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Diffractive photoproduction of heavy quarks in hadronic collisions V.P. Gonçalves a and M.V.T. Machado b a Instituto de F´ısica e Matemática, Universidade Federal de Pelotas Caixa Postal 354, CEP 96010-090, Pelotas, RS, Brazil b Centro de Ciências Exatas e Tecnológicas, Universidade Federal de Pelotas Campus de Bagé, Rua Carlos Barbosa. CEP 96400-970. Bagé, RS, Brazil In this letter we study the diffractive photoproduction of heavy quarks in hadronic (pp/pA/AA) interactions for Tevatron and LHC energies. The integrated cross section and rapidity distribution for the process h1h2 → h1h2QQ (hi = p,A and Q = c,b) are estimated using the Color Glass Condensate (CGC) formalism. Our results indicate that this production channel has larger cross sections than the competing reactions of double diffractive production and coherent AA reactions initiated bytwo-photon collisions. 7 PACSnumbers: 12.38.Bx;13.60.Hb 0 0 2 Introduction. TheQCDdynamicsathighenergiesisof tonstemmingfromtheelectromagneticfieldofoneofthe n utmost importance for building a realistic description of two colliding nuclei can interact with one photon of the a pp/pA/AAcollisionsatLHC.Theoretically,athighener- othernucleus(two-photonprocess)orcanpenetrateinto J giestheQCDevolutionleadstoasystemwithhighgluon the other nucleus andinteract with its hadrons(photon- 1 density,characterizedbythelimitationonthe maximum nucleus process), both possibilities has been studied in 3 phase-space parton density that can be reached in the the literature. In principle, the experimental signature hadronwavefunction(partonsaturation). Thetransition ofthesetwoprocessesisdistinctanditcaneasilybesep- 2 v is specified by a typical scale,which is energy dependent arated. While in two-photon interactions we expect the 5 andiscalledsaturationscaleQ (Forrecentreviewssee presenceoftworapiditiesgapsandnohadronbreakup,in sat 6 Ref. [1]). Signalsofpartonsaturationhavealreadybeen the inclusive heavy quarkphoton-hadronproduction the 2 observed both in ep deep inelastic scattering at HERA hadron target we expect only one rapidity gap and the 2 and in deuteron-gold collisions at RHIC (See, e.g. Refs. dissociation of the hadron. One of the main motivations 1 [2, 3]). However, the observation of this new regime still to analyze the diffractive heavy quark photoproduction 6 0 needs confirmation and so there is an active search for isthatweexpectthepresenceoftworapiditygapsinthe / new experimental signatures. Among them, the observ- final state, similarly to two-photon interactions. Conse- h ablesmeasuredindiffractiveprocessesdeservespecialat- quently, it is important to determine the magnitude of p tention. As shown in Ref. [4], the total diffractive cross thiscrosssectioninordertoestimatethebackgroundfor - p section is much more sensitive to large-size dipoles than two-photoninteractions. As discussedin Refs. [8, 9, 10], e the inclusive one. As saturation effects screen large-size theheavyquarkproductioninγγ interactionsisapprox- h dipole (soft) contributions, one has that a fairly large imately two or three orders of magnitude smaller than : v fractionofthecrosssectionishardandhenceeligiblefor the inclusive photoproduction cross sections. However, i aperturbativetreatment. Therefore,thestudyofdiffrac- the magnitude of the diffractive photoproduction cross- X tiveprocessesbecomesfundamentalinordertoconstrain section is still an open question. Another motivation for r a the QCD dynamics at high energies. our study is that the contribution of this process can be In this paper we propose to study diffractive interac- important in proton-proton collisions, where there is a tions in ultra-peripheral collisions of hadrons, which can