PoS(EPS-HEP2017)192. Suppression of heavy quarkonia in pa collisions. B. Kopeliovich, Ivan Schmidt, Marat Siddikov

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1 Suppression of heav quarkonia in collisions B. Kopeliovich, Ivan Schmidt, Departamento de Física, Universidad Técnica Federico Santa María, Centro Científico - Tecnológico de Valparaíso, Casilla 110-V, Valparaíso, Chile Marat.Siddikov@usm.cl In this proceeding we present results of our studies of quarkonium suppression in collisions. We estimated the nuclear suppression due to absorption, energ loss and gluon shadowing. In addition, we found that at high energies a sizeable additive contribution comes from multinucleon production. We demonstrate that the suggested approach can simultaneousl explain a relativel small nuclear suppression of J/ψ and ϒ, as well as a strong suppression of ψs observed at RHIC and LHC in proton-ion collisions. PoSEPS-HEP01719 EPS-HEP 017, European Phsical Societ conference on High Energ Phsics 5-1 Jul 017 Venice, Ital Speaker. A footnote ma follow. c Copright owned b the authors under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License CC BY-NC-ND

2 1. Introduction The dnamics of the heav quarkonium is described b perturbative CD see [1,, 3] for a review of current situation, for this reason quarkonium propagation inside a medium serves as a clean probe of the gluon content of the target. This motivated extensive theoretical and experimental studies of quarkonium dnamics, which recentl got a new impetus after the discover of various -containing exotic tetraquark and pentaquark candidates [4]. Inside nuclei, it is expected that in a heav quark mass limit the nuclear suppression of quarkonia should vanish, though this behaviour might be modified at forward rapidities due to the energ loss corrections [5, 6, 7]. The small nuclear effects predicted in energ loss based models from the first sight are consistent with almost no suppression of J/ψ and ϒ observed at RHIC. However, in such models it is challenging to explain wh for ψs a considerabl stronger nuclear suppression is observed both at RHIC [8] and LHC [9]. This difference hints that the transverse size of the charmonia formall a higher twist effect should be taken into account. Naivel, the suppression effects should grow with energ [10], reflecting the energ dependence of the underling dipolenucleon cross-section [11]. However, recent result from LHC [1] did not confirm this expectation and found approximatel the same suppression as at RHIC. We revisited the problem and found that the controvers is solved b a novel mechanism in which two nucleons from the heav ion participate in quarkonium production. This additional contribution is enhanced b A 1/3 inside heav nuclei, is growing as a function of energ faster than single-nucleon process, and compensates increasing with energ nuclear suppression expected for single-nucleon term. At the same time, this contribution becomes quite small for the heav bottomonium, and for this reason allows us to construct a consistent description of nuclear suppression for all the aforementioned quarkonia. The paper is structured as follows. In the Section we describe briefl the framework used for evaluations see [13] for mode details. In Section 3 we present our results and draw conclusions.. uarkonium production in a dipole approach Production of the quarkonium on single nucleons up to absorptive corrections coincides with production in pp collisions extensivel studied in the literature [14, 15, 16]. The Color Singlet Model CSM gives a ver reasonable description of data, provided k T -dependent parton distributions are used [17]. The evaluations in the CSM model are performed in a momentum space, neglecting for simplicit the relative motion of the inside quarkonium in the heav quark mass limit. For evaluation of the nuclear suppression, this approximation is not justified since nuclear effects are controlled b the transverse size of the dipole. For evaluations of nuclear effects it is more convinient to work in the coordinate representation and rewrite the k T -factorization results in the framework of the color dipole approach [11, 18]. The cross-section of the quarkonia production in pp collisions in this approach is given b [13] PoSEPS-HEP01719 dσ pp d = 9 8 gx 1 dα G dα 1 d r 1 dα d r d r G Ψ M α 1, r1 Ψ M α, r.1 1

3 σ 6 n,n =1 [ η n η n Tr Λ M Φ ε n, r n 1 x, b 1 n b n, Φ G δ n, r 1 G,n ] [ ] Tr Λ M Φ ε n, r n Φ G δ n, r G,n where we use notation gx for the projectile gluon densit and x 1, are related to rapidit and transverse momenta p T of quarkonia as x 1, M + p e± / s. The wave function Ψ M α, r of quarkonium is taken form the literature [0], Φ ε n, r n and Φ G δ n, r G are the gluon splitting and emission wave functions matrices in helicit space, σ x, r is the color singlet dipole cross-section [18], and all the other notations are explained in [13]. The dnamics of small dipoles moving inside a nuclear matter depends cruciall on the production time, t and quarkonium formation time t f [1]. For the high energ scattering at central and forward rapidities, the formation time t f significantl exceeds the nuclear size, for this reason the pair traverses the nucleus with frozen transverse size, though might interact via soft gluon exchanges with neighboring nucleons. The mean number of such inelastic interactions for the dipole of transverse quark separation r is given b n coll r, b = σ x, rt A b, where T A b is the nuclear thickness function. The parameter n coll is quite small for RHIC kinematics, however grows with energ and becomes comparable to one in LHC kinematics. This implies that in addition to the CSM mechanism, there could be additional multinucleon contributions to the total crosssections. Figure 1: Color online Multiple color-exchange interaction of a high energ cc pair propagating through a nucleus. For the S-wave quarkonia, the two-nucleon contribution gnn J/ψ X shown in the Figure 1 presents a special concern, since it contributes in the same order over O α s m /m as the single-nucleon term and requires a dedicated stud. Due to difference of final states, the one- and two-nucleon contributions do not interfere and contribute to the nuclear cross-section additivel. For this reason in what follows, we will refer to their contributions to suppression factor as R 1N = dσ 1N /Adσ pp single-nucleon term and R N = dσ N /Adσ pp two-nucleon term respectivel. For the single-nucleon term the cross-section differs from.1 onl b additional absorptive factor in the integrand, d bdzρ A b, z. σ 4 x, α 1,r1,r G + σ 4 x, α,r,r G x, r 1 + σ x, r exp σ T b, z T + b, z, PoSEPS-HEP01719 where b and z are the impact parameter and longitudinal coordinate of the nucleon inside the nucleus, ρ A b, z is the nuclear densit, and the relation of the cross-section σ 4 with color singlet dipole cross-section σx, r is explained in [13]. The cross-section of the two-nucleon mechanism is given b dσ N d = gx 1 d b dz 1 dz dα 1 d r 1 dα d r ρ A b, z 1 ρ A b, z.3

