Agnieszka Sorensen, Dmytro Oliinychenko, Volker Koch, and Larry McLerran, Speed of Sound and Baryon Cumulants in Heavy-Ion Collisions,  Phys. Rev. Lett. 127, 042303 (2021)

We present a method that may allow an estimate of the value of the speed of sound as well as its logarithmic derivative with respect to the baryon number density in matter created in heavy-ion collisions. To this end, we use well-known observables: cumulants of the baryon number distribution. In analyses aimed at uncovering the phase diagram of strongly interacting matter, cumulants gather considerable attention as their qualitative behavior along the explored range of collision energies is expected to aid in detecting the QCD critical point. We show that the cumulants may also reveal the behavior of the speed of sound in the temperature and baryon chemical potential plane. We demonstrate the applicability of such estimates within two models of nuclear matter and explore what might be understood from known experimental data.

We find that a combination of cumulants, 1 – (k₃k₁)/(k₂²), is approximately equal to the sum of the isothermal speed of sound and its logarithmic derivative with respect to the baryon number density.

Figure: Contour plot of 1 – (k₃k₁)/(k₂²) in a simple model of dense nuclear matter with two 1st order phase transitions: the well-known nuclear-liquid gas phase transition in ordinary nuclear matter, and a postulated phase transition with a critical point at high baryon density (n = 3n₀) and high temperature (T = 100 MeV), modeling the conjectured QCD phase transition. Yellow and black lines correspond to the spinodal and coexistence lines of these transitions, respectively. The softening of the equation of state, marked by negative values of 1 – (k₃k₁)/(k₂²), occurs in two regions of the phase diagram corresponding to the ordinary nuclear matter phase transition and to the conjectured QCD—like phase transition. Light green stars denote positions of the experimentally measured freeze-out parameters (T_fo,μ_fo), while dark purple stars denote points (T,μ), taken along lines informed by average phase diagram trajectories for STAR collision energies, where the values of 1 – (k₃k₁)/(k₂²) match the experimentally measured values for a given collision energy. As the beam energy is lowered, these values first decrease, and then steeply rise for the very low collision energy studied in the HADES experiment. This suggests a significant change in the thermodynamic behavior of nuclear matter created in these collisions.