# Quarkonium Production in the QGP

## Abstract

**:**

## 1. Introduction

## 2. Quarkonium in Thermal Equilibrium

## 3. In-Medium Quarkonium Real-Time Dynamics

## 4. Summary

## Funding

## Conflicts of Interest

## References

- Adamczyk, L.; et al. [STAR Collaboration]. Y production in U + U collisions at $\sqrt{{s}_{NN}}$ = 193 GeV measured with the STAR experiment. Phys. Rev. C
**2016**, 94, 064904. [Google Scholar] [CrossRef] - Sirunyan, A.M.; et al. [CMS Collaboration]. Suppression of Excited Y States Relative to the Ground State in Pb-Pb Collisions at $\sqrt{{s}_{NN}}$ = 5.02 TeV. Phys. Rev. Lett.
**2018**, 120, 142301. [Google Scholar] [CrossRef] - Krouppa, B.; Rothkopf, A.; Strickland, M. Bottomonium suppression using a lattice QCD vetted potential. Phys. Rev. D
**2018**, 97, 016017. [Google Scholar] [CrossRef] [Green Version] - Acharya, S.; et al. [ALICE Collaboration]. Study of J/ψ azimuthal anisotropy at forward rapidity in Pb-Pb collisions at $\sqrt{{s}_{NN}}$ = 5.02 TeV. J. High Energy Phys.
**2019**, 2019, 12. [Google Scholar] [CrossRef] - Aarts, G.; Allton, C.; Harris, T.; Kim, S.; Lombardo, M.P.; Ryan, S.M.; Skullerud, J.I. The bottomonium spectrum at finite temperature from N
_{f}= 2 + 1 lattice QCD. J. High Energy Phys.**2014**, 2014, 97. [Google Scholar] [CrossRef] - Kim, S.; Petreczky, P.; Rothkopf, A. Quarkonium in-medium properties from realistic lattice NRQCD. J. High Energy Phys.
**2018**, 2018, 88. [Google Scholar] [CrossRef] - Ding, H.T.; Francis, A.; Kaczmarek, O.; Karsch, F.; Satz, H.; Soeldner, W. Charmonium properties in hot quenched lattice QCD. Phys. Rev. D
**2012**, 86, 014509. [Google Scholar] [CrossRef] - Kelly, A.; Rothkopf, A.; Skullerud, J.I. Bayesian study of relativistic open and hidden charm in anisotropic lattice QCD. Phys. Rev. D
**2018**, 97, 114509. [Google Scholar] [CrossRef] [Green Version] - Koma, Y.; Koma, M.; Wittig, H. Relativistic corrections to the static potential at O(1/m) and O(1/m**2). PoS LATTICE
**2007**, 2007, 111. [Google Scholar] - Brambilla, N.; Pineda, A.; Soto, J.; Vairo, A. Effective field theories for heavy quarkonium. Rev. Mod. Phys.
**2005**, 77, 1423. [Google Scholar] [CrossRef] - Burnier, Y.; Rothkopf, A. Disentangling the timescales behind the non-perturbative heavy quark potential. Phys. Rev. D
**2012**, 86, 051503. [Google Scholar] [CrossRef] - Laine, M.; Philipsen, O.; Romatschke, P.; Tassler, M. Real-time static potential in hot QCD. J. High Energy Phys.
**2007**, 2007, 054. [Google Scholar] [CrossRef] - Beraudo, A.; Blaizot, J.-P.; Ratti, C. Real and imaginary-time Q anti-Q correlators in a thermal medium. Nucl. Phys. A
**2008**, 806, 312. [Google Scholar] [CrossRef] - Brambilla, N.; Ghiglieri, J.; Vairo, A.; Petreczky, P. Static quark-antiquark pairs at finite temperature. Phys. Rev. D
**2008**, 78, 014017. [Google Scholar] [CrossRef] - Akamatsu, Y.; Rothkopf, A. Stochastic potential and quantum decoherence of heavy quarkonium in the quark-gluon plasma. Phys. Rev. D
**2012**, 85, 105011. [Google Scholar] [CrossRef] - Rothkopf, A.; Hatsuda, T.; Sasaki, S. Proper heavy-quark potential from a spectral decomposition of the thermal Wilson loop. Soryushiron Kenkyu Electron.
**2010**, 118, A145–A147. [Google Scholar] - Rothkopf, A.; Hatsuda, T.; Sasaki, S. Complex Heavy-Quark Potential at Finite Temperature from Lattice QCD. Phys. Rev. Lett.
**2012**, 108, 162001. [Google Scholar] [CrossRef] - Rothkopf, A. Bayesian techniques and applications to QCD. arXiv
**2019**, arXiv:1903.02293. [Google Scholar] - Tripolt, R.A.; Gubler, P.; Ulybyshev, M.; von Smekal, L. Numerical analytic continuation of Euclidean data. Comput. Phys. Commun.
**2019**, 237, 129. [Google Scholar] [CrossRef] - Burnier, Y.; Rothkopf, A. Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories. Phys. Rev. Lett.
**2013**, 111, 182003. [Google Scholar] [CrossRef] [PubMed] - Petreczky, P.; et al. [TUMQCD Collaboration]. Lattice Calculations of Heavy Quark Potential at Finite Temperature. Nucl. Phys. A
**2017**, 967, 592–595. [Google Scholar] [CrossRef] - Bazavov, A.; Petreczky, P.; Weber, J.H. Equation of State in 2 + 1 Flavor QCD at High Temperatures. Phys. Rev. D
**2018**, 97, 014510. [Google Scholar] [CrossRef] - Bazavov, A.; et al. [HotQCD Collaboration]. Equation of state in (2 + 1)-flavor QCD. Phys. Rev. D
**2014**, 90, 094503. [Google Scholar] [CrossRef] - Petreczky, P.; Rothkopf, A.; Weber, J. Realistic in-medium heavy-quark potential from high statistics lattice QCD simulations. Nucl. Phys. A
**2019**, 982, 735–738. [Google Scholar] [CrossRef] - Burnier, Y.; Kaczmarek, O.; Rothkopf, A. Quarkonium at finite temperature: Towards realistic phenomenology from first principles. J. High Energy Phys.
**2015**, 2015, 101. [Google Scholar] [CrossRef] - Lafferty, D.; Rothkopf, A. Quarkonium phenomenology from a generalised Gauss-law. Universe
**2019**, in press. [Google Scholar] - Kajimoto, S.; Akamatsu, Y.; Asakawa, M.; Rothkopf, A. Dynamical dissociation of quarkonia by wave function decoherence. Phys. Rev. D
**2018**, 97, 014003. [Google Scholar] [CrossRef] [Green Version] - Andronic, A.; Beutler, F.; Braun-Munzinger, P.; Redlich, K.; Stachel, J. Statistical hadronization of heavy flavor quarks in elementary collisions: Successes and failures. Phys. Lett. B
**2009**, 678, 350. [Google Scholar] [CrossRef] - Andronic, A.; Braun-Munzinger, P.; Köhler, M.K.; Stachel, J. Testing charm quark thermalisation within the Statistical Hadronisation Model. Nucl. Phys. A
**2019**, 982, 759–762. [Google Scholar] [CrossRef] - Akamatsu, Y. Real-time quantum dynamics of heavy quark systems at high temperature. Phys. Rev. D
**2013**, 87, 045016. [Google Scholar] [CrossRef] - Akamatsu, Y. Heavy quark master equations in the Lindblad form at high temperatures. Phys. Rev. D
**2015**, 91, 056002. [Google Scholar] [CrossRef] - De Boni, D. Fate of in-medium heavy quarks via a Lindblad equation. J. High Energy Phys.
**2017**, 2017, 64. [Google Scholar] [CrossRef] - Blaizot, J.P.; Escobedo, M.A. Quantum and classical dynamics of heavy quarks in a quark-gluon plasma. J. High Energy Phys.
**2018**, 2018, 34. [Google Scholar] [CrossRef] - Brambilla, N.; Escobedo, M.A.; Soto, J.; Vairo, A. Heavy quarkonium suppression in a fireball. Phys. Rev. D
**2018**, 97, 074009. [Google Scholar] [CrossRef] [Green Version] - Yao, X.; Mehen, T. Quarkonium in-Medium Transport Equation Derived from First Principles. arXiv
**2019**, arXiv:1811.07027. [Google Scholar] - Brambilla, N.; Escobedo, M.A.; Vairo, A.; Griend, P.V. Transport coefficients from in medium quarkonium dynamics. arXiv
**2019**, arXiv:1903.08063. [Google Scholar] - Akamatsu, Y.; Asakawa, M.; Kajimoto, S.; Rothkopf, A. Quantum dissipation of a heavy quark from a nonlinear stochastic Schrödinger equation. J. High Energy Phys.
**2018**, 2018, 29. [Google Scholar] [CrossRef]

