Speed of Sound and Baryon Cumulants in Heavy-Ion Collisions

Abstract

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 heavyion collisions. To this end, we utilize 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 behaviour 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.

Thermodynamic approach to proton number fluctuations in baryon-rich heavy-ion matter created at moderate collision energies

“…Our results agree with the simplified estimates of Ref. [21] qualitatively, while quantitatively they indicate a smaller c 2 T and a larger d(ln c 2 T )/d(ln n B ) at the HADES collision energy than originally obtained in [21].…”

“…The extracted susceptibilities can also be used to improve upon the analysis presented in Ref. [21], where it was shown that the cumulants can be used to estimate the (isothermal) speed of sound as well as its logarithmic derivative with respect to baryon density. To do that one needs to determine the true grand-canonical cumulants of baryon number whereas in Ref.…”

“…To do that one needs to determine the true grand-canonical cumulants of baryon number whereas in Ref. [21] direct measurements of the momentum space proton number cumulants were used as a proxy instead. Utilizing Eqs.…”

Reaching percolation and conformal limits in neutron stars

“…In QCD, the chiral critical point (CP) belongs to the Z(2) universality class; thus, it is expected for the fluctuations to diverge at CP, which makes them useful probes of remnants of critical behavior in the relativistic heavy-ion collisions. It has also been recently argued that at low temperatures and large baryon densities, experimentally measured cumulants may allow for direct measurement of the sound velocity [36].…”

Speed of sound in QCD matter

“…The study in [30][31][32] shows that c 2 s as a function of charged particle multiplicity dN ch /dη can reveal the dynamics of heavy-ion collision. Recently, in [33] the authors estimate c s as a function of the logarithmic derivative with respect to the baryon density of QCD matter, and try to build a connection with the baryon number cumulants to aid in detecting the QCD critical endpoint.…”