- Open Access
Quenching through the QCD chiral phase transition
Phys. Rev. D 112, 114019 – Published 12 December, 2025
DOI: https://doi.org/10.1103/plfm-z5xx
Abstract
We present a detailed numerical and analytical study of the out-of-equilibrium dynamics of Model G, the dynamical universality class relevant to the chiral phase transition. We perform numerical 3D stochastic (Langevin) simulations of the critical point for large lattices in the chiral limit. We quench the system from the high-temperature unbroken phase to the broken phase and study the nonequilibrium dynamics of pion fields. Strikingly, the nonequilibrium evolution of the two-point functions exhibits a regime of growth, a parametrically large enhancement, and a subsequent slow relaxation to equilibrium. We analyze our numerical results using dynamic critical scaling and mean-field theory. The growth of the two-point functions is determined by the nonlinear dynamics of an ideal non-Abelian superfluid, which is a limit of Model G that reflects the broken chiral symmetry. We also relate the nonequilibrium two-point functions to a long-lived parametric enhancement of soft pion yields relative to thermal equilibrium following a quench.
Physics Subject Headings (PhySH)
See Also
Supercooled Goldstone Bosons at the QCD Chiral Phase Transition
Article Text
References (67)
- Brookhaven National Laboratory, Report of the Workshop on GeV/Nucleon Collisions of Heavy Ions: How and Why, November 29–December 1, 1974, Bear Mountain, New York (Brookhaven National Laboratory, Upton, NY, 1974).
- Wit Busza, Krishna Rajagopal, and Wilke van der Schee, Heavy ion collisions: The big picture, and the big questions, Annu. Rev. Nucl. Part. Sci. 68, 339 (2018).
- Govert Nijs and Wilke van der Schee, Hadronic nucleus-nucleus cross section and the nucleon size, Phys. Rev. Lett. 129, 232301 (2022).
- D. Everett et al. (JETSCAPE Collaboration), Phenomenological constraints on the transport properties of QCD matter with data-driven model averaging, Phys. Rev. Lett. 126, 242301 (2021).
- Z. Citron et al., Report from Working Group 5: Future physics opportunities for high-density QCD at the LHC with heavy-ion and proton beams, CERN Yellow Rep. Monogr. 7, 1159 (2019).
- Shreyasi Acharya et al. (ALICE Collaboration), The ALICE experiment: A journey through QCD, Eur. Phys. J. C 84, 813 (2024).
- John W. Harris and Berndt Müller, “QGP signatures” revisited, Eur. Phys. J. C 84, 247 (2024).
- P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys. 49, 435 (1977).
- Betty Abelev et al. (ALICE Collaboration), Centrality dependence of , K, p production in Pb-Pb collisions at , Phys. Rev. C 88, 044910 (2013).
- Shreyasi Acharya et al. (ALICE Collaboration), Production of charged pions, kaons, and (anti-)protons in Pb-Pb and inelastic collisions at , Phys. Rev. C 101, 044907 (2020).
- D. Devetak, A. Dubla, S. Floerchinger, E. Grossi, S. Masciocchi, A. Mazeliauskas, and I. Selyuzhenkov, Global fluid fits to identified particle transverse momentum spectra from heavy-ion collisions at the Large Hadron Collider, J. High Energy Phys. 06 (2020) 044.
- Govert Nijs, Wilke van der Schee, Umut Gürsoy, and Raimond Snellings, Bayesian analysis of heavy ion collisions with the heavy ion computational framework Trajectum, Phys. Rev. C 103, 054909 (2021).
- D. Everett et al. (JETSCAPE Collaboration), Multisystem Bayesian constraints on the transport coefficients of QCD matter, Phys. Rev. C 103, 054904 (2021).
- Pengzhong Lu, Rafet Kavak, Andrea Dubla, Silvia Masciocchi, and Ilya Selyuzhenkov, Quantification of the low- pion excess in heavy-ion collisions at the LHC and top RHIC energy, Nuclear Science and Techniques 36, 142 (2025).
- Aleksas Mazeliauskas and Vytautas Vislavicius, Temperature and fluid velocity on the freeze-out surface from , , spectra in pp, p-Pb and Pb-Pb collisions, Phys. Rev. C 101, 014910 (2020).
- Ivan Melo and Boris Tomášik, Kinetic freeze-out in central heavy-ion collisions between 7.7 and 2760 GeV per nucleon pair, J. Phys. G 47, 045107 (2020).
- Viktor Begun and Wojciech Florkowski, Bose-Einstein condensation of pions in heavy-ion collisions at the CERN Large Hadron Collider (LHC) energies, Phys. Rev. C 91, 054909 (2015).
