- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Lattice study of correlators of chromoelectric fields for heavy quarkonium dynamics in the quark-gluon plasma

Nora Brambilla1,2,3,*, Saumen Datta4,†, Marc Janer1,‡, Viljami Leino5,6,§, Julian Mayer-Steudte1,3,∥, Peter Petreczky7,¶, and Antonio Vairo1,** (TUMQCD Collaboration)

  • *Contact author: nora.brambilla@ph.tum.de
  • †Contact author: saumen@theory.tifr.res.in
  • ‡Contact author: m.janer@tum.de
  • §Contact author: viljami.leino@uni-mainz.de
  • ∥Contact author: julian.mayer-steudte@tum.de
  • Contact author: petreczk@bnl.gov
  • **Contact author: antonio.vairo@ph.tum.de
PDF

Phys. Rev. D 112, 074509 – Published 17 October, 2025

DOI: https://doi.org/10.1103/387k-mdl1

Abstract

We perform a lattice calculation of the correlators of two chromoelectric fields in the adjoint representation connected by adjoint Wilson lines at nonzero temperature. These correlators arise in the study of quarkonium dynamics and of adjoint heavy quark diffusion in deconfined matter. We work in SU(3) gauge theory using either gradient flow or multilevel algorithms for noise reduction, and discuss the renormalization of the correlators on the lattice. We find that a Casimir factor rescaling relates the adjoint correlators corresponding to the diffusion of an adjoint heavy quark and the octet-octet quarkonium transitions to the chromoelectric correlator in the fundamental representation describing the diffusion of a heavy quark.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (52)

