We solve the Lindblad equation describing the Brownian motion of a Coulombic heavy quark-antiquark pair in a strongly coupled quark-gluon plasma using the highly efficient Monte Carlo wave-function method. The Lindblad equation has been derived in the framework of pNRQCD and fully accounts for the quantum and non-Abelian nature of the system. The hydrodynamics of the plasma is realistically implemented through a 3+1D dissipative hydrodynamics code. We compute the bottomonium nuclear modification factor and compare with the most recent LHC data. The computation does not rely on any free parameter, as it depends on two transport coefficients that have been evaluated independently in lattice QCD. Our final results, which include late-time feed down of excited states, agree well with the available data from LHC 5.02 TeV PbPb collisions.
We estimate bottomonium yields in relativistic heavy-ion collisions using a lattice QCD vetted, complex-valued, heavy-quark potential embedded in a realistic, hydrodynamically evolving medium background. We find that the lattice-vetted functional form and temperature dependence of the proper heavy-quark potential dramatically reduces the dependence of the yields on parameters other than the temperature evolution, strengthening the picture of bottomonium as QGP thermometer. Our results also show improved agreement between computed yields and experimental data produced in RHIC 200 GeV/nucleon co…
In this proceedings contribution I review recent work which computes the suppression of bottomonium production in heavy-ion collisions using open quantum systems methods applied within the potential non-relativistic quantum chromodynamics (pNRQCD) effective field theory. I discuss how the computation of bottomonium suppression can be reduced to solving a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) quantum master equation for the evolution of the b-bbar reduced density matrix. The open quantum systems approach used allows one to take into account the non-equilibrium dynamics and decoherence of…
I discuss recent calculations of the thermal suppression of bottomonium states in relativistic heavy ion collisions. I present results for the inclusive Upsilon(1s) and Upsilon(2s) suppression as a function of centrality. I compare with recent preliminary CMS data available at central rapidities and make predictions at forward rapidities which are within the acceptance of the ALICE dimuon spectrometer.
In this paper we consider the suppression of bottomonium states in ultrarelativistic heavy ion collisions. We compute the suppression as a function of centrality, rapidity, and transverse momentum for the states Upsilon(1s), Upsilon(2s), Upsilon(3s), chi_b1, and chi_b2. Using this information, we then compute the inclusive Upsilon(1s) suppression as a function of centrality, rapidity, and transverse momentum including feed down effects. Calculations are performed for both RHIC sqrt(s_NN)=200 GeV Au-Au collisions and LHC sqrt(s_NN)=2.76 TeV Pb-Pb collisions. From the comparison of our theoretic…
The strong suppression of heavy quarkonia is a good indicator that one has generated a quark-gluon plasma (QGP) in an ultrarelativistic heavy ion collision. Recent advancements in first principles calculations of the heavy quark potential provide additional insight into this suppression and can be used to further pin down the in-medium properties of the QGP. Realistic 3+1d dissipative hydrodynamical models can be used to simulate the QGP and, with bottomonium as a probe, one can make inferences for the initial temperature of the QGP and other phenomenological parameters such as the shear visco…
We show that we can reach a global and coherent description of bottomonium suppression in both proton-nucleus and nucleus-nucleus collisions at the LHC energies. The measured relative suppression of the excited bottomonium states as compared to their ground state allows us to constrain the scattering cross sections between the bottomonia and the comovers created during the collisions. Our result hints at a similar energy distribution of these comovers in the environment created by proton-nucleus and nucleus-nucleus collisions. Along the way of our study, we also update our knowledge for the bo…
We compute the suppression and elliptic flow of bottomonium using real-time solutions to the Schrödinger equation with a realistic in-medium complex-valued potential. To model the initial production, we assume that, in the limit of heavy quark masses, the wave-function can be described by a lattice-smeared (Gaussian) Dirac delta wave-function. The resulting final-state quantum-mechanical overlaps provide the survival probability of all bottomonium eigenstates. Our results are in good agreement with available data for $R_{AA}$ as a function of $N_{\rm part}$ and $p_T$ collected at $\sqrt{s_{\rm…
We refine our dynamical Schroedinger-Langevin scheme designed for dealing with the suppression of quarkonium states in URHIC in order to allow for feed-downs from higher states and present updated results for the $R_{AA}$ as a function of the centrality.
