In-Medium Bottomonium Production in Heavy-Ion Collisions
aa r X i v : . [ h e p - ph ] A p r Nuclear Physics A 00 (2017) 1–4
NuclearPhysics A / locate / procedia In-Medium Bottomonium Production in Heavy-Ion Collisions
Xiaojian Du , Min He , Ralf Rapp Cyclotron Institute and Department of Physics & Astronomy, Texas A & M University, College Station, TX 77843-3366, USA Department of Applied Physics, Nanjing University of Science and Technology, Nanjing, China
Abstract
We study bottomonium production in heavy-ion collisions using a transport model which utilizes kinetic-rate and Boltz-mann equations to calculate the energy, centrality and transverse-momentum ( p T ) dependence of the yields. Both gluo-dissociation and inelastic parton-induced break-up including interference e ff ects are improved over previous work byusing in-medium binding energies from a thermodynamic T -matrix approach. A coalescence model with bottom-quarkspectra from Langevin simulations is implemented to account for thermal o ff -equilibrium e ff ects in the p T -spectra of theregeneration contribution. We also update the equation of state for the bulk medium by extracting it from lattice-QCDresults. A systematic analysis of bottomonium observables is conducted in comparison to RHIC and LHC data. Inparticular, the o ff -equilibrium bottom-quark spectra are found to play an important role in the bottomonium p T spectra. Keywords:
Bottomonium, Transport, Heavy-Ion Collision
1. Introduction
Intense experimental [1, 2, 3, 4, 5, 6, 7, 8] and theoretical [9, 10, 11, 12, 13, 14, 15, 16] e ff orts areunderway to measure and interpret the systematics of bottomonium production in ultra-relativistic heavy-ion collisions (URHICs). Recent data on Υ (1S), Υ (2S) and Υ (3S) states suggest a sequential suppressionpattern. Unlike charmonia, where large contributions from regeneration have been established at LHCenergies, bottomonium production could be dominated by the suppressed primordial contribution, whichis supported by decreasing production yields with energy and centrality. However, the quantitative role ofregeneration and its impact on the interpretation of current data remains an open issue.In this paper we employ a rate equation approach for bottomonia, improved over previous work by theuse of in-medium binding energies and extended to compute p T spectra (Sec. 2), to calculate observablesand compare them to the most recent data from RHIC and the LHC (Sec. 3). We conclude in Sec. 4.
2. Transport model for bottomonia production
The rate equation for bottomonium production in URHICs in the medium’s rest frame [9],d N Y ( τ )d τ = − Γ Y ( T ) h N Y ( τ ) − N eq Y ( T ) i , (1) / Nuclear Physics A 00 (2017) 1–4
Binding Energies Υ vac χ b vac Υ ’ vac Υχ b Υ ’ E [ G e V ] T[GeV]
Reaction Rates ΥΥ ’ χ b Γ ( M e V ) T(GeV)
Fig. 1. Left panel: In-medium Y binding energies extracted from T -matrix calculations [17] (solid (dash-dotted) lines for η = Υ (1 S ), χ b and Υ (2 S ), respectively.Right panel: Inelastic reaction rates corresponding to the in-medium binding energies in the left panel with the band reflecting η = involves two transport coe ffi cients: the inelastic reaction rate, Γ Y , and the thermal equilibrium limit N eq Y ( T )for each state Y = Υ (1 S ) , Υ (2 S ) , χ c , ... .For the reation rates in the quark-gluon plasma (QGP) we include both gluo-dissociation and quasi-freemechanisms. The bottomonium binding energies strongly a ff ect the reaction rates. We here employ thein-medium binding energy for Υ (1 S ) from microscopic T -matrix calculations (using the internal-energypotential) [17], and infer the ones for the excited states by assuming the in-medium Y masses to be at theirvacuum values (as suggested by the weak temperature dependence of lattice-QCD correlators [18]), cf. Fig 1left. To account for pertinent theoretical uncertainties, we allow for deviations from the T -matrix results bydefining a rescaling parameter η so that E vac − E med ( T ) = η ( E vac − E T mat ( T )), where η> ff