nogima ,S.F. Novaes , T. Nunnemann , G. Obrant , D. Onoprienko , J. Orduna , N. Osman , J. Osta , R. Otec ,G.J. Otero y Garz´on , M. Owen , M. Padilla , P. Padley , M. Pangilinan , N. Parashar , V. Parihar ,S.-J. Park , S.K. Park , J. Parsons , R. Partridge , N. Parua , A. Patwa , B. Penning , M. Perfilov ,K. Peters , Y. Peters , P. P´etroff , R. Piegaia , J. Piper , M.-A. Pleier , P.L.M. Podesta-Lerma ,f ,V.M. Podstavkov , M.-E. Pol , P. Polozov , A.V. Popov , M. Prewitt , D. Price , S. Protopopescu ,J. Qian , A. Quadt , B. Quinn , M.S. Rangel , K. Ranjan , P.N. Ratoff , I. Razumov , P. Renkel ,P. Rich , M. Rijssenbeek , I. Ripp-Baudot , F. Rizatdinova , S. Robinson , M. Rominsky , C. Royon ,P. Rubinov , R. Ruchti , G. Safronov , G. Sajot , A. S´anchez-Hern´andez , M.P. Sanders , B. Sanghi ,G. Savage , L. Sawyer , T. Scanlon , D. Schaile , R.D. Schamberger , Y. Scheglov , H. Schellman ,T. Schliephake , S. Schlobohm , C. Schwanenberger , R. Schwienhorst , J. Sekaric , H. Severini ,E. Shabalina , V. Shary , A.A. Shchukin , R.K. Shivpuri , V. Simak , V. Sirotenko , N.B. Skachkov ,P. Skubic , P. Slattery , D. Smirnov , G.R. Snow , J. Snow , S. Snyder , S. S¨oldner-Rembold ,L. Sonnenschein , A. Sopczak , M. Sosebee , K. Soustruznik , B. Spurlock , J. Stark , V. Stolin ,D.A. Stoyanova , J. Strandberg , M.A. Strang , E. Strauss , M. Strauss , R. Str¨ohmer , D. Strom ,L. Stutte , P. Svoisky , M. Takahashi , A. Tanasijczuk , W. Taylor , B. Tiller , M. Titov , V.V. Tokmenin ,D. Tsybychev , B. Tuchming , C. Tully , P.M. Tuts , R. Unalan , L. Uvarov , S. Uvarov , S. Uzunyan ,P.J. van den Berg , R. Van Kooten , W.M. van Leeuwen , N. Varelas , E.W. Varnes , I.A. Vasilyev ,P. Verdier , A.Y. Verkheev , L.S. Vertogradov , M. Verzocchi , M. Vesterinen , D. Vilanova , P. Vint ,P. Vokac , H.D. Wahl , M.H.L.S. Wang , J. Warchol , G. Watts , M. Wayne , G. Weber , M. Weber ,g ,M. Wetstein , A. White , D. Wicke , M.R.J. Williams , G.W. Wilson , S.J. Wimpenny , M. Wobisch ,D.R. Wood , T.R. Wyatt , Y. Xie , C. Xu , S. Yacoob , R. Yamada , W.-C. Yang , T. Yasuda ,Y.A. Yatsunenko , Z. Ye , H. Yin , K. Yip , H.D. Yoo , S.W. Youn , J. Yu , C. Zeitnitz , S. Zelitch ,T. Zhao , B. Zhou , J. Zhu , M. Zielinski , D. Zieminska , L. Zivkovic , V. Zutshi , and E.G. Zverev (The DØ Collaboration) Universidad de Buenos Aires, Buenos Aires, Argentina LAFEX, Centro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, Brazil Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil Universidade Federal do ABC, Santo Andr´e, Brazil Instituto de F´ısica Te´orica, Universidade Estadual Paulista, S˜ao Paulo, Brazil Simon Fraser University, Burnaby, British Columbia,Canada; and York University, Toronto, Ontario, Canada University of Science and Technology of China, Hefei, People’s Republic of China Universidad de los Andes, Bogot´a, Colombia Center for Particle Physics, Charles University,Faculty of Mathematics and Physics, Prague, Czech Republic Czech Technical University in Prague, Prague, Czech Republic Center for Particle Physics, Institute of Physics,Academy of Sciences of the Czech Republic, Prague, Czech Republic Universidad San Francisco de Quito, Quito, Ecuador LPC, Universit´e Blaise Pascal, CNRS/IN2P3, Clermont, France LPSC, Universit´e Joseph Fourier Grenoble 1, CNRS/IN2P3,Institut National Polytechnique de Grenoble, Grenoble, France CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France LAL, Universit´e Paris-Sud, IN2P3/CNRS, Orsay, France LPNHE, IN2P3/CNRS, Universit´es Paris VI and VII, Paris, France CEA, Irfu, SPP, Saclay, France IPHC, Universit´e de Strasbourg, CNRS/IN2P3, Strasbourg, France IPNL, Universit´e Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universit´e de Lyon, Lyon, France III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany Physikalisches Institut, Universit¨at Bonn, Bonn, Germany Physikalisches Institut, Universit¨at Freiburg, Freiburg, Germany II. Physikalisches Institut, Georg-August-Universit¨at G¨ottingen, G¨ottingen, Germany Institut f¨ur Physik, Universit¨at Mainz, Mainz, Germany Ludwig-Maximilians-Universit¨at M¨unchen, M¨unchen, Germany Fachbereich Physik, University of Wuppertal, Wuppertal, Germany Panjab University, Chandigarh, India Delhi University, Delhi, India Tata Institute of Fundamental Research, Mumbai, India University College Dublin, Dublin, Ireland Korea Detector Laboratory, Korea University, Seoul, Korea SungKyunKwan University, Suwon, Korea CINVESTAV, Mexico City, Mexico FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands Joint Institute for Nuclear Research, Dubna, Russia Institute for Theoretical and Experimental Physics, Moscow, Russia Moscow State University, Moscow, Russia Institute for High Energy Physics, Protvino, Russia Petersburg Nuclear Physics Institute, St. Petersburg, Russia Stockholm University, Stockholm, Sweden, and Uppsala University, Uppsala, Sweden Lancaster University, Lancaster, United Kingdom Imperial College London, London SW7 2AZ, United Kingdom The University of Manchester, Manchester M13 9PL, United Kingdom University of Arizona, Tucson, Arizona 85721, USA University of California, Riverside, California 92521, USA Florida State University, Tallahassee, Florida 32306, USA Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA University of Illinois at Chicago, Chicago, Illinois 60607, USA Northern Illinois University, DeKalb, Illinois 60115, USA Northwestern University, Evanston, Illinois 60208, USA Indiana University, Bloomington, Indiana 47405, USA Purdue University Calumet, Hammond, Indiana 46323, USA University of Notre Dame, Notre Dame, Indiana 46556, USA Iowa State University, Ames, Iowa 50011, USA University of Kansas, Lawrence, Kansas 66045, USA Kansas State University, Manhattan, Kansas 66506, USA Louisiana Tech University, Ruston, Louisiana 71272, USA University of Maryland, College Park, Maryland 20742, USA Boston University, Boston, Massachusetts 02215, USA Northeastern University, Boston, Massachusetts 02115, USA University of Michigan, Ann Arbor, Michigan 48109, USA Michigan State University, East Lansing, Michigan 48824, USA University of Mississippi, University, Mississippi 38677, USA University of Nebraska, Lincoln, Nebraska 68588, USA Rutgers University, Piscataway, New Jersey 08855, USA Princeton University, Princeton, New Jersey 08544, USA State University of New York, Buffalo, New York 14260, USA Columbia University, New York, New York 10027, USA University of Rochester, Rochester, New York 14627, USA State University of New York, Stony Brook, New York 11794, USA Brookhaven National Laboratory, Upton, New York 11973, USA Langston University, Langston, Oklahoma 73050, USA University of Oklahoma, Norman, Oklahoma 73019, USA Oklahoma State University, Stillwater, Oklahoma 74078, USA Brown University, Providence, Rhode Island 02912, USA University of Texas, Arlington, Texas 76019, USA Southern Methodist University, Dallas, Texas 75275, USA Rice University, Houston, Texas 77005, USA University of Virginia, Charlottesville, Virginia 22901, USA and University of Washington, Seattle, Washington 98195, USA (Dated: August 7, 2018)We have used a sample of γ + 3 jets events collected by the D0 experiment with an integratedluminosity of about 1 fb − to determine the fraction of events with double parton scattering ( f DP )in a single p ¯ p collision at √ s = 1 .