In the present article, we have studied the equation of state and dissociation temperature of bottomonium state by correcting the full Cornell potential in isotropic medium by employing the effective fugacity quasi-particle Debye mass. We had also calculated the bottomonium suppression in an expanding, dissipative strongly interacting QGP medium produced in relativistic heavy-ion collisions. Finally we compared our results with experimental data from RHIC 200GeV/nucleon Au-Au collisions, LHC 2.76 TeV/nucleon Pb-Pb, and LHC 5.02 TeV/nucleon Pb-Pb collisions as a function of number of participan…
We compute bottomonium suppression and elliptic flow within the pNRQCD effective field theory using an open quantum systems approach. For the hydrodynamical background, we use 2+1D MUSIC second-order viscous hydrodynamics with IP-Glasma initial conditions and evolve bottom/antibottom quantum wave packets in real time in these backgrounds. We find that the impact of fluctuating initial conditions is small when compared to results obtained using smooth initial conditions. Including the effect of fluctuating initial conditions, we find that the Upsilon(1S) integrated elliptic flow is v_2[1S] = 0.…
We have studied the thermal suppression of the bottomonium states in relativistic heavy-ion collision at LHC energies as function of centrality, rapidity, transverse momentum etc. to explain the CMS data. Our investigation mainly spans over three problems: a) how the theoretical predictions might still be modified by the remnants of the non-perturbative confining force, b) how does the presence of a not necessarily isotropic QCD medium modify the potential (both the real and imaginary part) acting between a static quark and antiquark pair, and c) finally how the additional time-zone of pre-equ…
We report predictions for the suppression and elliptic flow of the $Υ(1S)$, $Υ(2S)$, and $Υ(3S)$ as a function of centrality and transverse momentum in ultra-relativistic heavy-ion collisions. We obtain our predictions by numerically solving a Lindblad equation for the evolution of the heavy-quarkonium reduced density matrix derived using potential nonrelativistic QCD and the formalism of open quantum systems. To numerically solve the Lindblad equation, we make use of a stochastic unraveling called the quantum trajectories algorithm. This unraveling allows us to solve the Lindblad evolution eq…
We solve the Lindblad equation describing the Brownian motion of a Coulombic heavy quark-antiquark pair in a strongly coupled quark gluon plasma using the Monte Carlo wave function method. The Lindblad equation has been derived in the framework of pNRQCD and fully accounts for the quantum and non-Abelian nature of the system. The hydrodynamics of the plasma is realistically implemented through a 3+1D dissipative hydrodynamics code. We compute the bottomonium nuclear modification factor and elliptic flow and compare with the most recent LHC data. The computation does not rely on any free parame…
We show that we can reproduce all the features of bottomonium suppression in both proton-nucleus and nucleus-nucleus collisions at LHC energies in a comover-interaction picture. For each collisions system, we use the measured {\it relative} suppression of the excited $Υ$(2S) and $Υ$(3S) states to $Υ$(1S) by ATLAS and CMS to parametrise the scattering cross sections of all $S$- and $P$-wave bottomonia with the comoving particles created during the collisions. In addition to a single nonpertubative parameter, these cross sections depend on the momentum distribution of these comovers which we fou…
System-size dependence of bottomonium suppression from Pb-Pb to light-ion collisions
Technical University of Munich（慕尼黑工业大学）；Institute for Advanced Study, Technische Universität München（慕尼黑工业大学高等研究院）；Munich Data Science Institute, Technische Universität München（慕尼黑工业大学慕尼黑数据科学研究所）
The strong suppression of bottomonia production in ultra-relativistic heavy-ion collisions is a smoking gun for the creation of a deconfined quark-gluon plasma (QGP). In this proceedings contribution, I review recent work that aims to provide a more comprehensive and systematic understanding of bottomonium dynamics in the QGP through the use of pNRQCD and an open quantum systems approach. This approach allows one to evolve the heavy-quarkonium reduced density matrix, taking into account non-unitary effective Hamiltonian evolution of the wave-function and quantum jumps between different angular…