ects, i.e. , weaker binding. The reaction rates are dominated by the quasi-free mechanism; gluo-dissociation is only significant at temperatures where the total rate is small, cf. right panel of Fig. 1.The thermal-equilibrium limit is evaluated in the QGP from the statistical model with bottom ( b ) quarkswith a mass following from the procedure outlined above; a thermal relaxation factor is implemented tosimulate incomplete thermalization of b quarks [19]. We neglect e ff ects of the hadronic phase.Using initial conditions obtained from data in pp collisions and potential cold-nuclear matter (CNM)e ff ects (see below), the bottomonium yields are evolved with the rate equation in an expanding fireballbackground. Its temperature evolution is obtained from a fixed total entropy S tot = s ( T ) V FB ( t ), adjusted toobtain the experimentally observed hadron yields at a chemical freezeout temperature of T c =
170 MeV. Thenuclear modification factor is defined as a ratio of AA to pp spectra, R AA = ( N AA ) / ( N coll N pp ), scaled by thebinary collision number, N coll , from the Glauber model.The calculation of p T spectra employs the final yields of the primordial and regenerated Y ’s from therate equation. The Boltzmann equation is used to calculate the p T -spectra of the primordial part via ∂ f ( ~ x , ~ p , t ) ∂ t + ~ pE p · ∂ f ∂~ x = − Γ Y ( ~ p , T ) f ( ~ x , ~ p , t ) (2)where f ( ~ x , ~ p , t ) is the bottomonium phase space distribution and E p = q p + m Y the Y energy. The initialdistribution f ( ~ x , ~ p , = f ( ~ x ) f ( ~ p ) is also calculated from the Glauber model for the spatial N coll distribution,and from spectra in pp collisions for the initial p T distribution. For the regeneration component, incomplete b -quark thermalization mandates to go beyond our previously used blastwave approximation for charmo-nia. Instead we employ b -quark spectra from Langevin simulations [20] to compute Y p T spectra from acoalescence model [21],d N Y ( p T , φ )d p T = C reg Z d p t d p t d N b d p t d N ¯ b d p t δ (2) ( ~ p T − ~ p t − ~ p t ) Θ " ∆ p − ( ~ p t − ~ p t ) + ( m t − m t ) . (3) Nuclear Physics A 00 (2017) 1–4 AuAu @ 200 GeV R AA ( Y ( S )) N part STAR Y(1S) |y|<0.5Y(1S) total η =1.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 0 50 100 150 200 250 300 350 400 AuAu @ 200 GeV R AA ( Y ( S + S )) N part STAR Y(2S+3S) |y|<0.5Y(2S) total η =1.1 Fig. 2. Centrality dependence of the R AA for Υ (1 S ) (left) and Υ (2 S ) (right) in 0.2 TeV Au-Au collisions at RHIC, compared to STARdata [24]. The uncertainty bands are due to CNM e ff ects represented by nuclear absorption cross sections, σ abs Y = PbPb @ 5.02 TeV |y|<2.4 R AA N part CMS Y(1S)CMS Y(2S)Y(1S) η =1.1Y(2S) η =1.1 0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 25 30 PbPb @ 5.02 TeV |y|<2.4 MB R AA p T CMS Y(1S)CMS Y(2S)Y(1S)Y(2S)
Fig. 3. Centrality (left) and transverse-momentum (right) dependence of the R AA for Υ (1 S ) and Υ (2 S ) in 5.02 TeV Pb-Pb collisions atthe LHC, compared to CMS data [25]. The bands represent a 0-15 % shadowing [22] on open-bottom and bottomonia.
3. Bottomonia production at RHIC and LHC
Our input cross section for bottom / onium production in pp collisions at √ s = √ s = Υ states is updated to about 30(50) % at low (high) p T . For simplicity, we assume a 30 % feeddownfrom higher excited states ( e.g. , 3 S , 2 P , 3 P ) to the Υ (2 S ) to be fully melted. The charged-particle density, d N ch d y , needed for the total entropy of the fireball is increased by 22.5 % over 2.76 TeV [23].In Figs. 2 and 3 we compare our predictions to the new mid-rapidity data presented by STAR (at √ s = √ s = η = η = Υ (1 S ) and Υ (2 S ) at both collision energies. In particular, the rather strong suppression of the Υ (2 S ) ob-served by STAR is accounted for (see right panel of Fig. 2). In addition, the calculated p T spectra at5.02 TeV (see right panel in Fig. 3) appear to capture the rather flat shapes in the CMS data. For the Υ (1 S )the data show a hint for a slight rise for p T .
