Abstract
We develop a framework of coupled transport equations for open heavy flavor and quarkonium states, in order to describe their transport inside the quark-gluon plasma. Our framework is capable of studying simultaneously both open and hidden heavy flavor observables in heavy-ion collision experiments and can account for both, uncorrelated and correlated recombination. Our recombination implementation depends on real-time open heavy quark and antiquark distributions. We carry out consistency tests to show how the interplay among open heavy flavor transport, quarkonium dissociation and recombination drives the system to equilibrium. We then apply our framework to study bottomonium production in heavy-ion collisions. We include ϒ(1S), ϒ(2S), ϒ(3S), χb(1P) and χb(2P) in the framework and take feed-down contributions during the hadronic gas stage into account. Cold nuclear matter effects are included by using nuclear parton distribution functions for the initial primordial heavy flavor production. A calibrated 2 + 1 dimensional viscous hydrodynamics is used to describe the bulk QCD medium. We calculate both the nuclear modification factor RAA of all bottomonia states and the azimuthal angular anisotropy coefficient v2 of the ϒ(1S) state and find that our results agree reasonably with experimental measurements. Our calculations indicate that correlated cross-talk recombination is an important production mechanism of bottomonium in current heavy-ion experiments. The importance of correlated recombination can be tested experimentally by measuring the ratio of RAA(χb(1P)) and RAA(ϒ(2S)).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Quigg and J.L. Rosner, Quarkonium level spacings, Phys. Lett. B 71 (1977) 153 [INSPIRE].
T. Matsui and H. Satz, J/ψ suppression by quark-gluon plasma formation, Phys. Lett. B 178 (1986) 416 [INSPIRE].
F. Karsch, M.T. Mehr and H. Satz, Color screening and deconfinement for bound states of heavy quarks, Z. Phys. C 37 (1988) 617 [INSPIRE].
L.D. McLerran and B. Svetitsky, Quark liberation at high temperature: a Monte Carlo study of SU(2) gauge theory, Phys. Rev. D 24 (1981) 450 [INSPIRE].
A. Mócsy and P. Petreczky, Color screening melts quarkonium, Phys. Rev. Lett. 99 (2007) 211602 [arXiv:0706.2183] [INSPIRE].
M. Laine, O. Philipsen, P. Romatschke and M. Tassler, Real-time static potential in hot QCD, JHEP 03 (2007) 054 [hep-ph/0611300] [INSPIRE].
A. Beraudo, J.-P. Blaizot and C. Ratti, Real and imaginary-time \( Q\overline{Q} \) correlators in a thermal medium, Nucl. Phys. A 806 (2008) 312 [arXiv:0712.4394] [INSPIRE].
R.L. Thews, M. Schroedter and J. Rafelski, Enhanced J/ψ production in deconfined quark matter, Phys. Rev. C 63 (2001) 054905 [hep-ph/0007323] [INSPIRE].
A. Andronic, P. Braun-Munzinger, K. Redlich and J. Stachel, Evidence for charmonium generation at the phase boundary in ultra-relativistic nuclear collisions, Phys. Lett. B 652 (2007) 259 [nucl-th/0701079] [INSPIRE].
L. Grandchamp, R. Rapp and G.E. Brown, In medium effects on charmonium production in heavy ion collisions, Phys. Rev. Lett. 92 (2004) 212301 [hep-ph/0306077] [INSPIRE].
L. Grandchamp, S. Lumpkins, D. Sun, H. van Hees and R. Rapp, Bottomonium production at RHIC and CERN LHC, Phys. Rev. C 73 (2006) 064906 [hep-ph/0507314] [INSPIRE].
L. Yan, P. Zhuang and N. Xu, Competition between J/ψ suppression and regeneration in quark-gluon plasma, Phys. Rev. Lett. 97 (2006) 232301 [nucl-th/0608010] [INSPIRE].
X. Zhao and R. Rapp, Transverse momentum spectra of J/ψ in heavy-ion collisions, Phys. Lett. B 664 (2008) 253 [arXiv:0712.2407] [INSPIRE].
Y.-P. Liu, Z. Qu, N. Xu and P.-F. Zhuang, J/ψ transverse momentum distribution in high energy nuclear collisions at RHIC, Phys. Lett. B 678 (2009) 72 [arXiv:0901.2757] [INSPIRE].
X. Zhao and R. Rapp, Charmonium in medium: from correlators to experiment, Phys. Rev. C 82 (2010) 064905 [arXiv:1008.5328] [INSPIRE].
