Testing charm quark equilibration in ultrahigh-energy heavy ion collisions with fluctuations

Recent lattice QCD data on higher order susceptibilities of charm quarks provide the opportunity to explore charm quark equilibration in the early quark gluon plasma (QGP) phase. Here, we propose to use the lattice data on second- and fourth-order net charm susceptibilities to infer the charm quark equilibration temperature and the corresponding volume, in the early QGP stage, via a combined analysis of experimentally measured multiplicity fluctuations. Furthermore, the first perturbative results for the second- and fourth-order charm quark susceptibilities and their ratio are presented.

Figure 1

Second-order charm quark susceptibilities from our pQCD NLO framework (full line) in comparison to lattice QCD calculations (symbols) by the RBC-Bielefeld collaboration in quenched approximation for the charm [13], from DeTar et al. in quenched approximation for the charm [22] and from Borsanyi et al. for dynamical charm quarks [23].

Figure 2

Fourth-order charm quark susceptibilities from our pQCD NLO framework (full line) in comparison to lattice QCD calculations (symbols) by the RBC-Bielefeld collaboration in quenched approximation for the charm [13], from DeTar et al. in quenched approximation for the charm [22].

Figure 3

Charm quark susceptibilities ratios from our pQCD NLO framework and extracted from lattice QCD calculations by the RBC-Bielefeld collaboration in quenched approximation for the charm [13] and from Bazazov et al. [20].

Figure 4

Fluctuation of the square root of net charm quark number $\sqrt{\langle {\left(\delta N_{c-\overline{c}}\right)}^2\rangle }$ over higher moments $\kappa {\sigma }^2$, where lines of constant temperatures (solid) in $\text{MeV}$ and lines of constant volumes (dashed) in ${\text{fm}}^3$ are included, extracted from lattice QCD calculations by the RBC-Bielefeld collaboration [13]. To provide an estimate for the uncertainty of the results, we use the errors of the pQCD calculations and show them as bands.