  1. T. Matsui and H. Satz, J/ψ suppression by quark-gluon plasma formation, Phys. Lett. B 178, 416 (1986).
  2. G. Aarts et al., Heavy-flavor production and medium properties in high-energy nuclear collisions—What next?, Eur. Phys. J. A 53, 93 (2017).
  3. Jiaxing Zhao, Kai Zhou, Shile Chen, and Pengfei Zhuang, Heavy flavors under extreme conditions in high energy nuclear collisions, Prog. Part. Nucl. Phys. 114, 103801 (2020).
  4. A. Andronic et al., Comparative study of quarkonium transport in hot QCD matter, Eur. Phys. J. A 60, 88 (2024).
  5. N. Brambilla et al., QCD and strongly coupled gauge theories: Challenges and perspectives, Eur. Phys. J. C 74, 2981 (2014).
  6. Nora Brambilla, Antonio Pineda, Joan Soto, and Antonio Vairo, Effective field theories for heavy quarkonium, Rev. Mod. Phys. 77, 1423 (2005).
  7. Nora Brambilla, Jacopo Ghiglieri, Antonio Vairo, and Peter Petreczky, Static quark-antiquark pairs at finite temperature, Phys. Rev. D 78, 014017 (2008).
  8. Nora Brambilla, Miguel Angel Escobedo, Jacopo Ghiglieri, Joan Soto, and Antonio Vairo, Heavy quarkonium in a weakly-coupled quark-gluon plasma below the melting temperature, J. High Energy Phys. 09 (2010) 038.
  9. Miguel Angel Escobedo and Joan Soto, Non-relativistic bound states at finite temperature (II): The muonic hydrogen, Phys. Rev. A 82, 042506 (2010).
  10. Alexander M. Eller, Jacopo Ghiglieri, and Guy D. Moore, Thermal quarkonium mass shift from Euclidean correlators, Phys. Rev. D 99, 094042 (2019).
  11. Nora Brambilla, Miguel A. Escobedo, Joan Soto, and Antonio Vairo, Quarkonium suppression in heavy-ion collisions: An open quantum system approach, Phys. Rev. D 96, 034021 (2017).
  12. Nora Brambilla, Miguel A. Escobedo, Joan Soto, and Antonio Vairo, Heavy quarkonium suppression in a fireball, Phys. Rev. D 97, 074009 (2018).
  13. Nora Brambilla, Miguel A. Escobedo, Antonio Vairo, and Peter Vander Griend, Transport coefficients from in medium quarkonium dynamics, Phys. Rev. D 100, 054025 (2019).
  14. Xiaojun Yao and Thomas Mehen, Quarkonium semiclassical transport in quark-gluon plasma: Factorization and quantum correction, J. High Energy Phys. 02 (2021) 062.
  15. Bruno Scheihing-Hitschfeld and Xiaojun Yao, Real time quarkonium transport coefficients in open quantum systems from Euclidean QCD, Phys. Rev. D 108, 054024 (2023); 109, 099902(E) (2024).
  16. Tobias Binder, Kyohei Mukaida, Bruno Scheihing-Hitschfeld, and Xiaojun Yao, Non-Abelian electric field correlator at NLO for dark matter relic abundance and quarkonium transport, J. High Energy Phys. 01 (2022) 137.
  17. Nora Brambilla, Tom Magorsch, Michael Strickland, Antonio Vairo, and Peter Vander Griend, Bottomonium suppression from the three-loop QCD potential, Phys. Rev. D 109, 114016 (2024).
  18. Nora Brambilla, Miguel Ángel Escobedo, Ajaharul Islam, Michael Strickland, Anurag Tiwari, Antonio Vairo, and Peter Vander Griend, Heavy quarkonium dynamics at next-to-leading order in the binding energy over temperature, J. High Energy Phys. 08 (2022) 303.
  19. Rishi Sharma, Quarkonium propagation in the quark–gluon plasma, Eur. Phys. J. Special Topics 230, 697 (2021).
  20. Martin Lüscher, Properties and uses of the Wilson flow in lattice QCD, J. High Energy Phys. 08 (2010) 071; 03 (2014) 92.
  21. Martin Lüscher and Peter Weisz, Locality and exponential error reduction in numerical lattice gauge theory, J. High Energy Phys. 09 (2001) 010.
  22. M. Foster and C. Michael (UKQCD Collaboration), Hadrons with a heavy color adjoint particle, Phys. Rev. D 59, 094509 (1999).
  23. Debasish Banerjee, Saumen Datta, Rajiv Gavai, and Pushan Majumdar, Heavy quark momentum diffusion coefficient from lattice QCD, Phys. Rev. D 85, 014510 (2012).
  24. A. Francis, O. Kaczmarek, M. Laine, T. Neuhaus, and H. Ohno, Nonperturbative estimate of the heavy quark momentum diffusion coefficient, Phys. Rev. D 92, 116003 (2015).
  25. Nora Brambilla, Viljami Leino, Peter Petreczky, and Antonio Vairo, Lattice QCD constraints on the heavy quark diffusion coefficient, Phys. Rev. D 102, 074503 (2020).
