Probing QCD Phase Structure by Baryon Multiplicity Distribution

Understand

The canonical partition functions $Z_n$ and the number distributions $P_n$ which are obervable in experiments, are related by a single parameter, the fugacities $\xi=\exp(\mu/T)$.

• With the charge parity invariance, $Z_n$ and $\xi$ can be determined.
• Thermodynamic quantities such as the number density susceptibility and the kurtosis are then calculated from the grand canonical partition function $Z(\xi,T)=\sum Z_n(T) \xi^n$, ($n=-N_{\rm max},\cdots, N_{\rm max}$), for any chemical potential $\mu$, although the region over which the results are reliable for these quantities is constrained by $N_{\rm max}$.
• We then calculate the Lee-Yang zeros, which are the zeros of $Z(\xi)$ in the complex fugacity plane, as poles of $d\log Z(\xi)/d\xi$ by using the Cauchy integral theorem.