96 TeV. The DP fraction and effective cross section ( σ eff ), aprocess-independent scale parameter related to the parton density inside the nucleon, are measuredin three intervals of the second (ordered in p T ) jet transverse momentum p jet2 T within the range15 ≤ p jet2 T ≤
30 GeV. In this range, f DP varies between 0 . ≤ f DP ≤ .
47, while σ eff has theaverage value σ aveeff = 16 . ± . ± . PACS numbers: 14.20Dh, 13.85.Qk, 12.38.Qk
I. INTRODUCTION
Many features of high energy inelastic hadron collisionsdepend directly on the parton structure of hadrons. Theinelastic scattering of nucleons need not to occur onlythrough a single parton-parton interaction and the con-tribution from double parton (DP) collisions can be sig-nificant. A schematic view of a double parton scatteringevent in a p ¯ p interaction is shown in Fig. 1. The rate ofevents with multiple parton scatterings depends on howthe partons are spatially distributed within the nucleon. Theoretical discussions and estimations [1–5] stimulatedmeasurements [6–9] of DP event fractions and DP crosssections. The latter can be expressed as σ DP ≡ m σ A σ B σ eff , (1)where σ A and σ B are the cross sections of two inde-pendent partonic scatterings A and B . The factor m is equal to unity when processes A and B are indistin-guishable while m = 2 otherwise [5, 10, 11]. The process-independent scaling parameter σ eff has the units of cross pp A s B s FIG. 1: Diagram of a double parton scattering event. section. Its relation to the spatial distribution of partonswithin the proton has been discussed in [1, 3–5, 10, 11].The ratio σ B /σ eff can be interpreted as the probabilityfor partonic process B to occur provided that process A has already occurred. If the partons are uniformlydistributed inside the nucleon (large σ eff ), σ DP will berather small and, conversely, it will be large for a highlyconcentrated parton spatial density (small σ eff ). The im-plication and possible correlations of parton momentadistribution functions in (1) are discussed in [12–14].In addition to constraining predictions from variousmodels of nucleon structure and providing a better under-standing of non-perturbative QCD dynamics, measure-ments of f DP and σ eff are also needed for the accurateestimation of backgrounds for many rare new physics pro-cesses as well as for Higgs boson searches at the Tevatronand LHC [15, 16].To date, there have been only four dedicated measure-ments studying double parton scattering: by the AFSCollaboration in pp collisions at √ s = 63 GeV [6], by theUA2 Collaboration in p ¯ p collisions at √ s = 630 GeV [7],and twice by the CDF Collaboration in p ¯ p collisions at √ s = 1 . σ DP and then σ eff ,and the γ +3 jets final state was used in [9] to extract f DP fractions and then σ eff . The obtained values of σ eff bythose experiments are σ eff ≈ σ eff > . σ eff = 12 . +10 . − . mb (CDF, four-jet)and σ eff = 14 . ± . +1 . − . mb (CDF, γ + 3 jets). Table Isummarizes all previous measurements of σ eff , σ DP , and f DP .This paper presents an analysis of hard inelastic eventswith a photon candidate (denoted below as γ ) and atleast 3 jets (referred to below as “ γ + 3 jets” events) col-lected with the D0 detector [17] at the Fermilab TevatronCollider with √ s = 1 .
96 TeV and an integrated luminos-ity of 1.02 ± − . In this final state, DP eventsare caused by two partonic scatterings, with γ +jets pro-duction in the first scattering and dijet production in thesecond. Thus, the rate of γ + 3 jets events and theirkinematics should be sensitive to a contribution from ad-ditional parton interactions. Differences in the types ofthe two final states ( γ +jets and dijets) and better en-ergy measurement of photons as compared with jets fa-cilitate differentiation between the two DP scatteringsas compared with the 4-jet measurements. Also, it was shown in [18] that a larger fraction of DP events is ex-pected in the γ + 3 jets final state as compared with the4-jet events. The large integrated luminosity allows usto select γ + 3 jets events at high photon transverse mo-mentum, 60 < p γT <
80 GeV (vs. p γT >
16 GeV inCDF [9]), with a larger photon purity [19]. The choiceof a high threshold on the photon momentum provides(a) a clean separation between the jet produced in thesame parton scattering from which the photon originatesand the jets originating from additional parton scatter-ings and (b) a better determination of the energy scale ofthe γ +jets process. Also, in contrast to [9], the jet trans-verse momenta are corrected to the particle level. Otherdifferences in the technique used for extracting σ eff aredescribed below.This paper is organized as follows. Section II briefly de-scribes the technique used to extract the σ eff parameter.Section III provides the description of the data samplesand selection criteria. Section IV describes the modelsused for signal and background events. In Section V weintroduce the variables which allow us to distinguish DPevents from other γ + 3 jets events and determine theirfraction. The procedure for finding the fractions of DPevents is described in Section VI. Section VII describesthe determination of other parameters needed to calcu-late σ eff . Results of the measurement are given in SectionVIII with their application to selected models of partondensity. II. TECHNIQUE FOR EXTRACTING σ eff FROMDATA
In the 4-jet analyses [6–8], σ eff was extracted from mea-sured DP cross sections using Monte Carlo (MC) mod-eling for signal and background events and QCD predic-tions for the dijet cross sections. Both MC modeling andthe QCD predictions suffer from substantial uncertaintiesleading to analogous uncertainties in σ eff . Another tech-nique for extracting σ eff was proposed in [9]. It uses onlyquantities determined from data and thus minimizes theimpact of theoretical assumptions. Here we follow thismethod and extract σ eff without theoretical predictionsof the γ + jets and dijets cross sections by comparing thenumber of γ + 3 jets events produced in DP interactionsin single p ¯ p collisions to the number of γ + 3 jets eventsproduced in two distinct hard interactions occurring intwo separate p ¯ p collisions in the same beam crossing. Thelatter class of events is referred to as double interaction(DI) events. Assuming uncorrelated parton scatteringsin the DP process [1–5, 11], DP and DI events should bekinematically identical. This assumption is discussed inAppendix A.Measurements of dijet production with jet p T & −
15 GeV [20] in both central and forward rapidity [21] re-gions indicate that the contribution from single and dou-ble diffraction events represents .