**Figure 1.**(

**left**) $\mathrm{Re}[V]$ obtained from Pade reconstructed spectral functions of the Wilson line correlator in Coulomb gauge on ${48}^{3}\times 12,16$ lattices with ${N}_{f}=2+1$ light quarks. The values are shifted by hand in y-direction for better readability from lowest temperature $T=151$ MeV on top to highest $T=1451$ MeV bottom. The gray data points denote the color singlet free energy in Coulomb gauge on the same lattices. (

**right**) Tentative values of $\mathrm{Im}[V]$ at a selection of temperatures extracted via Bayesian inference from the same lattice data.

**Figure 2.**(

**left**) Charmonium in-medium spectral functions from the continuum corrected in-medium heavy quark potential [25]. (

**right**) Survival probabilities of the ground state in a one-dimensional model calculation of the real-time dynamics of bottomonium in the open-quantum systems approach [27]. The blue and green curve correspond to the stochastic potential computation with different correlation lengths. The pink and dark red curves arise from a naive Schrödinger equation with complex potential.

© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rothkopf, A.
Quarkonium Production in the QGP. *Universe* **2019**, *5*, 117.
https://doi.org/10.3390/universe5050117

**AMA Style**

Rothkopf A.
Quarkonium Production in the QGP. *Universe*. 2019; 5(5):117.
https://doi.org/10.3390/universe5050117

**Chicago/Turabian Style**

Rothkopf, Alexander.
2019. "Quarkonium Production in the QGP" *Universe* 5, no. 5: 117.
https://doi.org/10.3390/universe5050117