T. Song, K.C. Han and C.M. Ko, Charmonium production in relativistic heavy-ion collisions, Phys. Rev. C 84 (2011) 034907 [arXiv:1103.6197] [INSPIRE].
T. Song, K.C. Han and C.M. Ko, Bottomonia suppression in heavy-ion collisions, Phys. Rev. C 85 (2012) 014902 [arXiv:1109.6691] [INSPIRE].
A. Emerick, X. Zhao and R. Rapp, Bottomonia in the quark-gluon plasma and their production at RHIC and LHC, Eur. Phys. J. A 48 (2012) 72 [arXiv:1111.6537] [INSPIRE].
R. Sharma and I. Vitev, High transverse momentum quarkonium production and dissociation in heavy ion collisions, Phys. Rev. C 87 (2013) 044905 [arXiv:1203.0329] [INSPIRE].
F. Nendzig and G. Wolschin, Bottomium suppression in Pb-Pb collisions at LHC energies, J. Phys. G 41 (2014) 095003 [arXiv:1406.5103] [INSPIRE].
B. Krouppa, R. Ryblewski and M. Strickland, Bottomonia suppression in 2.76 TeV Pb-Pb collisions, Phys. Rev. C 92 (2015) 061901 [arXiv:1507.03951] [INSPIRE].
B. Chen and J. Zhao, Bottomonium continuous production from unequilibrium bottom quarks in ultrarelativistic heavy ion collisions, Phys. Lett. B 772 (2017) 819 [arXiv:1704.05622] [INSPIRE].
J. Zhao and B. Chen, Strong diffusion effect of charm quarks on J/ψ production in Pb-Pb collisions at the LHC, Phys. Lett. B 776 (2018) 17 [arXiv:1705.04558] [INSPIRE].
X. Du, R. Rapp and M. He, Color screening and regeneration of bottomonia in high-energy heavy-ion collisions, Phys. Rev. C 96 (2017) 054901 [arXiv:1706.08670] [INSPIRE].
S. Aronson, E. Borras, B. Odegard, R. Sharma and I. Vitev, Collisional and thermal dissociation of J/ψ and ϒ states at the LHC, Phys. Lett. B 778 (2018) 384 [arXiv:1709.02372] [INSPIRE].
E.G. Ferreiro and J.-P. Lansberg, Is bottomonium suppression in proton-nucleus and nucleus-nucleus collisions at LHC energies due to the same effects?, JHEP 10 (2018) 094 [Erratum ibid. 03 (2019) 063] [arXiv:1804.04474] [INSPIRE].
X. Yao, W. Ke, Y. Xu, S. Bass and B. Müller, Quarkonium production in heavy ion collisions: coupled Boltzmann transport equations, Nucl. Phys. A 982 (2019) 755 [arXiv:1807.06199] [INSPIRE].
X. Du and R. Rapp, In-medium charmonium production in proton-nucleus collisions, JHEP 03 (2019) 015 [arXiv:1808.10014] [INSPIRE].
X. Du, S.Y.F. Liu and R. Rapp, Extraction of the heavy-quark potential from bottomonium observables in heavy-ion collisions, Phys. Lett. B 796 (2019) 20 [arXiv:1904.00113] [INSPIRE].
J. Hong and S.H. Lee, ϒ(1S) transverse momentum spectra through dissociation and regeneration in heavy-ion collisions, Phys. Lett. B 801 (2020) 135147 [arXiv:1909.07696] [INSPIRE].
B. Chen, M. Hu, H. Zhang and J. Zhao, Probe the tilted quark-gluon plasma with charmonium directed flow, Phys. Lett. B 802 (2020) 135271 [arXiv:1910.08275] [INSPIRE].
O. Kaczmarek, F. Karsch, P. Petreczky and F. Zantow, Heavy quark anti-quark free energy and the renormalized Polyakov loop, Phys. Lett. B 543 (2002) 41 [hep-lat/0207002] [INSPIRE].
TUMQCD collaboration, Color screening in (2 + 1)-flavor QCD, Phys. Rev. D 98 (2018) 054511 [arXiv:1804.10600] [INSPIRE].
Y. Burnier, O. Kaczmarek and A. Rothkopf, Static quark-antiquark potential in the quark-gluon plasma from lattice QCD, Phys. Rev. Lett. 114 (2015) 082001 [arXiv:1410.2546] [INSPIRE].
M.E. Peskin, Short distance analysis for heavy quark systems. 1. Diagrammatics, Nucl. Phys. B 156 (1979) 365 [INSPIRE].
G. Bhanot and M.E. Peskin, Short distance analysis for heavy quark systems. 2. Applications, Nucl. Phys. B 156 (1979) 391 [INSPIRE].
N. Brambilla, A. Pineda, J. Soto and A. Vairo, Potential NRQCD: an effective theory for heavy quarkonium, Nucl. Phys. B 566 (2000) 275 [hep-ph/9907240] [INSPIRE].
N. Brambilla, A. Pineda, J. Soto and A. Vairo, Effective field theories for heavy quarkonium, Rev. Mod. Phys. 77 (2005) 1423 [hep-ph/0410047] [INSPIRE].
S. Fleming and T. Mehen, Doubly heavy baryons, heavy quark-diquark symmetry and NRQCD, Phys. Rev. D 73 (2006) 034502 [hep-ph/0509313] [INSPIRE].
N. Brambilla, J. Ghiglieri, A. Vairo and P. Petreczky, Static quark-antiquark pairs at finite temperature, Phys. Rev. D 78 (2008) 014017 [arXiv:0804.0993] [INSPIRE].
N. Brambilla, M.A. Escobedo, J. Ghiglieri and A. Vairo, Thermal width and gluo-dissociation of quarkonium in pNRQCD, JHEP 12 (2011) 116 [arXiv:1109.5826] [INSPIRE].
N. Brambilla, M.A. Escobedo, J. Ghiglieri and A. Vairo, Thermal width and quarkonium dissociation by inelastic parton scattering, JHEP 05 (2013) 130 [arXiv:1303.6097] [INSPIRE].
S. Biondini and S. Vogl, Coloured coannihilations: dark matter phenomenology meets non-relativistic EFTs, JHEP 02 (2019) 016 [arXiv:1811.02581] [INSPIRE].
S. Biondini and S. Vogl, Scalar dark matter coannihilating with a coloured fermion, JHEP 11 (2019) 147 [arXiv:1907.05766] [INSPIRE].
T. Binder, B. Blobel, J. Harz and K. Mukaida, Dark matter bound-state formation at higher order: a non-equilibrium quantum field theory approach, JHEP 09 (2020) 086 [arXiv:2002.07145] [INSPIRE].
A. Dumitru, Y. Guo and M. Strickland, The heavy-quark potential in an anisotropic (viscous) plasma, Phys. Lett. B 662 (2008) 37 [arXiv:0711.4722] [INSPIRE].
A. Dumitru, Y. Guo and M. Strickland, The imaginary part of the static gluon propagator in an anisotropic (viscous) QCD plasma, Phys. Rev. D 79 (2009) 114003 [arXiv:0903.4703] [INSPIRE].
Q. Du, A. Dumitru, Y. Guo and M. Strickland, Bulk viscous corrections to screening and damping in QCD at high temperatures, JHEP 01 (2017) 123 [arXiv:1611.08379] [INSPIRE].
H. Liu, K. Rajagopal and U.A. Wiedemann, An AdS/CFT calculation of screening in a hot wind, Phys. Rev. Lett. 98 (2007) 182301 [hep-ph/0607062] [INSPIRE].
M.A. Escobedo, J. Soto and M. Mannarelli, Non-relativistic bound states in a moving thermal bath, Phys. Rev. D 84 (2011) 016008 [arXiv:1105.1249] [INSPIRE].
X. Yao and T. Mehen, Quarkonium in-medium transport equation derived from first principles, Phys. Rev. D 99 (2019) 096028 [arXiv:1811.07027] [INSPIRE].
X. Yao, W. Ke, Y. Xu, S.A. Bass, T. Mehen and B. Müller, Quarkonium production in heavy ion collisions: from open quantum system to transport equation, in 28th international conference on ultrarelativistic nucleus-nucleus collisions, (2020) [arXiv:2002.04079] [INSPIRE].
C. Young and K. Dusling, Quarkonium above deconfinement as an open quantum system, Phys. Rev. C 87 (2013) 065206 [arXiv:1001.0935] [INSPIRE].
N. Borghini and C. Gombeaud, Heavy quarkonia in a medium as a quantum dissipative system: master equation approach, Eur. Phys. J. C 72 (2012) 2000 [arXiv:1109.4271] [INSPIRE].
Y. Akamatsu and A. Rothkopf, Stochastic potential and quantum decoherence of heavy quarkonium in the quark-gluon plasma, Phys. Rev. D 85 (2012) 105011 [arXiv:1110.1203] [INSPIRE].
Y. Akamatsu, Heavy quark master equations in the Lindblad form at high temperatures, Phys. Rev. D 91 (2015) 056002 [arXiv:1403.5783] [INSPIRE].
J.-P. Blaizot, D. De Boni, P. Faccioli and G. Garberoglio, Heavy quark bound states in a quark-gluon plasma: dissociation and recombination, Nucl. Phys. A 946 (2016) 49 [arXiv:1503.03857] [INSPIRE].
R. Katz and P.B. Gossiaux, The Schrödinger-Langevin equation with and without thermal fluctuations, Annals Phys. 368 (2016) 267 [arXiv:1504.08087] [INSPIRE].
S. Kajimoto, Y. Akamatsu, M. Asakawa and A. Rothkopf, Dynamical dissociation of quarkonia by wave function decoherence, Phys. Rev. D 97 (2018) 014003 [arXiv:1705.03365] [INSPIRE].
D. De Boni, Fate of in-medium heavy quarks via a Lindblad equation, JHEP 08 (2017) 064 [arXiv:1705.03567] [INSPIRE].
J.-P. Blaizot and M.A. Escobedo, Quantum and classical dynamics of heavy quarks in a quark-gluon plasma, JHEP 06 (2018) 034 [arXiv:1711.10812] [INSPIRE].
J.-P. Blaizot and M.A. Escobedo, Approach to equilibrium of a quarkonium in a quark-gluon plasma, Phys. Rev. D 98 (2018) 074007 [arXiv:1803.07996] [INSPIRE].
Y. Akamatsu, M. Asakawa, S. Kajimoto and A. Rothkopf, Quantum dissipation of a heavy quark from a nonlinear stochastic Schrödinger equation, JHEP 07 (2018) 029 [arXiv:1805.00167] [INSPIRE].
T. Miura, Y. Akamatsu, M. Asakawa and A. Rothkopf, Quantum Brownian motion of a heavy quark pair in the quark-gluon plasma, Phys. Rev. D 101 (2020) 034011 [arXiv:1908.06293] [INSPIRE].
R. Sharma and A. Tiwari, Quantum evolution of quarkonia with correlated and uncorrelated noise, Phys. Rev. D 101 (2020) 074004 [arXiv:1912.07036] [INSPIRE].
N. Brambilla, M.A. Escobedo, J. Soto and A. Vairo, Quarkonium suppression in heavy-ion collisions: an open quantum system approach, Phys. Rev. D 96 (2017) 034021 [arXiv:1612.07248] [INSPIRE].
N. Brambilla, M.A. Escobedo, J. Soto and A. Vairo, Heavy quarkonium suppression in a fireball, Phys. Rev. D 97 (2018) 074009 [arXiv:1711.04515] [INSPIRE].
N. Brambilla, M.A. Escobedo, A. Vairo and P. Vander Griend, Transport coefficients from in medium quarkonium dynamics, Phys. Rev. D 100 (2019) 054025 [arXiv:1903.08063] [INSPIRE].
P.B. Gossiaux and J. Aichelin, Towards an understanding of the RHIC single electron data, Phys. Rev. C 78 (2008) 014904 [arXiv:0802.2525] [INSPIRE].
P.B. Gossiaux, R. Bierkandt and J. Aichelin, Tomography of a quark gluon plasma at RHIC and LHC energies, Phys. Rev. C 79 (2009) 044906 [arXiv:0901.0946] [INSPIRE].
J. Uphoff, O. Fochler, Z. Xu and C. Greiner, Elastic and radiative heavy quark interactions in ultra-relativistic heavy-ion collisions, J. Phys. G 42 (2015) 115106 [arXiv:1408.2964] [INSPIRE].
S. Cao, T. Luo, G.-Y. Qin and X.-N. Wang, Linearized Boltzmann transport model for jet propagation in the quark-gluon plasma: heavy quark evolution, Phys. Rev. C 94 (2016) 014909 [arXiv:1605.06447] [INSPIRE].
W. Ke, Y. Xu and S.A. Bass, Linearized Boltzmann-Langevin model for heavy quark transport in hot and dense QCD matter, Phys. Rev. C 98 (2018) 064901 [arXiv:1806.08848] [INSPIRE].
Y. Xu, J.E. Bernhard, S.A. Bass, M. Nahrgang and S. Cao, Data-driven analysis for the temperature and momentum dependence of the heavy-quark diffusion coefficient in relativistic heavy-ion collisions, Phys. Rev. C 97 (2018) 014907 [arXiv:1710.00807] [INSPIRE].
X. Yao and B. Müller, Quarkonium inside the quark-gluon plasma: diffusion, dissociation, recombination, and energy loss, Phys. Rev. D 100 (2019) 014008 [arXiv:1811.09644] [INSPIRE].