1% of the total dijetcross section. Therefore γ + jets and dijet events with jet TABLE I: Summary of the results, experimental parameters, and event selections for the double parton analyses performed bythe AFS, UA2 and CDF Collaborations.Experiment √ s (GeV) Final state p minT (GeV) η range σ eff σ DP , f DP AFS ( pp ), 1986 [6] 63 4 jets p jetT > | η jet | < ∼ σ DP /σ dijet = (6 ± . ± . p ¯ p ), 1991 [7] 630 4 jets p jetT > | η jet | < > . σ DP = 0 . ± .
20 nbCDF ( p ¯ p ), 1993 [8] 1800 4 jets p jetT > | η jet | < . . +10 . − . mb σ DP = (63 +32 − ) nb, f DP = (5 . +1 . − . )%CDF ( p ¯ p ), 1997 [9] 1800 γ + 3 jets p jetT > | η jet | < . p γ T > | η γ | < . . ± . +1 . − . mb f DP = (52 . ± . ± . p T >
15 GeV are produced predominantly as a result ofinelastic non-diffractive (hard) p ¯ p interactions. In a p ¯ p beam crossing with two hard collisions the probability fora DI event in that crossing can be expressed as P DI = 2 σ γj σ hard σ jj σ hard . (2)Here σ γj and σ jj are the cross sections to produce theinclusive γ + jets and dijet events, which combined givethe γ + 3 jets final state, and σ hard is the total hard p ¯ p interaction cross section. The factor 2 takes into accountthat the two hard scatterings, producing a γ + jets or di-jet event, can be ordered in two ways with respect to thetwo collision vertices in the DI events. The number of DIevents, N DI , can be obtained from P DI , after correctionfor the efficiencies to pass geometric and kinematic selec-tion criteria ǫ DI , the two-vertex event selection efficiency, ǫ , and the number of beam crossings with two hardcollisions, N : N DI = 2 σ γj σ hard σ jj σ hard N ǫ DI ǫ . (3)Analogously to P DI , the probability for DP events, P DP , in a beam crossing with one hard collision, is P DP = σ DP σ hard = σ γj σ eff σ jj σ hard , (4)where we used Eq. (1). Then the number of DP events, N DP , can be expressed from P DP with a correction forthe geometric and kinematic selection efficiency ǫ DP , thesingle-vertex event selection efficiency ǫ , and the num-ber of beam crossings with one hard collision, N : N DP = σ γj σ eff σ jj σ hard N ǫ DP ǫ . (5)The ratio of N DP to N DI allows us to obtain the ex-pression for σ eff in the following form: σ eff = N DI N DP ε DP ε DI R c σ hard , (6)where R c ≡ (1 / N /N )( ε /ε ). The σ γj and σ jj cross sections do not appear in this ratio and all the remaining efficiencies for DP and DI events enteronly as ratios, resulting in a reduction of the impact ofmany correlated systematic uncertainties.Figure 2 shows the possible configurations of signal γ + 3 jets DP events produced in a single p ¯ p interactionand having one parton scattering in the final state witha γ and at least one jet, superimposed with another par-ton scattering into a final state with at least one jet.We define different event topologies as follows. Eventsin which both jets from the second parton scattering arereconstructed, pass the selection cuts and are selectedas the second and third jets, in order of decreasing jet p T , are defined as Type I. In Type II events, the secondjet in the dijet process is either lost due to the finite jetreconstruction efficiency of detector acceptance or takesthe fourth position after the jet p T ordering. We also dis-tinguish Type III events, in which a jet from the secondparton interaction becomes the leading jet of the final3-jets system, although they are quite rare given the p T range selected for the photon.The main background for the DP events are single par-ton (SP) scatterings with hard gluon bremsstrahlung inthe initial or final state qg → qγgg , q ¯ q → gγgg that givethe same γ + 3 jets signature. They are also shown inFig. 2. The fraction of DP events is determined in thisanalysis using a set of variables sensitive to the kinematicconfigurations of the two independent scatterings of par-ton pairs (see Secs. V and VI).The DI events differ from the DP events by the factthat the second parton scattering happens at a separate p ¯ p collision vertex. The DI events, with the photon andat least one jet from one p ¯ p collision, and at least onejet from another p ¯ p collision are shown in Fig. 3 with asimilar (to DP) set of DI event types. The background toDI events is due to two-vertex SP events with hard γ +3 jets events from one p ¯ p interaction with an additionalsoft interaction, i.e. having no reconstructed jets. Thediagrams for these non-DI events are also shown in Fig. 3. III. D0 DETECTOR AND DATA SAMPLES
The D0 detector is described in detail in [17]. Photoncandidates are identified as isolated clusters of energydepositions in the uranium and liquid-argon sampling
DP Type I DP Type II DP Type III SP g T p g T p g T p g T p jet1T p jet1T p jet1T p jet1T p jet2T p jet2T p jet2T p jet2T p jet3T p jet3T p jet3T p jet3T p FIG. 2: Diagrams of DP Types I, II, III and SP γ + 3 jetsevents. For DP events, the light and bold lines correspond totwo separate parton interactions. The dotted line representsunreconstructed jet. DI Type I DI Type II DI Type III SP g T p g T p g T p g T p jet1T p jet1T p jet1T p jet1T p jet2T p jet2T p jet2T p jet2T p jet3T p jet3T p jet3T p jet3T p FIG. 3: Diagrams of DI Types I, II, III and SP γ + 3 jetsevents. For DI events, the light and bold lines correspondto two separate p ¯ p interactions. The dotted line representsunreconstructed jet. calorimeter. The central calorimeter covers the pseudo-rapidity [22] range | η | < . . < | η | < .
2. The electromagnetic (EM) sectionof the calorimeter is segmented longitudinally into fourlayers and transversely into cells in pseudorapidity andazimuthal angle ∆ η × ∆ φ = 0 . × . . × .
05 in thethird layer of the EM calorimeter). The hadronic por-tion of the calorimeter is located behind the EM section.The calorimeter surrounds a tracking system consistingof silicon microstrip and scintillating fiber trackers, bothlocated within a 2 T solenoidal magnetic field.The events used in this analysis should first pass trig-gers based on the identification of high p T clusters inthe EM calorimeter with loose shower shape require-ments for photons. These triggers are 100% efficient for p γT >
35 GeV. To select photon candidates in our datasamples, we use the following criteria [19]. EM objectsare reconstructed using a simple cone algorithm with acone size R = p (∆ η ) + (∆ φ ) = 0 .
2. Regions withpoor photon identification capability and limited p γT res-olution, at the boundaries between calorimeter modulesand between the central and endcap calorimeters, areexcluded from analysis. Each photon candidate was re-quired to deposit more than 96% of detected energy inthe EM section of the calorimeter and to be isolated inthe angular region between R = 0 . R = 0 . E isoTot − E isoCore ) /E isoCore < . E isoTot is overall (EM+hadronic) tower energy in the( η, φ ) cone of radius R = 0 . E isoCore is EM tower en-ergy within a radius of R = 0 .