dedicatedprogramtosearchevidenceoftheHiggsand/or be defined as collisions where no hadronic interactions new physics in centraldouble diffractive productionpro- occur because the large spatial separation between processes [13], which also are characterized by two rapidity jectile and target and the interaction is mediated by the gaps and has as main background the exclusive bb pro- electromagneticfield(ForrecentreviewsseeRef. [5]). In duction. particular,weanalyzethediffractive heavyquarkphoto- Ultra-peripheral collisions. The basic idea in ultra- production in pp/pA/AA collisions, which at the Large peripheral hadron collisions is that the total cross sec- HadronCollider(LHC)willallowphoton-hadroninterac- tion for a given process can be factorized in terms of tionstobestudiedatenergieshigherthanatanyexisting the equivalent flux of photons of the hadron projectile accelerator. In relativistic heavy ion colliders, the heavy andthephoton-photonorphoton-targetproductioncross nucleigiverisetostrongelectromagneticfields,whichcan section[5]. Inparticular,thephoton-hadroninteractions interactwitheachother. Inasimilarway,theseprocesses can be divided into exclusive and inclusive reactions. In also occur when considering energetic protons in pp(p¯) the first case, a certain particle is produced while the colliders. Over the past years a comprehensive analysis target remains in the ground state (or is only internally of the inclusive heavy quark [6, 7, 8, 9, 10, 11, 12] pro- excited). Ontheotherhand,ininclusiveinteractionsthe duction in ultraperipheral heavy ion collisions was made particle produced is accompanied by one or more parti- considering different theoretical approaches. As a pho- clesfromthebreakupofthetarget. Thetypicalexamples 2 oftheseprocessesaretheexclusivevectormesonproduc- h1h2 Collider cc bb tion,describedbytheprocessγh Vh(V =ρ,J/Ψ,Υ), → pp(p) RHIC 3.4 nb 3 ×10−3 nb and the inclusive heavy quark production [γh XY → TEVATRON 12.6 nb 0.021 nb (X =cc,bb)], respectively. In the last years we have dis- cussed in detail both processes considering pp [11, 14], LHC 92.0 nb 0.2 nb pA [15] and AA [10, 14] collisions as an alternative to pA LHC 54.0 µb 0.09 µb constrain the QCD dynamics at high energies. Here we AA LHC 59.0 mb 0.01 mb propose to analyze another exclusive process, characterized by the diffractive photoproduction of heavy quarks anddescribedbytheγh Xhreaction. Inthiscase,the → TABLEI:Theintegrated cross sectionforthediffractivepho- crosssectionforthediffractivephotoproductionofafinal toproduction of heavy quarks in pp/pA/AA collisions. state X in a ultra-peripheral hadron-hadron collision is given by with the notation Ω = 1 + [(0.71GeV2)/Q2 ] and ∞ min dN (ω) Q2 =ω2/[γ2(1 2ω/√S )] (ω/γ )2. σ(h1h2 →h1h2X) = dω dγω σγh→Xh Wγ2h ,(1) mQinCD dynamLics−at high enNeNrgies≈. TheLphoton-hadron ωmZin (cid:0) (cid:1) interaction at high energy (small x) is usually described in the infinite momentum frame of the hadron in terms where ω is the photon energy and dNγ(ω) is the equiva- of the scattering of the photon off a sea quark, which dω lent flux of photons from a charged hadron. Moreover, is typically emitted by the small-x gluons in the proton. ωmin = MX2/4γLmp, γL is the Lorentz boost of a single However,inordertodescribediffractiveinteractionsand beam, Wγ2h = 2ω√SNN and √SNN is the c.m.s energy disentangle the small-x dynamics of the hadron wave- of the hadron-hadron system. It is important to em- function, it is more adequate to consider the photon- phasize that the equivalent photon energies at the LHC hadron scattering in the dipole frame, in which most will be higher than at any existing accelerator. For in- of the energy is carried by the hadron, while the pho- stance, considering pPb collisions at LHC, the Lorentz ton has just enough energy to dissociate into a quark- factor is γL = 4690, giving the maximum c.m.s. γh en- antiquark pair before the scattering. In this represen- ergyWγp 1500GeV.Therefore,whilestudiesofphoto- tation the probing projectile fluctuates into a quark- ≈ production at HERA are limited to photon-proton cen- antiquark pair (a dipole) with transverse separation r ter of mass energies of about 200 GeV, photon-hadron longaftertheinteraction,whichthenscattersoffthetar- interactions at LHC can reach one order of magnitude get[17]. Themainmotivationtousethiscolordipoleap- higher on energy. Consequently, studies of γh interac- proachisthatitgivesasimpleunifiedpictureofinclusive tions at LHC could provide valuable information on the and diffractive processes. In particular, in this approach QCD dynamics at high energies. In this work we con- thediffractiveheavyquarkphotoproductioncrosssection sider that the produced state X represents a QQ pair. [γh QQh, h=p,A] reads as, Since photon emission is coherent over the entire pro- → ton/nucleus and the photon is colorless we expect that σD = d2bdzd2r Ψγ (z,r,Q2)2 2(x¯,r,b) ,(4) the diffractive eventsto be characterizedby tworapidity T,L | T,L | N Z gaps, in contrastwith the inclusive heavy quark produc- where Ψγ is the light-cone wavefunction of the photon tion. In these two-rapidity gaps events the heavy quark T,L [17]. The variable r defines the relative transverse sepa- pair is produced in the central rapidity region, whereas rationofthepair(dipole)andz(1 z)isthelongitudinal the beam particles often leave the interaction region in- − momentumfractionsofthequark(antiquark). Thebasic tact, and can be measured using very forwarddetectors. blocks are the photon wavefunction, Ψγ and the dipole- In the calculations what follows we consider that the target forward amplitude . For photoproduction we photon spectrum for a nuclei is given by [5] N have that longitudinal piece does not contribute, since dNγ(ω) = 2Z2αem η¯K0(η¯)K1(η¯)+ η¯2 (η¯) (2) |tΨroLd|u2c∝ingQt2h,eaanpdprthopertiaotteadl cmroassssasencdticohnarisgecoofmtphuetcehdarinm- dω πω 2 U (cid:20) (cid:21) or bottom quark. where η¯= ωR /γ and (η¯)=K2(η¯) K2(η¯), with In the Color Glass Condensate (CGC) formalism R = R +Reff(RL =U2R ) for1pA (A−A)0collisions. [18, 19, 20], encodes all the information about the eff p A eff A N On the other hand, for a proton, we assume that the hadronic scattering, and thus about the non-linear and photon spectrum is given by [16], quantum effects in the hadron wave function. The function can be obtained by solving an appropriate evo- N dN (ω) α 2ω 2 lution equation in the rapidity y ln(1/x). The main γ = em 1+ 1 properties of are: (a) for the ≡interaction of a small dω 2πω " (cid:18) − √SNN(cid:19) # dipole (r 1N/Q ), 1, which characterizes that sat ≪ N ≪ 11 3 3 1 this system is weakly interacting; (b) for a large dipole lnΩ + + , (3) − 6 Ω − 2Ω2 3Ω3 (r 1/Qsat), the system is strongly absorbed which (cid:18) (cid:19) ≫ 3 implies 1. This property is associate to the large Charm N ≈ density of saturatedgluons in the hadronwave function. 12 In our analysis of diffractive heavy quark production in photon-nucleus interactions we will consider the phe- pp (x 106) nomenological saturation model proposed in Ref. [21] 10 pA (x 103) AA which describes the experimental data for the nuclear structure function, with the forward dipole-nucleus am- ) 8 b plitude parameterized as follows m ( Y 6 1 d NA(x¯,r,b)=1−exp −2ATA(b)σ0Np(x¯,r2) ,(5) σd/ (cid:20) (cid:21) 4 whereT (b)is the nuclearprofilefunction, whichwillbe A obtained from a 3-parameter Fermi distribution for the 2 Q2+4m2 nuclear density, and x¯ = f . (For details see, e.g., W2 γp 0 Ref. [22]). Moreover, describes the dipole-proton in- -8 -6 -4 -2 0 2 4 6 8 Np Y teraction. In the literaturethere are severalphenomeno- logical models for this quantity. Here we will consider FIG.1: Rapiditydistributionfordiffractivecharmphotopro- the GBW model [4], which encodes the basic properties duction on pp/pA/AAreactions for LHCenergies (see text). of the saturation physics and assumes that Q2(x¯)r2 Bottom (x¯, r2) = 1 exp s , (6) p N − − 4 0.03 (cid:20) (cid:18) (cid:19)(cid:21) with Q2(x¯) = x0 λ GeV2 being the saturation scale, pp (x 106) s x¯ 0.025 pA (x 103) which depends on energy and defines the onset of AA (cid:0) (cid:1) the saturation phenomenon. The parameters were ob- 0.02 tained from a fit to the HERA data producing σ0 = b) m 23.03(29.12) mb, λ = 0.288(0.277) and x = 3.04 0 ( 10−4(0.41 10−4)fora3-flavor(4-flavor)analysis[4]. Itis· Y 0.015 important·to emphasizethatthe Eq. (5)sums upallthe σ/d d multipleelasticrescatteringdiagramsoftheqqpairandis 0.01 justified for large coherence length, where the transverse separation r of partons in the multiparton Fock state of 0.005 the photon becomes as gooda conservedquantity as the angular momentum, i. e. the size of the pair r becomes 0 eigenvalue of the scattering matrix. In our calculations -6 -4 -2 0 2 4 6 Y ofthediffractiveheavyquarkproductioninhadroniccol- lisionswewillassumethattheforwarddipole-targetam- FIG.2: Rapiditydistributionfordiffractivebottomphotopro- plitude is givenbyEq. (5)inthe caseofanucleartarget duction on pp/pA/AAreactions for LHCenergies (see text). and by Eq. (6) for a proton target. Results. The distribution on rapidity Y of the produced final state can be directly computed from Eq. as its luminosity is several orders of magnitude larger, (1), by using its relation with the photon energy ω, i.e. Namely, the corresponding luminosities are = 1034 pp Y ln(2ω/mX). Explicitly, the rapidity distribution is cm−2s−1, = 7.4 1029 cm2s−1 and L = 4.2 wr∝itten down as, 1026 cm−2Ls−p1P.b × LPbPb × Let us now compare the results to processes having dσ [h h h h X] dN (ω) 1 2 1 2 γ → =ω σγh→Xh(ω). (7) similar final state configuration. This analysis is im- dy dω portant since they are competing reactions. In Ref. Consequently, given the photon flux, the rapidity distri- [23], the double diffractive (DD) production of heavy bution is thus a direct measure of the diffractive pho- quarkshasbeen computed(without consideringrapidity toproduction cross section for a given energy. In Figs. gap survival correction, which diminishes the cross sec- 1 and 2 we present our results for the diffractive heavy tion). Summarizingthoseestimations,onehasforcharm quIanrkTpahbo.toIporondeupcrtieosnenattsLthHeCcoenrreersgpieosn.dent integrated σpbcDc¯D(L=HC45).−Fo2r08boptbto(mTe,voanterohna)saσnbDd¯bDσcD=c¯D17=−47−86p.b56(T×e1v0a4- crosssections. We havethatthe largercrosssectionsare tron)andσDD =0.5 1.5 104pb(LHC).Ourresultfor b¯b − × obtainedintheAAmode, followedbypAandpp modes. the pp mode are at least one order of magnitude larger. However,theeventratesshouldbehigherintheppmode Other process with similar configuration is the double 4 photon process in the AA mode. In Ref. [9], we ob- further addressed. tain the following values for coherent PbPb collision at It is important to emphasize that the same reaction, LHC energies: for charm, σγγ = 1.8 mb and for bottom h h h h X, also occurs via fusion of two Pomerons, cc¯ 1 2 1 1 σγγ = 2 µb. Our results are higher by a factor 30 for the so→-called central diffraction processes. However, the cc¯ charm and a factor 5 for bottom. transverse momenta of the scattered hadrons are pre- Summary. The QCD dynamics at high energies is of dicted to be much larger than in two-photon interac- utmost importance for building a realistic description of tions, which implies that the