In this proceedings contribution I review recent progress concerning the suppression of bottomonium production in the quark-gluon plasma. Making use of open quantum system methods applied to potential non-relativistic quantum chromodynamics one can show that the dynamics of heavy-quarkonium bound states satisfying the scale hierarchy 1/a_0 >> pi T ~ m_D >> E obey a Lindblad equation whose solution provides the quantum evolution of the heavy-quarkonium reduced density matrix. To solve the resulting Lindblad equation we use a quantum trajectories algorithm which allows one to include all possibl…
We present a model to explain the bottomonium suppression in Pb+Pb collisions at mid rapidity obtained from Large Hadron Collider (LHC) energy, $\sqrt{s_{NN}}=2.76$ TeV. The model consists of two decoupled mechanisms namely, color screening during bottomonium production followed by gluon induced dissociation along with collisional damping. The quasi-particle model (QPM) is used as equation of state (EOS) for the Quark-Gluon Plasma (QGP) medium. The feed-down from higher $Υ$ states, such as $Υ(1P)$, $Υ(2S)$ and $Υ(2P)$, dilated formation times for bottomonium states and viscous effect of QGP me…
We introduce a framework called Heavy Quarkonium Quantum Dynamics (HQQD) which can be used to compute the dynamical suppression of heavy quarkonia propagating in the quark-gluon plasma using real-time in-medium quantum evolution. Using HQQD we compute large sets of real-time solutions to the Schrödinger equation using a realistic in-medium complex-valued potential. We sample 2 million quarkonia wave packet trajectories and evolve them through the QGP using HQQD to obtain their survival probabilities. The computation is performed using three different HQQD model parameter sets in order to estim…
The suppression of bottomonia in ultrarelativistic heavy-ion collisions is a smoking gun for the production of a strongly interacting final state in ultrarelativistic heavy-ion collisions. Furthermore, these final state interactions are consistent with the production of a hot hydrodynamically expanding quark-gluon plasma with initial temperatures on the order of 600-700 MeV at LHC collision energies. Models which incorporate plasma screening and bound-state breakup based on high-temperature quantum chromodynamics are in good agreement with the centrality, transverse-momentum, and rapidity depe…
We had been gradually working towards building a comprehensive quarkonia suppression formalism to explain all 3 dependencies of quarkonium suppression obtained from heavy-ion collision experiments. We present here the improved version of quarkonia suppression framework. It assumes bottomonia produced in the early stage which dissociates due to color screening, gluonic dissociation, and collisional damping in addition to the shadowing as an initial state effect. The QGP medium formed in the collisions is assumed to evolve under ($3+1$)-dimensional relativistic viscous hydrodynamics which is mod…
Bottomonium production in heavy ion collisions is modified compared with any simple extrapolation from elementary collisions. This modification is most likely caused by the presence of a deconfined system of quarks and gluons for times of several fm/c. In such a medium, bottomonium can be destroyed, but the constituent bottom quarks will likely stay spatially correlated due to small mean free paths in this system. With these facts in mind, we describe bottomonium formation with a coupled set of equations. A rate equation describes the destruction of $Υ(1S)$ particles, while a Langevin equation…
We present here a comprehensive model to describe the bottomonium suppression data obtained from the CERN Large Hadron Collider (LHC) at center-of-mass energy of $\sqrt{s_{NN}}=2.76$ TeV. We employ a quasiparticle model (QPM) equation of state for the quark-gluon plasma (QGP) expanding under Bjorken's scaling law. The current model includes the modification of the formation time based on the temperature of the QGP, color screening during bottomonium production, gluon induced dissociation and collisional damping due to the imaginary part of the potential between the $b\bar b$ pair. We propose a…
We present here a model to describe the bottomonium suppression in Pb$+$Pb collisions at Large Hadron Collider (LHC), at $\sqrt{s_{NN}}=2.76$ TeV by using the quasi-particle model (QPM) equation of state (EOS) for the Quark-Gluon Plasma (QGP) expanding under Bjorken's hydrodynamical expansion. The current model includes the modification of the formation time based on the temperature of QGP, color screening during bottomonium production, gluon induced dissociation and collisional damping. The cold nuclear matter (CNM) effects and decay of higher resonances of bottomonium have also been included…