10 GeV. In the calculations a similar trend is generated bythe coalescence component which features a maximum structure around p T ≃
10 GeV. This structure is dueto the radial flow of the coalescing b -quarks. However, it would be much more pronounced (and lead toa discrepancy with the data) if thermalized b -quark spectra were assumed instead of the transport b -quarkspectra. The comparison of our results to the newest forward-rapidity ALICE 5.02 TeV data can be found / Nuclear Physics A 00 (2017) 1–4 in Ref. [26]; the agreement improves relative to 2.76 TeV, where the ALICE data show significantly moresuppression than our calculations.
4. Conclusions
We have calculated bottomonium production yields using a rate equation with in-medium transportcoe ffi cients in a QGP, augmented by a Boltzmann equation and coalescence model to compute p T -spectra.The comparison of our predictions to the newest experimental data released by STAR at 0.2 TeV and by CMSand ALICE at 5.02 TeV show fair agreement. Our calculations are compatible with appreciable reductions inthe Y binding energies, leading to a dissolution of the excited states at RHIC, while the ground-state Υ (1 S )starts to dissolve at the LHC. The Υ (1 S ) suppression indeed shows a promising sensitivity to its in-mediumbinding energy, which can ultimately be used to determine more quantitatively the in-medium modificationsof the QCD force, once other model uncertainties, such as the evolution of the fireball, CNM e ff ects orthe role of regeneration are controlled more precisely. At this point, regeneration plays a sub-dominant butsignificant role for the Υ (1 S ), possibly supported by the rising trend in the p T spectra of CMS at low p T .Non-thermalized bottom-quark spectra turn out to play an essential role in the description of the p T spectraof the coalescence component. For the strongly suppressed Υ (2 S ) yields at the LHC, especially in centralcollisions, regeneration turns out to be the dominant production source. The slight over-prediction of ourmodel for the centrality integrated Υ (2 S ) yields at both 2.76 TeV and 5.02 TeV might indicate a somewhattoo large regeneration component. A potential resolution to this problem could be the emergence of B -meson states as T c is approached from above, which leads to smaller b -quark fugacities and thus reduces theequilibrium limit of bottomonia in the regime near T c . Work in this direction is in progress [27]. Acknowledgement
This work is supported by U.S National Science Foundation under grant no. PHY-1614484.
References [1] A. Adare et al. [PHENIX Collaboration], Phys. Rev. C (2015) no.2, 024913.[2] L. Adamczyk et al. [STAR Collaboration], Phys. Lett. B (2014) 127 Erratum: [Phys. Lett. B (2015) 537].[3] L. Adamczyk et al. [STAR Collaboration], Phys. Rev. C (2016) no.6, 064904.[4] B. B. Abelev et al. [ALICE Collaboration], Phys. Lett. B (2014) 361.[5] G. G. Fronz, arXiv:1612.06691.[6] S. Chatrchyan et al. [CMS Collaboration], Phys. Rev. Lett. (2012) 222301.[7] V. Khachatryan et al. [CMS Collaboration], arXiv:1611.01510.[8] CMS Collaboration [CMS Collaboration], CMS-PAS-HIN-16-008.[9] L. Grandchamp, S. Lumpkins, D. Sun, H. van Hees and R. Rapp, Phys. Rev. C , (2006) 064906.[10] A. Emerick, X. Zhao and R. Rapp, Eur. Phys. J. A , (2012) 72.[11] M. Strickland and D. Bazow, Nucl. Phys. A (2012) 25.[12] T. Song, K. C. Han and C. M. Ko, Nucl. Phys. A (2013) 141.[13] K. Zhou, N. Xu and P. Zhuang, Nucl. Phys. A (2014) 654.[14] B. Krouppa and M. Strickland, Universe (2016) no.3, 16.[15] J. Hoelck, F. Nendzig and G. Wolschin, Phys. Rev. C (2017) no.2, 024905.[16] N. Brambilla, M. A. Escobedo, J. Soto and A. Vairo, arXiv:1612.07248.[17] F. Riek and R. Rapp, Phys. Rev. C (2010) 035201.[18] G. Aarts, C. Allton, T. Harris, S. Kim, M. P. Lombardo, S. M. Ryan and J. I. Skullerud, arXiv:1402.6210.[19] L. Grandchamp and R. Rapp, Nucl. Phys. A (2002) 415.[20] M. He, R. J. Fries and R. Rapp, Phys. Lett. B , (2014) 445.[21] V. Greco, C. M. Ko and P. Levai, Phys. Rev. C , (2003) 034904.[22] K. J. Eskola, H. Paukkunen and C. A. Salgado, JHEP , 065 (2009).[23] H. Niemi, K. J. Eskola, R. Paatelainen and K. Tuominen, Phys. Rev. C93