G.T. Bodwin, E. Braaten and G. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev. D 51 (1995) 1125 [Erratum ibid. 55 (1997) 5853] [hep-ph/9407339] [INSPIRE].
X. Yao and B. Müller, Approach to equilibrium of quarkonium in quark-gluon plasma, Phys. Rev. C 97 (2018) 014908 [Erratum ibid. 97 (2018) 049903] [arXiv:1709.03529] [INSPIRE].
T. Sjöstrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
K.J. Eskola, P. Paakkinen, H. Paukkunen and C.A. Salgado, EPPS16: nuclear parton distributions with LHC data, Eur. Phys. J. C 77 (2017) 163 [arXiv:1612.05741] [INSPIRE].
A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].
STAR collaboration, Γ measurements in Au+Au collisions at \( \sqrt{s_{NN}} \) = 200 GeV with the STAR experiment, Nucl. Phys. A 982 (2019) 723 [INSPIRE].
J.S. Moreland, J.E. Bernhard and S.A. Bass, Alternative ansatz to wounded nucleon and binary collision scaling in high-energy nuclear collisions, Phys. Rev. C 92 (2015) 011901 [arXiv:1412.4708] [INSPIRE].
H. Song and U.W. Heinz, Causal viscous hydrodynamics in 2 + 1 dimensions for relativistic heavy-ion collisions, Phys. Rev. C 77 (2008) 064901 [arXiv:0712.3715] [INSPIRE].
C. Shen, Z. Qiu, H. Song, J. Bernhard, S. Bass and U. Heinz, The iEBE-VISHNU code package for relativistic heavy-ion collisions, Comput. Phys. Commun. 199 (2016) 61 [arXiv:1409.8164] [INSPIRE].
J.E. Bernhard, J.S. Moreland, S.A. Bass, J. Liu and U. Heinz, Applying Bayesian parameter estimation to relativistic heavy-ion collisions: simultaneous characterization of the initial state and quark-gluon plasma medium, Phys. Rev. C 94 (2016) 024907 [arXiv:1605.03954] [INSPIRE].
CMS collaboration, Measurement of nuclear modification factors of ϒ(1S), ϒ(2S), and ϒ(3S) mesons in Pb-Pb collisions at \( \sqrt{s_{NN}} \) = 5.02 TeV, Phys. Lett. B 790 (2019) 270 [arXiv:1805.09215] [INSPIRE].
CMS collaboration, Suppression of ϒ(1S), ϒ(2S) and ϒ(3S) production in Pb-Pb collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, Phys. Lett. B 770 (2017) 357 [arXiv:1611.01510] [INSPIRE].
ALICE collaboration, Measurement of ϒ(1S) elliptic flow at forward rapidity in Pb-Pb collisions at \( \sqrt{s_{NN}} \) = 5.02 TeV, Phys. Rev. Lett. 123 (2019) 192301 [arXiv:1907.03169] [INSPIRE].
CMS collaboration, Measurement of the azimuthal anisotropy of ϒ(1S) and ϒ(2S) mesons in Pb-Pb collisions at \( \sqrt{s_{NN}} \) = 5.02 TeV, arXiv:2006.07707 [INSPIRE].
M.A. Winn, private communication.
J.E. Bernhard, J.S. Moreland and S.A. Bass, Bayesian estimation of the specific shear and bulk viscosity of quark-gluon plasma, Nature Phys. 15 (2019) 1113 [INSPIRE].
X. Yao, Application of effective field theory in nuclear physics, Ph.D. thesis, Duke U., Durham, NC, U.S.A. (2019) [arXiv:1911.08500] [INSPIRE].
S. Mrowczynski, Heavy quarks in turbulent QCD plasmas, Eur. Phys. J. A 54 (2018) 43 [arXiv:1706.03127] [INSPIRE].
X. Yao and B. Müller, Doubly charmed baryon production in heavy ion collisions, Phys. Rev. D 97 (2018) 074003 [arXiv:1801.02652] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
CMS collaboration, Measurement of the production cross section ratio σ(X b2(1P))/σ(X b1(1P)) in pp collisions at \( \sqrt{s} \) = 8 TeV, Phys. Lett. B 743 (2015) 383 [arXiv:1409.5761] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2004.06746
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Yao, X., Ke, W., Xu, Y. et al. Coupled Boltzmann transport equations of heavy quarks and quarkonia in quark-gluon plasma. J. High Energ. Phys. 2021, 46 (2021). https://doi.org/10.1007/JHEP01(2021)046
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2021)046