4 Ψ α 1 J/ψ, r1 Ψ J/ψ α, r Σ 8 x, α 1, r1,α, r ] ] Tr [Λ M Φ cc ε n 1, r n 1 Tr [Λ M Φ cc ε n, r n Σ tr x, α 1, r1,α, r σ 3 x, α 1 exp,r1 + σ 3 x, α,r T b, z 1 Σ 8 x, α 1, r1,α, r T A b, z 1, z σ x, r 1 + σ x, r T + b, z, and the expressions for the the cross-sections σ 3, Σ 8 and Σ tr 1 8 +, as well as description of additional corrections due to gluon shadowing and energ loss, ma be found in [13]. 3. Results and discussion As was discussed in previous section, the nuclear suppression factor R gets additive contributions from one- and two-nucleons terms R 1N,N which we will present together with the total result. In the Figure we plot the nuclear suppression factor R for different quarkonia at RHIC and LHC energies. For J/ψ, our framework gives a reasonable description of available LHC data as well as RHIC data at forward rapidities. At central rapidities description of RHIC data in a dipole model slightl overestimates available data. This happens because tpical values of x in this kinematics reach 10, a value where an underling eikonal approximation might be not ver accurate. Although at LHC the found value of R is close to one, we can see that this happens due to compensation of large absorption and contribution from two-nucleon term, rather than due to inherentl weak nuclear effects. For ψs, the nuclear suppression is considerabl larger, in agreement with RHIC [8] and LHC [9] data. This happens due to a node in a radial part of ψs wave function and partial cancellation of contributions of small and large dipoles. For ϒ1S, we can see that our model agrees with available RHIC [] data. Due to higher mass of ϒ and smaller dipole sizes, all nuclear effects are smaller for this meson except energ loss corrections, which leads to sizable suppression at forward rapidities. The two-nucleon mechanism for ϒ production is smaller than for J/ψ because additional gluon interactions is suppressed b smaller dipole size. To summarize, we found that at high energies the nuclear suppression in collisions gets a sizeable contribution from the multinucleon processes. We studied in detail the largest correction of this tpe, which includes the two nucleons from the target, and found that it presents a substantial contribution up to 30% to charmonia production. This contribution explains a weak change of suppression from RHIC [3] to LHC [1], despite of significant increase of the absorptive crosssection. In the same framework we managed to describe a weak suppression of J/ψ and ϒ and a large suppression of ψ S observed at RHIC [8] and LHC [9]. While for ϒ our results ma be interpreted as inherentl weak nuclear effects in heav mass limit, for J/ψ this interpretation is not accurate and happens due to partial compensation of one- and two-nucleon contributions. We expect that at even higher energies the multinucleon contributions will become more pronounced, and the cross-section will remain finite in a black disk limit, despite the fact that a contribution of single-nucleon term vanishes due to absorption. PoSEPS-HEP

5 0. 0. R 1N +R N R 1N R N J/ψ, RHIC 0 1 R 1N R N R 1N +R N J/Ψ, LHC R N R 1N +R N R 1N ψs, RHIC 0 1 R 1N R N R 1N +R N ψs, LHC R 1N +R N R 1N R N Υ1S, RHIC 0 1 R 1N +R N R 1N R N Υ1S, LHC Figure : Color online Suppression of different quarkonia in heav ion collisions for s=00 GeV upper row, and s=5 TeV lower row. Blue and green lines correspond to contribution of one- and two-nucleon terms, black line top is a total suppression. Data are from [1, 3, 8, 9, ]. Acknowledgements We thank our colleagues at UTFSM universit for encouraging discussions. This research was partiall supported b the Fondect Chile grants , and , CONICYT Chile grants PIA ACT1406 and ACT1413, and Proecto Basal FB 081 Chile. Powered@NLHPC: This research was partiall supported b the supercomputing infrastructure of the NLHPC ECM-0. Also, we thank Yuri Ivanov for technical support of the USM HPC cluster where part of evaluations were done. Also, we thank William Brooks for providing the link [4]. References PoSEPS-HEP01719 [1] N. Brambilla et al. [uarkonium Working Group Collaboration], hep-ph/ [] M. Bedjidian et al., hep-ph/ [3] S. J. Brodsk and J. P. Lansberg, Phs. Rev. D 81, [arxiv: [hep-ph]] [4] C. Patrignani et al. [Particle Data Group Collaboration], Chin. Phs. C 40, no. 10, [5] B.Z. Kopeliovich, F. Niedermaer, Nuclear screening in J/ψ and Drell-Yan pair production, JINR-E , Dubna, 1984; KEK librar: hep.net/record/ [6] S. J. Brodsk and P. Hoer, Phs. Lett. B 98, [7] F. Arleo, S. Peigne and T. Sami, Phs. Rev. D 83,

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