"Figure 2d" of "Measurement of higher cumulants of net-charge multiplicity distributions in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=7.7-200$ GeV"

We report the measurement of cumulants ($C_{n}$, $n$ = 1, . . . ,4) of the net-charge distributions measured within pseudorapidity (|$\eta$| < 0.35) in Au + Au collisions at $\sqrt{s_{NN}}$ = 7.7–200 GeV with the PHENIX experiment at the Relativistic Heavy Ion Collider. The cumulants (e.g., $C_1/C_2$, $C_3/C_1$) of the net-charge distributions, which can be related to volume independent susceptibility ratios, are studied as a function of centrality and energy. These quantities are important to understand the quantum-chromodynamics phase diagram and possible existence of a critical end point. The measured values are very well described by expectation from negative binomial distributions. We do not observe any nonmonotonic behavior in the ratios of the cumulants as a function of collision energy. The measured values of $C_1/C_2$ and $C_3/C_1$ can be directly compared to lattice quantum-chromodynamics calculations and thus allow extraction of both the chemical freeze-out temperature and the baryon chemical potential at each center-of-mass energy. The extracted baryon chemical potentials are in excellent agreement with a thermal-statistical analysis model.