2. Candidate EM clusters matched to a reconstructed track are excluded from theanalysis. Clusters are matched to a reconstructed trackby computing a χ function which evaluates the consis-tency, within uncertainties, between the reconstructed η and φ positions of the cluster and of the closest trackextrapolated to the finely-segmented third layer of theEM calorimeter. The corresponding χ probability isrequired to be < . . ≤ R ≤ . .
7. Jets must satisfy quality cri-teria which suppress background from leptons, photons,and detector noise effects. To reject background fromcosmic rays and W → ℓν decay, the missing transversemomentum in the event is required to be less than 0 . p γT .All pairs of objects in the event, (photon, jet) or (jet,jet), also are required to be separated in η − φ space by∆ R > . γ in the rapidityregion | y | < . . < | y | < . | y | < .
0. Events are selected with γ transversemomentum 60 < p γT <
80 GeV, leading (in p T ) jet p T >
25 GeV, while the next-to-leading (second) and third jetsmust have p T >
15 GeV. The jet transverse momentaare corrected to the particle level. The high p γT scale (i.e.the scale of the first parton interaction) allows a betterseparation of the first and second parton interactions inmomentum space.Data events with a single p ¯ p collision vertex, whichcompose the sample of DP candidates (“1Vtx” sample),are selected separately from events with two verticeswhich compose the sample of DI candidates (“2Vtx” sam-ple). The collision vertices in both samples are requiredto have at least three associated tracks and to be within60 cm of the center of the detector along the beam ( z )axis.The p T spectrum for jets from dijet events falls fasterthan that for jets resulting from initial or final state radi-ation in the γ + jets events, and thus DP fractions shoulddepend on the jet p T [1, 3, 4, 10]. The DP fractionsand σ eff are determined in three p jet2 T bins: 15–20, 20–25,and 25–30 GeV. The total numbers of 1Vtx and 2Vtx γ + 3 jets events remaining in each of the three p jet2 T binsafter all selection criteria are given in Table II. TABLE II: The numbers of selected 1Vtx and 2Vtx γ + 3 jetsevents in bins of p jet2 T .Data p jet2 T (GeV)Sample 15 −
20 20 −
25 25 − IV. DP AND DI MODELS
To study properties of DP and DI events and calcu-late their fractions in the 1Vtx and 2Vtx samples, re-spectively, we construct DP and DI models by pairingdata events. The DP model is constructed by overlay-ing in a single event one event of an inclusive sampleof γ + ≥ p T from the MB events is recalculatedrelative to the vertex of the γ +jet event. The resultingmixed events, with jets re-ordered in p T , are requiredto pass the γ + 3 jets event selections described above.This model of DP events, called MixDP, assumes inde-pendent parton scatterings, with γ + jets and dijet finalstates, by construction. The mixing procedure is shownschematically in Fig. 4. + a) b) + MixDP
FIG. 4: Description of the mixing procedure used to preparethe MixDP signal sample. Two combinations of mixing γ + 1jet and two jets from dijet events (a) and γ + 2 jets andone jet from dijet events (b) are considered. The dotted linerepresents a jet failing the selection requirements. In the DI model, called MixDI, each event is con-structed by mixing one event of the γ + ≥ ≥ ≥ p T , are required tooriginate from the same vertex using the position alongthe beam axis of the point of closest approach to a ver-tex for the tracks associated to each jet and a cut on theminimal jet charged particle fraction, as discussed in Ap-pendix B. We consider the two-vertex γ + jets and dijetevents, components of the MixDI model, to better takeinto account the underlying energy, coming from the softinteractions of the spectator partons. The amount of thisenergy is different for single– and two-vertex events andcauses a difference in the photon and jet identificationefficiencies in the DP and DI events (see Section VII).As a background to the DI events, we consider the two-vertex γ +3 jets sample without a hard interaction at thesecond vertex (Bkg2Vtx sample), obtained by imposingthe direct requirement that all three jets originate fromthe same vertex using the jet track information.The fractions of Type I (II) events in the MixDP andMixDI samples are the same within 1 .
5% for each p jet2 T bin and vary for both samples from 26% (73%) at 15 < p jet2 T <
20 GeV to (14–15)% [(84–86)%] at 25 < p jet2 T <
30 GeV. Type III events are quite rare and their fractiondoes not exceed 1%. The MixDP and MixDI sampleshave similar kinematic ( p T and η ) distributions for thephoton and all the jets. They differ only by the amountof energy coming from soft parton interactions in eitherone or two p ¯ p collisions, which may affect the photon andthe jet selection efficiencies. V. DISCRIMINATING VARIABLES
A distinctive feature of the DP events is the presenceof two independent parton-parton scatterings within thesame p ¯ p collision. We define variables sensitive to thekinematics of DP events, specifically to the difference be-tween the p T imbalance of the two object pairs in DP andSP γ + 3 jets events as [4]:∆ S ≡ ∆ φ ( ~p T ( γ, i ) , ~p T ( j, k )) , (7)where the indices i, j, k (= 1 , ,
3) run over the jets inthe event. Here ~p T ( γ, i ) = ~p γT + ~p jet i T and ~p T ( j, k ) = ~p jet j T + ~p jet k T , where the two object pairs, ( γ , jet i ) and (jet j , jet k ), are selected to give the minimal p T imbalance.These pairs are found by minimizing S p T , or S p ′ T , or S φ defined as S p T = 1 √ s(cid:18) | ~p T ( γ, i ) | δp T ( γ, i ) (cid:19) + (cid:18) | ~p T ( j, k ) | δp T ( j, k ) (cid:19) , (8) S p ′ T = 1 √ vuuut | ~p T ( γ, i ) || ~p γT | + (cid:12)(cid:12) ~p iT (cid:12)(cid:12) ! + | ~p T ( j, k ) | (cid:12)(cid:12)(cid:12) ~p jT (cid:12)(cid:12)(cid:12) + (cid:12)(cid:12) ~p kT (cid:12)(cid:12) , (9) S φ = 1 √ s(cid:20) ∆ φ ( γ, i ) δφ ( γ, i ) (cid:21) + (cid:20) ∆ φ ( j, k ) δφ ( j, k ) (cid:21) . (10)In Eq. (10) ∆ φ ( γ, i ) = | π − φ ( γ, i ) | is the supplementto π of the minimal azimuthal angle between the vectors ~p γT and ~p jet i T , φ ( γ, i ).The uncertainties δp T ( γ, i ) in Eq. (8) and δφ ( γ, i ) inEq. (10) are calculated as root-mean-square values ofthe | ~p T ( γ, i ) | and ∆ φ ( γ, i ) distributions using the sig-nal MixDP sample for each of the three possible pair-ings. Azimuthal angles and uncertainties for jets j and k are defined analogously to those for the photon and jet i . Any