  26. Luis Altenkort, Alexander M. Eller, Olaf Kaczmarek, Lukas Mazur, Guy D. Moore, and Hai-Tao Shu, Heavy quark momentum diffusion from the lattice using gradient flow, Phys. Rev. D 103, 014511 (2021).
  27. Nora Brambilla, Viljami Leino, Julian Mayer-Steudte, and Peter Petreczky (TUMQCD Collaboration), Heavy quark diffusion coefficient with gradient flow, Phys. Rev. D 107, 054508 (2023).
  28. Luis Altenkort, Olaf Kaczmarek, Rasmus Larsen, Swagato Mukherjee, Peter Petreczky, Hai-Tao Shu, and Simon Stendebach (HotQCD Collaboration), Heavy quark diffusion from 2+1 flavor lattice QCD with 320 MeV pion mass, Phys. Rev. Lett. 130, 231902 (2023).
  29. Jorge Casalderrey-Solana and Derek Teaney, Heavy quark diffusion in strongly coupled N=4 Yang-Mills, Phys. Rev. D 74, 085012 (2006).
  30. Simon Caron-Huot, Mikko Laine, and Guy D. Moore, A way to estimate the heavy quark thermalization rate from the lattice, J. High Energy Phys. 04 (2009) 053.
  31. Nora Brambilla, Miguel Angel Escobedo, Ajaharul Islam, Michael Strickland, Antonio Vairo, and Peter Vander Griend, Anatomy of quarkonium transport coefficients, TUM-EFT 191/24, FERMILAB-PUB-24-0451-T.
  32. Sundance O. Bilson-Thompson, Derek B. Leinweber, and Anthony G. Williams, Highly improved lattice field strength tensor, Ann. Phys. (Amsterdam) 304, 1 (2003).
  33. R. Narayanan and H. Neuberger, Infinite N phase transitions in continuum Wilson loop operators, J. High Energy Phys. 03 (2006) 064.
  34. Martin Lüscher, Trivializing maps, the Wilson flow and the HMC algorithm, Commun. Math. Phys. 293, 899 (2010).
  35. Nora Brambilla, Viljami Leino, Julian Mayer-Steudte, and Antonio Vairo, Static force from generalized Wilson loops on the lattice using the gradient flow, Phys. Rev. D 109, 114517 (2024).
  36. Martin Lüscher and Peter Weisz, Perturbative analysis of the gradient flow in non-abelian gauge theories, J. High Energy Phys. 02 (2011) 051.
  37. http://physics.utah.edu/∼detar/milc.html.
  38. Kenneth G. Wilson, Confinement of quarks, Phys. Rev. D 10, 2445 (1974).
  39. A. Francis, O. Kaczmarek, M. Laine, T. Neuhaus, and H. Ohno, Critical point and scale setting in SU(3) plasma: An update, Phys. Rev. D 91, 096002 (2015).
  40. Patrick Fritzsch and Alberto Ramos, The gradient flow coupling in the Schrödinger Functional, J. High Energy Phys. 10 (2013) 008.
  41. Alexei Bazavov and Thomas Chuna, Efficient integration of gradient flow in lattice gauge theory and properties of low-storage commutator-free Lie group methods, arXiv:2101.05320.
  42. David de la Cruz, Alexander M. Eller, and Guy D. Moore, QCD field-strength correlators on a Polyakov loop with gradient flow at next-to-leading order, Phys. Rev. D 110, 094057 (2024).
  43. Sourendu Gupta, Kay Huebner, and Olaf Kaczmarek, Renormalized Polyakov loops in many representations, Phys. Rev. D 77, 034503 (2008).
  44. Nora Brambilla, Panayiotis Panayiotou, Saga Säppi, and Antonio Vairo, The chromoelectric adjoint correlators in Euclidean space at next-to-leading order, J. High Energy Phys. 08 (2025) 219.
  45. Nora Brambilla, Dolors Eiras, Antonio Pineda, Joan Soto, and Antonio Vairo, New predictions for inclusive heavy quarkonium P wave decays, Phys. Rev. Lett. 88, 012003 (2002).
  46. Nora Brambilla, Dolors Eiras, Antonio Pineda, Joan Soto, and Antonio Vairo, Inclusive decays of heavy quarkonium to light particles, Phys. Rev. D 67, 034018 (2003).
  47. Nora Brambilla, Hee Sok Chung, Daniel Müller, and Antonio Vairo, Decay and electromagnetic production of strongly coupled quarkonia in pNRQCD, J. High Energy Phys. 04 (2020) 095.
  48. https://www.gauss-centre.eu
  49. https://www.lrz.de
  50. https://www.origins-cluster.de/
  51. Murray Gell-Mann, Symmetries of baryons and mesons, Phys. Rev. 125, 1067 (1962).
  52. Martin Lüscher and Peter Weisz, Computation of the relation between the bare lattice coupling and the MS coupling in SU(N) gauge theories to two loops, Nucl. Phys. B452, 234 (1995).

Outline

Information

Phys. Rev. D 112, 074509– Published 17 October, 2025
  • Received 30 May 2025
  • Accepted 11 September 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation