Evidence for dynamical chiral condensate in high-energy heavy ion collisions

Abstract

Quantum chromodynamics with light quarks features an approximate global symmetry, known as chiral symmetry, that is believed to be spontaneously broken by the vacuum expectation value of a scalar and isoscalar composite field, in addition to a small explicit breaking due to finite quark masses. For a high enough temperature, as achieved in the early universe or the fireball created by a high-energy heavy ion collision, this symmetry is expected to be restored. We show theoretically that a coherent deviation of the corresponding quantum field from its usual vacuum expectation value on the freeze-out hypersurface of a heavy-ion collision leads, after resonance decays, to a characteristic contribution to the transverse momentum spectrum of charged pions, in the very soft regime, consistent with experimental data from the Relativistic Heavy Ion Collider and the Large Hadron Collider. Taken together, the experimental data with the new theoretical results provide compelling support for the existence of a chiral condensation mechanism with partial restoration of chiral symmetry at high temperature.

Figures (4)

• Figure 1: Potential of the chiral condensate for different temperature regimes. Before the collision, the chiral condensate is at its vacuum value $\sigma = f_\pi$. At temperatures above the chiral crossover, the effective potential is modified such that it has its minimum at vanishing or very small $\sigma$ (1), leading to a relaxation of the condensate toward the new minimum (2). When the fireball expands and cools down, the vacuum form of the potential is restored for low enough temperatures. If the cooling takes place quickly, the chiral condensate can lag behind and still deviate from the vacuum expectation value at the moment of freeze-out (3). This difference has the physical significance of a coherent field, finally resulting in an extra production mechanism for low momentum pions.
• Figure 2: Spectral function of the $\sigma$/$f_0(500)$ using the Sill parametrization according to GiacosaEtAl_2021. Most importantly, with the chosen parametrization, the spectral function vanishes below the mass threshold given by twice the pion mass, thereby respecting kinematic constraints of the decay process -- a crucial improvement over the usual Breit-Wigner parametrization.
• Figure 3: In a restframe of the heavier $\sigma$-resonance, we assume an isotropic distribution of the three-momenta of the decay products, with the allowed momenta being limited by three-momentum and energy conservation. In a frame where the resonance has non-vanishing three-momentum, the momentum distribution of the decay products is boosted accordingly. By this mechanism, the final momentum distribution of the decay products is a convolution of the momentum distribution of the primary resonance with the decay function SollfrankEtAl_1990Mazeliauskas:2018irt.
• Figure 4: Comparison of pion spectra from experimental data PHENIX:2003iijALICE:2013mezALICE:2021lsv with the fit result from LuEtAl_2025 and the contribution from the partially restored chiral condensate for different collision systems. We find a similar magnitude of pion enhancement at low momenta as found in the experimental results for all systems.