- Pasi Huovinen, Pok Man Lo, Michał Marczenko, Kenji Morita, Krzysztof Redlich, and Chihiro Sasaki, Effects of -meson width on pion distributions in heavy-ion collisions, Phys. Lett. B 769, 509 (2017).
- Yuuka Kanakubo, Yasuki Tachibana, and Tetsufumi Hirano, Nonequilibrium components in the region of very low transverse momentum in high-energy nuclear collisions, Phys. Rev. C 106, 054908 (2022).
- Krishna Rajagopal and Frank Wilczek, Emergence of coherent long wavelength oscillations after a quench: Application to QCD, Nucl. Phys. B404, 577 (1993).
- Jean-Paul Blaizot and Andre Krzywicki, Soft pion emission in high-energy heavy ion collisions, Phys. Rev. D 46, 246 (1992).
- J. D. Bjorken, K. L. Kowalski, and C. C. Taylor, Baked Alaska, in 7th Les Rencontres de Physique de la Vallee d’Aoste: Results and Perspectives in Particle Physics (1993), pp. 507–528.
- B. Mohanty and Julien Serreau, Disoriented chiral condensate: Theory and experiment, Phys. Rep. 414, 263 (2005).
- ALICE Collaboration, Letter of intent for ALICE 3: A next-generation heavy-ion experiment at the LHC, arXiv:2211.02491.
- A. Pandav, D. Mallick, and B. Mohanty, Search for the QCD critical point in high energy nuclear collisions, Prog. Part. Nucl. Phys. 125, 103960 (2022).
- D. T. Son and M. A. Stephanov, Dynamic universality class of the QCD critical point, Phys. Rev. D 70, 056001 (2004).
- Chandrodoy Chattopadhyay, Josh Ott, Thomas Schaefer, and Vladimir V. Skokov, Simulations of stochastic fluid dynamics near a critical point in the phase diagram, Phys. Rev. Lett. 133, 032301 (2024).
- Chandrodoy Chattopadhyay, Josh Ott, Thomas Schaefer, and Vladimir Skokov, Dynamic scaling of order parameter fluctuations in model B, Phys. Rev. D 108, 074004 (2023).
- Johannes V. Roth, Yunxin Ye, Sören Schlichting, and Lorenz von Smekal, Universal critical dynamics near the chiral phase transition and the QCD critical point, Phys. Rev. D 111, L111901 (2025).
- Szabolcs Borsanyi, Zoltan Fodor, Jana N. Guenther, Sandor K. Katz, Kalman K. Szabo, Attila Pasztor, Israel Portillo, and Claudia Ratti, Higher order fluctuations and correlations of conserved charges from lattice QCD, J. High Energy Phys. 10 (2018) 205.
- A. Bazavov et al. (HotQCD Collaboration), Chiral crossover in QCD at zero and non-zero chemical potentials, Phys. Lett. B 795, 15 (2019).
- H. T. Ding et al. (HotQCD Collaboration), Chiral phase transition temperature in ()-Flavor QCD, Phys. Rev. Lett. 123, 062002 (2019).
- O. Kaczmarek, F. Karsch, A. Lahiri, L. Mazur, and C. Schmidt, QCD phase transition in the chiral limit, NIC Ser. 50, 193 (2020).
- Andrey Yu. Kotov, Maria Paola Lombardo, and Anton Trunin, QCD transition at the physical point, and its scaling window from twisted mass Wilson fermions, Phys. Lett. B 823, 136749 (2021).
- Francesca Cuteri, Owe Philipsen, and Alessandro Sciarra, On the order of the QCD chiral phase transition for different numbers of quark flavours, J. High Energy Phys. 11 (2021) 141.
- Sören Schlichting, Dominik Smith, and Lorenz von Smekal, Spectral functions and critical dynamics of the O(4) model from classical-statistical lattice simulations, Nucl. Phys. B950, 114868 (2020).
- Adrien Florio, Eduardo Grossi, Alexander Soloviev, and Derek Teaney, Dynamics of the critical point in QCD, Phys. Rev. D 105, 054512 (2022).
- Adrien Florio, Eduardo Grossi, and Derek Teaney, Dynamics of the O(4) critical point in QCD: Critical pions and diffusion in Model G, Phys. Rev. D 109, 054037 (2024).
- Mustafa A. Amin, Mark P. Hertzberg, David I. Kaiser, and Johanna Karouby, Nonperturbative dynamics of reheating after inflation: A review, Int. J. Mod. Phys. D 24, 1530003 (2014).
- D. Boyanovsky, H. J. de Vega, R. Holman, and J. F. J. Salgado, Analytic and numerical study of preheating dynamics, Phys. Rev. D 54, 7570 (1996).