In this proceedings contribution, I review recent work that aims to provide a more comprehensive and systematic understanding of bottomonium dynamics in the quark-gluon plasma using an open quantum system (OQS) approach that is applied in the framework of the potential non-relativistic QCD (pNRQCD) effective field theory and coupled to realistic hydrodynamical backgrounds that have been tuned to soft hadron observables. I review how the computation of bottomonium suppression can be reduced to solving a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation for the evolution of the b-bbar reduce…
I review recent calculations of the suppression of bottomonium states in heavy ion collisions. A non-relativistic potential is used which is complex valued. This allows one to extract the binding energies and decay widths of the ground and excited states of bottomonium as a function of the typical plasma particle momentum and momentum-space anisotropy. The decay widths determined are used as input and integrated over space-time taking into account the dynamical evolution of the typical particle momentum and momentum-space anisotropy. The suppression of Upsilon(1s), Upsilon(2s), Upsilon(3s), ch…
Properties of bottomonia (Upsilon, chi_b and Upsilon') in the Quark-Gluon Plasma (QGP) are investigated by assessing inelastic reaction rates and their interplay with open-bottom states (b-quarks or B-mesons) and color-screening. The latter leads to vanishing quarkonium binding energies at sufficiently high temperatures (close to the dissolution point), which, in particular, renders standard gluo-dissociation, g+Upsilon -> b + b-bar, inefficient due to a substantial reduction in final-state phase space. This problem is overcome by invoking a "quasifree" destruction mechanism, g,q,q-bar + Upsil…
We estimate differential rapidity cross sections for $J/Ψ$, $Ψ(2S)$, $Υ(1S)$, $Υ(2S)$, and $Υ(3S)$ production; and $Ψ(2S)$ to $J/Ψ(1S)$, $Υ(3S)$ to $Υ(1S)$ suppression via Xe-Xe collisions at proton-proton energy $\equiv \sqrt{s_{pp}}$ =5.44 TeV. For the $Ψ(2S)$, $Υ(3S)$ states we use the mixed heavy quark hybrid theory, with these states being approximately 50\% standard and 50\% hybrid charmonium, bottomonium meson states.
Deconfined QCD matter in heavy-ion collisions has been a topic of paramount interest for many years. Quarkonia suppression in heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) experiments indicate the quark-gluon plasma (QGP) formation in such collisions. Recent experiments at LHC has given some indications of hot matter effect in asymmetric p$-$Pb nuclear collisions. Here, we employ a theoretical model to investigate the bottomonium suppression in Pb$-$Pb at $\sqrt{s_{NN}}=2.76$, $5.02$ TeV, and in p$-$Pb at $\sqrt{s_{NN}}=5.02$ TeV center-of-m…
We study the production of bottomonium states in heavy-ion reactions at collider energies available at RHIC and LHC. We employ an earlier constructed rate equation approach which accounts for both suppression and regeneration mechanisms in the quark-gluon plasma (QGP) and hadronization phases of the evolving thermal medium. Our previous predictions utilizing two limiting cases of strong and weak bottomonium binding in the QGP are updated by (i) checking the compatibility of the pertinent spectral functions with lattice-QCD results for euclidean correlators, (ii) adapting the initial conditions…
The bottomonium states due to their varying binding energies dissolve at different temperatures and thus their nuclear modification factors and relative yields have potential to map the properties of Quark Gluon Plasma (QGP). We estimate the suppression of bottomonia states due to color screening in an expanding QGP of finite lifetime and size with the conditions relevant for PbPb collisions at LHC. The properties of $Υ$ states and recent results on their dissociation temperatures have been used as ingredient in the study. The nuclear modification factors and the ratios of yields of $Υ$ states…
Recently it has been shown that the gross structure of the bottomonium spectrum is reproduced reasonably well within the non-relativistic boundstate theory based on perturbative QCD. In that calculation, however, the fine splittings and the S-P level splittings are predicted to be considerably narrower than the corresponding experimental values. We investigate the bottomonium spectrum within a specific framework based on perturbative QCD, which incorporates all the corrections up to O(alpha_S^5 m_b) and O(alpha_S^4 m_b), respectively, in the computations of the fine splittings and the S-P spli…
