Locating the QCD critical point with finite-size scaling of proton cumulants

Abstract

We perform a finite-size scaling analysis of net-proton number cumulants in Au+Au collisions at center-of-mass energies between $\sqrt{s_{\rm{NN}}} = 2.4$ and $200~\rm{GeV}$ to search for evidence of a critical point in the QCD phase diagram. We use the second-order susceptibility and Binder cumulant, whose scaling with the system size is studied by using their dependence on the rapidity bin width $W$. We find that for collisions at $\sqrt{s_{\rm{NN}}} \geq 7.7~\rm{GeV}$, the susceptibility depends only weakly on $W$ but increases as a power law in the baryon chemical potential $\mu_B$, $(\mu_B - \mu_{B,c})^{-\gamma}$ with $\mu_{B,c}=700\pm130~{\rm MeV}$ and $\gamma=1.6\pm0.5$, consistent with several recent theory estimates for the location of the QCD critical point. We also find that the Binder cumulant appears to show a crossing within a similar range of $\mu_B$ values. A comparable scaling behavior, however, is also found in dynamical simulations without critical fluctuations. Moreover, we find that a Skellam distribution leads to apparent scaling of the second-order susceptibility when evaluated along the freeze-out line. Simulations also show that the crossing of the Binder cumulant may be sensitive to changes in experimental acceptance at different beam energies. We conclude that while the observed scaling and crossing are consistent with the presence of a critical point, they cannot yet be taken as definitive evidence.