of the S-variables in Eqs. (8)–(10) represents asignificance of the pairwise p T -imbalance. On average, itshould be higher for the SP events than for the DP events.Also, each S-variable effectively splits the γ + 3 jets sys-tem into γ +jet and dijet pairs, based on the best pairwisebalance.The two best p T -balancing pairs, which give the min-imum S for each of three variables in Eqs. (8) – (10),are used to calculate the corresponding ∆ S variables,∆ S p T , ∆ S p ′ T and ∆ S φ , according to Eq. (7). The∆ S p T , ∆ S p ′ T variables are also used in [7, 9], while the∆ S φ is first introduced in this measurement.Figure 5 illustrates a possible orientation of the trans-verse momenta vectors of the photon and jets as well astheir p T imbalances vectors, ~ P and ~ P , in γ + 3 jetsevents. In SP events, the topologies with the two radia-tion jets emitted close to the leading jet (recoiling againstthe photon direction in φ ) are preferred. The resultingpeak at ∆ S = π is smeared by the effects of additionalgluon radiation and detector resolution. For a simplemodel of DP events, we have exact pairwise balance in p T and thus ∆ S will be undefined. The exact p T balancein the pairs can be violated due to either detector resolu-tion or additional gluon radiation. Both effects introducean additional random contribution to the azimuthal an-gle between the γ +jet and the dijet p T imbalance vectors,broadening the ∆ S distribution (see also Fig. 9 below). g T p jet1T p jet2T p jet3T p P PS D FIG. 5: A possible orientation of photon and jets transversemomenta vectors in γ + 3 jets events. Vectors ~ P and ~ P are the p T imbalance vectors of γ +jet and jet-jet pairs. Thefigure illustrates a general case for the production of γ +3 jets+X events. VI. FRACTIONS OF DP AND DI EVENTSA. Fractions of DP events
To extract the fractions of DP events, we exploitthe difference in the p T spectrum of DP and radiationjets, mentioned in Sec. III, and consider data in twoadjacent p jet2 T intervals: DP-enriched at smaller p jet2 T andDP-depleted at larger p jet2 T [1, 3, 4]. The distribution foreach ∆ S variable in data ( D ) can be expressed as a sumof signal (DP) and background (SP) distributions: D = f M + (1 − f ) B (11) D = f M + (1 − f ) B , (12)where M i and B i stand for the signal MixDP and back-ground distributions, f i is the DP fraction, (1 − f i ) isthe SP fraction, and indices 1, 2 correspond to the DP-enriched and DP-depleted data sets. Multiplying (12) by λK and subtracting from (11) we obtain: D − λKD = f M − λKCf M , (13) where λ = B /B is the ratio of the background distri-butions, and K = (1 − f ) / (1 − f ) and C = f /f arethe ratios of the SP and DP fractions between the DP-enriched and DP-depleted samples, respectively. In con-trast to [9], we introduce a factor λ that corrects for therelative difference of ∆ S shapes for the SP distributionsin adjacent p jet2 T intervals. It is obtained using MonteCarlo (MC) γ + 3 jets events generated with pythia [25]without multiple parton interactions and with a full sim-ulation of the detector response and is found to be in therange 0 . − . S . The factor C is extracted using ratios of the numbers of events in dataand MixDP samples in the adjacent bins by C = (cid:0) N MixDP2 /N data2 (cid:1) / (cid:0) N MixDP1 /N data1 (cid:1) , (14)i.e. without actual knowledge of DP fractions in thosebins. Thus, the only unknown parameter in Eq. (13)is the DP fraction f . It is obtained from a χ mini-mization of Eq. (13) using minuit [26]. The fit was per-formed for each pair of p jet2 T bins (15 − / −
25 GeVand 20 − / −
30 GeV) and for each of ∆ S variables(8)–(10). The DP fractions in the last bin, 25 < p jet2 T <
30 GeV, are calculated from f = Cf . The extractedDP fractions are shown in Fig. 6. The DP fractions, av- (GeV) jet2T p
16 18 20 22 24 26 28 30 F r ac t i on o f D P eve n t s f S D from T p S D from T p’ S D from -1 = 1.0 fb int DØ, L
FIG. 6: Fractions of DP events extracted with the ∆ S φ ,∆ S p T , and ∆ S p ′ T variables in the three p jet2 T intervals. eraged over the three ∆ S variables (with uncertainties),are summarized in Table III. The location of the pointsin Fig. 6 corresponds to the mean p jet2 T for the DP modelin a given bin. They are also shown in Table III as h p jet2 T i .The uncertainties are mainly caused by the statistics ofthe data and MixDP samples (used in the fitting) andpartially by the determination of λ (2 − TABLE III: Fractions of DP events in the three p jet2 T bins. p jet2 T GeV h p jet2 T i (GeV) f DP −
20 17 . . ± . −
25 22 . . ± . −
30 27 . . ± . Since each component of a MixDP signal event maycontain two jets, where one jet may be caused by an f S D f S D / N d N / d f S D f S D / N d N / d ) M DP model (f) Data (D (a) -1 = 1.0 fb int DØ, L < 20 GeV jet2T
15 < p f S D f S D / N d N / d f S D f S D / N d N / d ) M DP model (f) Data (D (b) < 25 GeV jet2T
20 < p f S D f S D / N d N / d f S D f S D / N d N / d DP modelData Prediction for DP (c) f S D f S D / N d N / d f S D f S D / N d N / d <20 GeV jet2T jet2T FIG. 7: Results of the two datasets fit for the ∆ S φ vari-able for the combination of two p jet2 T bins 15 −
20 GeV and20 −
25 GeV. (a) and (b) show distributions for data (points)and the DP model (shaded area); (c) shows the predictionfor DP from data (points), corrected to remove SP contribu-tion, and the DP model (shaded area) as a difference betweenthe corresponding distributions of (a) and (b); (d) shows theextracted SP distributions in the two bins. The error barsin (a) and (b) are only statistical, while in (c) and (d) theyrepresent total (statistic and systematic) uncertainty. additional parton interaction, the MixDP sample shouldsimulate the properties of the double plus triple parton(TP) interactions (DP+TP), and thus the fractions inTable III take into account a contribution from tripleinteractions as well. In this sense, the DP cross sectioncalculated using Eqs. (1) and (6) is inclusive [27, 28].Figure 7 shows tests of the fit results for f usingthe ∆ S φ variable for the combination of two p jet2 T bins,15 −
20 GeV and 20 −
25 GeV. Figure 7(a) show the ∆ S φ distributions for the DP-enriched data set in data ( D )and the MixDP sample ( M ) weighted with its fraction f . Figure 7(b) shows analogous distributions for theDP-depleted dataset: data ( D ) and the MixDP sample( M ) weighted with its fraction f . It can be concludedfrom the two distributions that the regions of small ∆ S φ ( . .
5) is mostly populated by signal events with two in-dependent hard interactions. Figure 7(c) shows the dif-ference between the data distributions of Figs. 7(a) and7(b), corrected to remove the SP contribution by the fac-tor λK (the factor λ corrects for the relative difference ofthe ∆ S φ shapes and K corrects for the difference in theSP fractions in the two adjacent p jet2 T bins) [left side ofEq. (13)] and compared to the MixDP prediction [rightside of Eq. (13)]. As expected, the difference is alwayspositive since the fractions of DP events drop with p jet2 T .The DP model provides an adequate description of the f S D f S D / N d N / d f S D f S D / N d N / d ) M DP model (f) Data (D (a) -1 = 1.0 fb int DØ, L < 25 GeV jet2T
20 < p f S D f S D / N d N / d f S D f S D / N d N / d ) M DP model (f) Data (D (b) < 30 GeV jet2T
25 < p f S D f S D / N d N / d f S D f S D / N d N / d DP modelData Prediction for DP (c) f S D f S D / N d N / d f S D f S D / N d N / d <25 GeV jet2T jet2T FIG. 8: Same as in Fig. 7 but for the other combination of p jet2 T bins, 20 −
25 GeV and 25 −
30 GeV. data. In Fig. 7(d) we extract the SP distributions by sub-tracting the estimated DP contributions from the data:( D − f M ) / (1 − f ) for the DP-enriched data set and( D − f M ) / (1 − f ) for the DP-depleted data sets. Fig-ure 8 shows the analogous test of the fit results for theother pair of p jet2 T bins, 20 −
25 GeV and 25 −
30 GeV.Predictions for SP events are obtained using pythia .The ∆ S p ′ T distribution for γ + 3 jets events simulatedwith initial and final state radiation (ISR and FSR) andwithout multiple parton interactions (MPI) is shown inFig. 9 for the interval 15 < p jet2 T <
20 GeV. Since the ~p T imbalance of the two additional jets should compen-sate the ~p T imbalance of the “ γ +leading jet” system, the∆ S p ′ T distribution is shifted towards π . This distribu-tions shows good agreement with the results for the SPsample shown in Fig. 7(d). The DP γ + 3 jets events are T p’ S D T p ’ S D / N d N / d T p’ S D T p ’ S D / N d N / d IFSR=ON, MPI=OFFIFSR=OFF, Tune A-CRPYTHIA 6.420
FIG. 9: ∆ S p ′ T distributions for γ + 3 jets events simulated us-ing pythia with ISR/FSR but with MPI switched off (shadedregion), as well as for γ + 3 jets events without ISR/FSR butMPI switched on using Tune A-CR (triangle markers). Thebin 15 < p jet2 T <
20 GeV is considered. pythia parameters Tune A-CR [25]. In this case, the two subleading jets may orig-inate only from the second parton interaction (as in DPevents of Type I, see Fig. 2). As expected, the ∆ S p ′ T dis-tribution for these events is uniform, since the two p T balance vectors for the two systems, γ + jets and dijets,are independent from each other.Another source of background to the single-vertex γ +3 jets DP events is caused by double p ¯ p collisions close toeach other along the beam direction, for which a singlevertex is reconstructed. This was estimated separatelyand found to be negligible with a probability < − . B. Fractions of DI events
The DI fractions, f DI , are extracted by fitting theshapes of the ∆ S distributions of the MixDI signal andBkg2Vtx background samples to that for the 2Vtx datausing the technique described in [29]. Uncertainties aremainly caused by the fitting procedure and by buildingBkg2Vtx and MixDI (in case of Type I events) mod-els. To estimate the uncertainty due to the Bkg2Vtx orMixDI models, we vary a cut on the minimal jet chargedparticle fraction (see Appendix B) from 0.5 to 0.75. Thefitted f DI in this case varies in different p jet2 T bins within(3 − f DI values with total uncertainties are 0 . ± .
029 for15 < p jet2 T <
20 GeV, 0 . ± .
027 for 20 < p jet2 T <
25 GeV,and 0 . ± .
025 for 25 < p jet2 T <
30 GeV. The relative f DI uncertainties grow with increasing p jet2 T . This is causedby a decreasing probability for a jet to originate from asecond p ¯ p collision vertex. As a consequence, the sen-sitivity to DI events in the 2Vtx data sample becomessmaller.Figure 10 shows the ∆ S φ distributions for the two-vertex γ + 3 jets events selected in three p jet2 T intervals,15 −
20 GeV, 20 −
25 GeV and 25 −
30 GeV, for the DImodel (MixDI) and the total sum of MixDI and Bkg2Vtxdistributions, weighted with the DI fraction, and com-pared to 2Vtx data. The weighted sums of the signaland background samples reproduce the shapes of the datadistributions.
VII. DP AND DI EFFICIENCIES, R c AND σ hard A. Ratio of photon and jet efficiencies in DP andDI events
The selection efficiencies for DP and DI events enterEq. (6) only as ratios, canceling many common correc-tion factors and correlated systematic uncertainties. TheDP and DI events differ from each other by the num-ber of p ¯ p collision vertices (one vs. two), and thereforetheir selection efficiencies ε DI and ε DP may differ due to f S D f S D / N d N / d f S D f S D / N d N / d jet2T
15 < p -1 = 1.0 fb int DØ, L (a) f S D f S D / N d N / d f S D f S D / N d N / d jet2T
20 < p (b) f S D f S D / N d N / d f S D f S D / N d N / d jet2T
25 < p (c)
FIG. 10: ∆ S φ distributions for two-vertex γ + 3 jets eventsin the three p jet2 T intervals: (a) 15 −
20 GeV, (b) 20 −
25 GeVand (c) 25 −
30 GeV. MixDI and the total sum of the MixDIand Bkg2Vtx distributions (shaded histograms) are weightedwith their fractions found from the fit, compared to 2Vtx data(black points). The shown uncertainties are only statistical. different amounts of soft unclustered energy in the sin-gle and double p ¯ p collision events. This could lead toa difference in the jet reconstruction efficiencies, due tothe different probabilities of passing the jet selection re-quirement p T > γ + jets and di-jet MC events and also MixDI and MixDP data sam-ples. The MC events are generated with pythia [25]and processed through a geant -based [30] simulation ofthe D0 detector response. In order to accurately modelthe effects of multiple proton-antiproton interactions anddetector noise, data events from random p ¯ p crossings areoverlaid on the MC events using data from the same timeperiod as considered in the analysis. These MC eventsare then processed using the same reconstruction code asfor the data. We also apply additional smearing to thereconstructed photon and jet p T so that the measure-ment resolutions in MC match those in data. The MCevents are preselected with the vertex cuts and split intothe single– and two-vertex samples.The efficiencies for the photon selection criteria areestimated using γ + jets MC events. We found that theratio of photon efficiencies in single-vertex ( ε γ ) to thatin two-vertex samples ( ε γ ) does not have a noticeabledependence on p jet2 T and can be taken as ε γ /ε γ = 0 . ± .
03. The purity of γ + jets events in the interval of 60
80 GeV in data is expected to be about 75% [19],and the remaining events are mostly dijet events with1one jet misidentified as photon. An analogous analysis ofthe MC dijet events gives the ratio of the efficiencies forjets to be misidentified as photons equal to 0 . ± . ε γ /ε γ value found with thesignal γ + jets sample.The ratio of jet efficiencies is calculated in two steps.First, the efficiencies are estimated with respect to a re-quirement to have at least three jets with p jet1 T >
25 GeV, p jet2 T >
15 GeV, and p jet3 T >
15 GeV. These efficienciesare calculated using MC γ + jets and dijet events mixedaccording to the fractions of the three main MixDP andMixDI event types, described in Sec. IV. The ratio ofefficiencies for other jet selections (e.g. to get into the p jet2 T interval and satisfy ∆ R and jet rapidity selections)has been calculated using MixDP and MixDI signal datasamples. The total ratio of DP/DI jet efficiencies isfound to be stable for all p jet2 T bins and equal to 0 . ∼
5% uncertainty. Thus, the overall ratio of photonand jet DP/DI selection efficiencies ε DP /ε DI is about 0 . p jet2 T bins varying within(5 . − . B. Vertex efficiencies
The vertex efficiency ε ( ε ) corrects for the single(double) collision events that are lost in the DP (DI)candidate sample due to the single (double) vertex cuts( | z vtx | <
60 cm and ≥ ε /ε iscalculated from the data and found to be 1 . ± .
01 forall p jet2 T bins. The probability to miss a hard interactionevent with at least one jet with p T >
15 GeV due toa non-reconstructed vertex is calculated in γ + jets andminimum bias data and found to be (0 . − . γ + jets and dijet MC events with atleast one reconstructed jet with p T >
15 GeV and foundto be less than 0 . C. Calculating σ hard , N and N The numbers of expected events with one ( N ) andtwo ( N ) p ¯ p collisions resulting in hard interactionsare calculated from the known instantaneous luminosityspectrum of the collected data ( L inst ), the frequency ofbeam crossings ( f cross ) for the Tevatron [17], and the hard p ¯ p interaction cross section ( σ hard ).The value of σ hard at √ s = 1 .
96 TeV is ob-tained in the following way. We use the inelas-tic cross section calculated at √ s = 1 .
96 TeV, σ inel (1 .
96 TeV) = 60 . ± . √ s = 1 . √ s = 1 .
96 TeV, σ SD (1 .
96 TeV) and σ DD (1 .
96 TeV), weuse SD and DD cross sections measured at √ s = 1 . σ SD (1 . . ± .
44 mb [32] and σ DD (1 . . ± . ± . √ s = 1 .
96 TeV using the slowasymptotic behaviour predicted in [35]. We find σ hard (1 .
96 TeV) = σ inel (1 .
96 TeV) − σ SD (1 .
96 TeV) − σ DD (1 .
96 TeV) = 44 . ± .
89 mb . (15)We also do analogous estimates by calculating first σ hard at √ s = 1 . √ s = 1 . σ hard (1 .
96 TeV) =43 . ± .
63 mb which agrees well with Eq. (15).In each bin of the L inst spectrum, we calculatethe average number of hard p ¯ p interactions h n i =( L inst /f cross ) σ hard and then N and N are de-termined from h n i using Poisson statistics. Summingover all L inst bins, weighted with their fractions, we get N / (2 N ) = 1 .
169 and thus R c σ hard = 56 . ± . R c and σ hard en-ter Eq. (6) for σ eff as a product. Any increase of σ hard leads to an increase of h n i and, as a consequence, to adecrease in R c , and vice versa. Specifically, while thefound value of σ hard has a 6.5% relative uncertainty, theproduct R c σ hard has approximately 2% uncertainty. VIII. RESULTSA. Effective cross section
The calculation of σ eff is based on Eq. (6) of Sec. I.The numbers N DP and N DI in each p jet2 T bin are ob-tained from the numbers of the 1Vtx and 2Vtx γ + 3 jetsevents in Table II, multiplying them by f DP and f DI .The determination of all other components of Eq. (6)are described in Sec. VII. The resulting values of σ eff with total uncertainties (statistical and systematic aresummed in quadrature) are shown in Fig. 11 and givenin Table IV for the three p jet2 T bins. The location of thepoints in Fig. 11 corresponds to the mean p jet2 T for theDP model in a given bin (the mean p jet2 T values for DImodel are the same within 0.15 GeV). These values arealso shown in Table IV. Table V summarizes the mainsources of uncertainties for each p jet2 T bin. The main sys-tematic uncertainties are related to the determinationsof the DI fractions (dominant uncertainty), DP fractions,the ε DP /ε DI ratio, jet energy scale (JES), and R c σ hard ,giving a total systematic uncertainty of (20 . − . TABLE IV: Effective cross section σ eff in the three p jet2 T bins. p jet2 T GeV h p jet2 T i (GeV) σ eff (mb)15 −
20 17 . . ± . −
25 22 . . ± . −
30 27 . . ± . TABLE V: Systematic ( δ syst ), statistic ( δ stat ) and total δ total uncertainties (in %) for σ eff in the three p jet2 T bins. p jet2 T Systematic uncertainty sources δ syst δ stat δ total (GeV) f DP f DI ε DP /ε DI JES R c σ hard (%) (%) (%)15 – 20 7.9 17.1 5.6 5.5 2.0 20.5 3.1 20.720 – 25 6.0 20.9 6.2 2.0 2.0 22.8 2.5 22.925 – 30 10.9 29.4 6.5 3.0 2.0 32.2 2.7 32.3 The measured σ eff values in the different p jet2 T binsagree with each other within their uncertainties, how-ever a slow decrease with p jet2 T can not be excluded. The σ eff value averaged over the three p jet2 T bins is σ aveeff = 16 . ± . ± . . (16) (GeV) jet2T p
15 20 25 30 ( m b ) e ff s -1 = 1.0 fb int DØ, L
FIG. 11: Effective cross section σ eff (mb) measured in thethree p jet2 T intervals. B. Models of parton spatial density
In this section we study the limits that can be obtainedon the parameters of three phenomenological models ofparton spatial density using the measured effective crosssection (16). In the discussion below we follow a sim-ple classical approach. For a given parton spatial densityinside the proton or antiproton ρ ( r ), one can define a(time-integrated) overlap O ( β ) between the parton dis-tributions of the colliding nucleons as a function of theimpact parameter β [10]. The larger the overlap (i.e.smaller β ), the more probable it is to have at least oneparton interaction in the colliding nucleons. The singlehard scattering cross sections (for example, γ + jets or di-jet production) should be proportional to O ( β ) and thecross section for the double parton scattering is propor-tional to the squared overlap, both integrated over allimpact parameters β [28, 36]: σ eff = [ R ∞ O ( β ) 2 πβ d β ] R ∞ O ( β ) πβ d β . (17)First, we consider the “solid sphere” model with a con-stant density inside the proton radius r p . In this model,the total hard scattering cross section can be written as σ hard = 4 πr p and σ eff = σ hard /f . Here f is thegeometrical enhancement factor of the DP cross sec-tion. It is obtained by solving Eq. (17) for two overlap-ping spheres with a boundary conditions that the par-ton density ρ ( r ) = constant for r ≤ r p and ρ ( r ) = 0for r > r p and found to be f = 2 .
19. The role ofthe enhancement factor can be seen better if we rewriteEq. (1) as σ DP = f σ A σ B /σ hard . The harder the single-parton interaction is the more it is biased towards thecentral hadron-hadron collision with a small impact pa-rameter, where we have a larger overlap of parton den-sities and, consequently, higher probability for a sec-ond parton interaction [5]. Using the measured σ eff ,for the solid sphere model we extract the proton ra-dius r p = 0 . ± .
06 fm and proton rms-radius R rms =0 . ± .
05 fm. The latter is obtained from averaging r as R ≡ R ∞ r πr ρ ( r ) dr = 4 π R ∞ ρ ( r ) r dr [37].The results are summarized in the line “Solid Sphere”of Table VI. The Gaussian model with ρ ( r ) ∝ e − r / a and exponential model with ρ ( r ) ∝ e − r/b have been alsotested. The relationships between the scale parameter( r p , a or b ) and rms-radius for all the models are given inTable VI. The relationships between the effective crosssection σ eff and parameters of the Gaussian and expo-nential models are taken from [38], neglecting the termsthat represent correlations in the transverse space. Thescale parameters and rms-radii for both models are alsogiven in Table VI. In spite of differences in the models,the proton rms-radii are in good agreement with eachother, with average values varied as 0 . − .
47 and withabout 12% uncertainty. On the other hand, having ob-tained rms-radius from other sources (for example, [39])and using the measured σ eff , the size of the transversecorrelations [38] can be estimated. IX. SUMMARY
We have analyzed a sample of γ + 3 jets events col-lected by the D0 experiment with an integrated lumi-nosity of about 1 fb − and determined the fraction ofevents with hard double parton scattering occurring ina single p ¯ p collision at √ s = 1 .
96 TeV. These fractionsare measured in three intervals of the second (orderedin p T ) jet transverse momentum p jet2 T and vary from0 . ± .
041 at 15 ≤ p jet2 T ≤
20 GeV to 0 . ± .
027 at25 ≤ p jet2 T ≤
30 GeV.In the same three p jet2 T intervals, we calculate an ef-3 TABLE VI: Parameters of parton spatial density models calculated from measured σ eff .Model for density ρ ( r ) σ eff R rms Parameter (fm) R rms (fm)Solid Sphere Constant, r < r p πr p / . p / r p . ± .
06 0 . ± . e − r / a πa √ a . ± .
03 0 . ± . e − r/b πb √ b . ± .
02 0 . ± . fective cross section σ eff , a process-independent scaleparameter which provides information about the par-ton spatial density inside the proton and define therate of double parton events. The measured σ eff val-ues agree for the three p jet2 T intervals with an average σ aveeff = 16 . ± . ± . σ eff with respect to the considered energy scales.Using the measured σ eff we have calculated scale pa-rameters and rms-radii of the proton for three models ofthe parton matter distribution. Acknowledgements
We would like to thank T. Sj¨ostrand and P. Skands forvery useful discussions. We also thank the staffs atFermilab and collaborating institutions, and acknowl-edge support from the DOE and NSF (USA); CEAand CNRS/IN2P3 (France); FASI, Rosatom and RFBR(Russia); CNPq, FAPERJ, FAPESP and FUNDUNESP(Brazil); DAE and DST (India); Colciencias (Colombia);CONACyT (Mexico); KRF and KOSEF (Korea); CON-ICET and UBACyT (Argentina); FOM (The Nether-lands); STFC and the Royal Society (United Kingdom);MSMT and GACR (Czech Republic); CRC Program,CFI, NSERC and WestGrid Project (Canada); BMBFand DFG (Germany); SFI (Ireland); The Swedish Re-search Council (Sweden); and CAS and CNSF (China).
X. APPENDIX A
In this measurement we assume that the two parton in-teractions in the DP γ + 3 jets events can be consideredto be independent from each other. Possible correlationmay appear both in momentum space, since the two in-teractions have to share the same proton momentum, andat the fragmentation stage.In the hypothesis of two independent scatterings, thekinematic properties of SP dijet events should be verysimilar to those produced in the second parton interac-tion in the DP γ + 3 jets events. We compare the p T and η distributions for the two cases using the pythia eventgenerator, which includes momentum and flavor corre-lations among the partons participating in MPI. It alsoprovides the possibility of choosing different MPI mod- (GeV) jetT p
10 20 30 40 50 60 70 j e t T / N d N / dp , DP dijets jet2T p , SP dijets jet1T p PYTHIA 6.420, Tune A-CR (a) (GeV) jetT p
10 20 30 40 50 60 70 j e t T / N d N / dp , DP dijets jet3T p , SP dijets jet2T p (b) jet h -4 -3 -2 -1 0 1 2 3 4 j e t h / N d N / d , DP dijets jet2T p , SP dijets jet1T p (c) jet h -4 -3 -2 -1 0 1 2 3 4 j e t h / N d N / d , DP dijets jet3 h , SP dijets jet2 h (d) FIG. 12: Comparison of dijet events properties in SP (trian-gles) and in γ + 3 jets DP events (black circles): (a) and (c)show comparisons of the p T and η distribution of the second(ordered in p T ) jet in γ + 3 jets DP events with the first jetfrom the SP dijet events; (b) and (d) show comparisons of the p T and η distribution of the third jet in γ + 3 jets DP eventswith the second jet from the SP dijet events. Both types ofevents are generated without ISR and FSR effects but withMPI Tune A-CR. els. In our comparison we use the pythia parametersTune A-CR, which is usually considered as an exampleof a model with a strong color reconnection with an ex-treme prediction for track multiplicities and/or averagehadron p T [40]. As a model for the DP events, we simu-late γ + 3 jets events using Tune A-CR but with ISR andFSR effects turned off and applied all selection criteriaas described in Sec. III. This configuration of the eventgenerator guarantees that the two jets produced in addi-tion to the leading jet (and γ ) in the γ + 3 jets final statearise only from additional parton interactions. The ∆ S distribution for these events is shown in Fig. 9 (by tri-angles). The SP dijets events are also generated withoutISR and FSR. Figure 12(a) compares the p T spectra ofthe first (in p T ) jet from the second partonic collision inDP events (second jet in γ +3 jets events) and the first jetin the SP dijet events, while Fig. 12(b) make analogouscomparisons of the next (in p T ) jet in both event types.Figures 12(c) and 12(d) compare the η distributions of4these jets. We can see good agreement between the kine-matics of jets produced in the second parton interactionand those from the regular SP dijet events. Analogouscomparisons were performed using Tunes A and S0 withsimilar good agreement. This indicates the absence ofvisible correlations between the two DP scatterings withour selection criteria. XI. APPENDIX B
In building signal and background DI models inSec. IV, we take into account information about tracksassociated with jets. We use two algorithms. In the first,we consider all tracks inside a jet radius ( R = 0 . p T -weighted position in z of allthe tracks (“jet − z ”). Here the track z position is cal-culated at the point of closest approach of this track tothe beam ( z ) axis. For each jet in the 2Vtx data sample(Sec. III) we can estimate the distance between the jet − z and the p ¯ p vertex closest in z , ∆ z (Vtx , jet i ). These dis- tributions are shown in Fig. 13 for each jet in the γ +3 jets2Vtx sample. About (95–96)% [(97–99%)] of events have∆ z (Vtx , jet i ) < . .
0) cm.We also use an algorithm that is based on a jet chargedparticle fraction (CPF) and define a discriminant whichmeasures the probability that a given jet originatesfrom a particular vertex (a jet, having originated froma vertex, may still have tracks coming from anothervertex). The CPF discriminant is based on the fractionof charged transverse energy in each jet i (in the form oftracks) originating from each identified vertex j in theevent:CPF(jet i , Vtx j ) = P k p T (trk jet i k , Vtx j ) P n P l p T (trk jet i l , Vtx n ) . (18)To confirm that a given jet originate from a vertex, werequire ∆ z < . > .
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