The present article is the follow-up of our work Bottomonium suppression in quasi-particle model, where we have extended the study for charmonium states using quasi-particle model in terms of quasi-gluons and quasi quarks/antiquarks as a equation of state. By employing medium modification to a heavy quark potential thermodynamic observables {\em viz.} pressure, energy density, speed of sound etc. have been calculated which nicely fit with the lattice equation of state for gluon, massless and as well {\em massive} flavored plasma. For obtaining the thermodynamic observables we employed the deby…
Comprehensive study of $Υ$($n$S) production in Oxygen+Oxygen collisions at LHC
Kent State University（肯特州立大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；University of California at Davis（加州大学戴维斯分校）；Texas A&M University（德克萨斯农工大学）
Experiments with gold-gold collisions at RHIC have revealed (i) stronger suppression of charmonium production at forward rapidity than at midrapidity and (ii) the similarity between the suppression degrees at RHIC and SPS energies. To describe these findings we employ the model that includes nuclear shadowing effects, calculated within the Glauber-Gribov theory, rapidity-dependent absorptive mechanism, caused by energy-momentum conservation, and dissociation and recombination of the charmonium due to interaction with co-moving matter. The free parameters of the model are tuned and fixed by com…
The production of ground-state and excited bottomonia in ultrarelativistic heavy-ion collisions is investigated within a kinetic-rate equation approach including regeneration. We augment our previous calculations by an improved treatment of medium effects, with temperature-dependent binding energies and pertinent reaction rates, $B$-meson resonance states in the equilibrium limit near the hadronization temperature, and a lattice-QCD based equation of state for the bulk medium. In addition to the centrality dependence of the bottomonium yields we compute their transverse-momentum ($p_T$) spectr…
Measurements made at the LHC have shown that the production of the ${\rm J}/ψ$, $ψ$(2S), $Υ$(1S) and $Υ$(2S) quarkonia is suppressed in Pb-Pb collisions, with respect to the extrapolation of the pp production yields. The $ψ$(2S) and $Υ$(2S) states are more strongly suppressed than the ground states and the level of the suppression changes with the centrality of the collision. We show that the measured patterns can be reproduced by a simple model, where all quarkonia are treated in a unified way, starting from the recent realisation that, in pp collisions, the probability of quarkonium formatio…
We present new results for the suppression of high transverse momentum charmonium [$J/ψ, ψ(2S)$] and bottomonium [$Υ(1S),Υ(2S),Υ(3S)$] states in Pb+Pb collisions at the Large Hadron Collider. Our theoretical formalism combines the collisional dissociation of quarkonia, as they propagate in the quark-gluon plasma, with the thermal wavefunction effects due to the screening of the $Q\bar{Q}$ attractive potential in the medium. We find that a good description of the relative suppression of the ground and higher excited quarkonium states, transverse momentum and centrality distributions is achieved…
A comprehensive phenomenological analysis of experimental data and some theoretical models is presented here (for mesons) to critically discuss how Regge trajectory parameters depend on flavor. Through analytic continuation of physical trajectories (obtained from resonance data) into the space like region, we derive the suppression factor for heavy flavor production. The case of our D Regge exchange, both for D and $Λ_c$ production, is considered in some detail. Good agreement with data is reached confirming that indeed the slopes of heavier flavors decrease. This result suggests that the conf…
We introduce an open-source package called QTraj that solves the Lindblad equation for heavy-quarkonium dynamics using the quantum trajectories algorithm. The package allows users to simulate the suppression of heavy-quarkonium states using externally-supplied input from 3+1D hydrodynamics simulations. The code uses a split-step pseudo-spectral method for updating the wave-function between jumps, which is implemented using the open-source multi-threaded FFTW3 package. This allows one to have manifestly unitary evolution when using real-valued potentials. In this paper, we provide detailed docu…
Complex-energy spectrum and dissociation of heavy quarkonia in an anisotropic collisional quark-gluon plasma
School of Physical Sciences, National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute（物理科学学院，国家科学教育与研究中心，霍米·巴巴国立学院）