separation between these pp/pA/AA collisions at LHC. In this limit QCD evolu- twoprocessesisfeasible. Inthe caseofdiffractivephoto- tion leads to a system with high gluon density. In this production we expect an asymmetric distribution of the letter we havestudied the diffractive photoproductionof scattered hadrons, since photon and pomeron exchange heavyquarks,whichprovideafeasibleandclearmeasure- are present in the process. Moreover, as almost all of ment of the underlying QCD dynamics at high energies. the photoproduced heavy quarks, similarly to the vec- The advantages of this process are the clear final state tor mesons, should have small transverse momenta, it is (rapidity gaps and low momenta particles) and no com- possibletointroduce aselectioncriterionto separatethe peting effect of dense nuclear environment if compared diffractive photoproduction processes. with hadroproduction. However, as the present analy- Acknowledgments sis is predominantly phenomenologicalseveralpoints de- serve more detailed studies. For instance, the model de- pendence as well as estimative of background processes ThisworkwaspartiallyfinancedbytheBrazilianfund- andtheanalysisoftheexperimentalseparationhastobe ing agencies CNPq and FAPERGS. [1] E. Iancu and R. Venugopalan, arXiv:hep-ph/0303204; 71, 014025 (2005). V.P.GoncalvesandM.V.T.Machado,Mod.Phys.Lett. [12] M.Strikman,R.VogtandS.White,Phys.Rev.Lett.96, 19, 2525 (2004); H. Weigert, Prog. Part. Nucl. Phys. 082001 (2006). 55,461 (2005); J. Jalilian-Marian and Y.V.Kovchegov, [13] V.A.Khoze,A.D.MartinandM.G.Ryskin,Eur.Phys. Prog. Part. Nucl. Phys.56, 104 (2006). J. C 23, 311 (2002); arXiv:hep-ph/0605189. [2] J.P.BlaizotandF.Gelis,Nucl.Phys.A750,148(2005). [14] V.P.GoncalvesandM.V.T.Machado,Eur.Phys.J.C [3] V. P. Goncalves, M. S. Kugeratski, M. V. T. Machado 40, 519 (2005). and F. S. Navarra, Phys.Lett. B 643, 273 (2006). [15] V. P. Goncalves and M. V. T. Machado, Phys. Rev. C [4] K. Golec-Biernat and M. Wu¨sthoff, Phys. Rev. D 59, 73, 044902 (2006). 014017 (1999), ibid. D60, 114023 (1999). [16] M. Drees and D. Zeppenfeld, Phys. Rev. D 39, 2536 [5] G. Baur, K. Hencken, D. Trautmann, S. Sadovsky, Y. (1989). Kharlov, Phys. Rep. 364, 359 (2002); C. A. Bertulani, [17] N. N. Nikolaev, B. G. Zakharov, Phys.Lett. B 332, 184 S. R. Klein and J. Nystrand, Ann. Rev. Nucl. Part. Sci. (1994); Z. Phys.C 64, 631 (1994). 55, 271 (2005). [18] E. Iancu, A. Leonidov and L. McLerran, Nucl.Phys. [6] Ch.Hofmann,G.Soff,A.SchaferandW.Greiner, Phys. A692(2001)583;E.Ferreiro,E.Iancu,A.Leonidovand Lett. B 262, 210 (1991); N. Baron and G. Baur, Phys. L. McLerran, Nucl. Phys.A701, 489 (2002). Rev. C 48, 1999 (1993); M. Greiner, M. Vidovic, Ch. [19] I. I. Balitsky, Nucl. Phys. B463, 99 (1996); Y.V. Hofman, A. Schafer and G. Soff, Phys. Rev. C 51, 911 Kovchegov, Phys.Rev.D 60, 034008 (1999). (1995); F. Krauss, M. Greiner and G. Soff, Prog. Part. [20] J. Jalilian-Marian, A. Kovner, L. McLerran and H. Nucl.Phys.39,503(1997);F.GelisandA.Peshier,Nucl. Weigert, Phys. Rev. D 55, 5414 (1997); J. Jalilian- Phys.A 697, 879 (2002). Marian, A. Kovner and H. Weigert, Phys. Rev. D [7] V. P. Gon¸calves and C. A. Bertulani, Phys. Rev. C 65, 59, 014014 (1999), ibid. 59, 014015 (1999), ibid. 59 054905 (2002). 034007 (1999); A. Kovner, J. Guilherme Milhano and [8] S. R. Klein, J. Nystrand, R. Vogt, Phys. Rev. C 66, H.Weigert,Phys.Rev.D62,114005(2000);H.Weigert, 044906 (2002). Nucl. Phys. A703, 823 (2002). [9] V.P.Gon¸calvesandM.V.Machado,Eur.Phys.J.C29, [21] N. Armesto, Eur. Phys. J. C 26, 35 (2002). 37 (2003). [22] V.P.GoncalvesandM.V.T.Machado,Eur.Phys.J.C [10] V.P.GoncalvesandM.V.T.Machado,Eur.Phys.J.C 30, 387 (2003). 31, 371 (2003) [23] M. Heyssler, Z. Phys.C 73, 299 (1997). [11] V. P. Goncalves and M. V. T. Machado, Phys. Rev. D