- Juergen Berges and Julien Serreau, Parametric resonance in quantum field theory, Phys. Rev. Lett. 91, 111601 (2003).
- Adrien Florio, Eduardo Grossi, Aleksas Mazeliauskas, Alexander Soloviev, and Derek Teaney, companion Letter, Supercooled goldstone bosons at the QCD chiral phase transition, Phys. Rev. Lett. 135, 242303 (2025).
- Krishna Rajagopal and Frank Wilczek, Static and dynamic critical phenomena at a second order QCD phase transition, Nucl. Phys. B399, 395 (1993).
- Eduardo Grossi, Alexander Soloviev, Derek Teaney, and Fanglida Yan, Transport and hydrodynamics in the chiral limit, Phys. Rev. D 102, 014042 (2020).
- Eduardo Grossi, Alexander Soloviev, Derek Teaney, and Fanglida Yan, Soft pions and transport near the chiral critical point, Phys. Rev. D 104, 034025 (2021).
- J. Engels and F. Karsch, Finite size dependence of scaling functions of the three-dimensional O(4) model in an external field, Phys. Rev. D 90, 014501 (2014).
- U. C. Täuber, Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior (Cambridge University Press, Cambridge, England, 2014).
- N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (CRC Press, Boca Raton, FL, 2018).
- Martin Hasenbusch, Three-dimensional -invariant models at criticality for , Phys. Rev. B 105, 054428 (2022).
- J. Engels and F. Karsch, The scaling functions of the free energy density and its derivatives for the 3d O(4) model, Phys. Rev. D 85, 094506 (2012).
- D. T. Son and Misha A. Stephanov, Pion propagation near the QCD chiral phase transition, Phys. Rev. Lett. 88, 202302 (2002).
- D. T. Son and Misha A. Stephanov, Real time pion propagation in finite temperature QCD, Phys. Rev. D 66, 076011 (2002).
- P. Hasenfratz and H. Leutwyler, Goldstone boson related finite size effects in field theory and critical phenomena with symmetry, Nucl. Phys. B343, 241 (1990).
- D. T. Son, Hydrodynamics of nuclear matter in the chiral limit, Phys. Rev. Lett. 84, 3771 (2000).
- Akash Jain, Theory of non-Abelian superfluid dynamics, Phys. Rev. D 95, 121701 (2017).
- Kristan Jensen, Matthias Kaminski, Pavel Kovtun, Rene Meyer, Adam Ritz, and Amos Yarom, Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109, 101601 (2012).
- A. Onuki, Phase Transition Dynamics (Cambridge University Press, Cambridge, England, 2002).
- J. Engels and O. Vogt, Longitudinal and transverse spectral functions in the three-dimensional O(4) model, Nucl. Phys. B832, 538 (2010).
- Juergen Berges, Alexander. Rothkopf, and Jonas Schmidt, Non-thermal fixed points: Effective weak-coupling for strongly correlated systems far from equilibrium, Phys. Rev. Lett. 101, 041603 (2008).
- J. Berges, K. Boguslavski, S. Schlichting, and R. Venugopalan, Universality far from equilibrium: From superfluid Bose gases to heavy-ion collisions, Phys. Rev. Lett. 114, 061601 (2015).
- Kirill Boguslavski, Understanding the dynamics of field theories far from equilibrium, Proc. Sci., Confinement2018 (2018) 136 [arXiv:1811.07171].
- Aleksandr N. Mikheev, Ido Siovitz, and Thomas Gasenzer, Universal dynamics and non-thermal fixed points in quantum fluids far from equilibrium, Eur. Phys. J. Spec. Top. 232, 3393 (2023).
- Jens Braun, Wei-jie Fu, Jan M. Pawlowski, Fabian Rennecke, Daniel Rosenblüh, and Shi Yin, Chiral susceptibility in ()-flavor QCD, Phys. Rev. D 102, 056010 (2020).
- Jens Braun et al., Soft modes in hot QCD matter, Phys. Rev. D 111, 094010 (2025).
- A. Florio, E. Grossi, A. Mazeliauskas, A. Soloviev, and D. Teaney (to be published).
- Ardit Krasniqi, Marco Cè, Renwick J. Hudspith, and Harvey B. Meyer, Hot QCD matter around the chiral crossover: A lattice study with O(a)-improved Wilson fermions, Phys. Rev. D 110, 114506 (2024).
- A. Florio, E. Grossi, A. Mazeliauskas, A. Soloviev, and D. Teaney, Plotting routines and data files for 2504.03514 and 2504.03516 (2025), 10.5281/zenodo.17600429.