Stable Yang-Lee zeros in a truncated fugacity series from the net baryon number multiplicity distribution

We investigate Yang-Lee zeros of grand partition functions as truncated fugacity polynomials of which coefficients are given by the canonical partition functions $Z(T,V,N)$ up to $N\le N_{\max }$. Such a partition function can be inevitably obtained from the net-baryon number multiplicity distribution in relativistic heavy ion collisions, where the number of the event beyond $N_{\max }$ has insufficient statistics, as well as from canonical approaches in lattice QCD. We use a chiral random matrix model as a solvable model for chiral phase transition in QCD and show that the closest edge of the distribution to the real chemical potential axis is stable against cutting the tail of the multiplicity distribution. A similar behavior is also found in lattice QCD at finite temperature for the Roberge-Weiss transition. In contrast, such a stability is found to be absent in the Skellam distribution which does not have a phase transition. We compare the number of $N_{\max }$ to obtain the stable Yang-Lee zeros with those of critical higher-order cumulants.

Figure 1

Phase diagram of the chiral random matrix model with periodicity in the imaginary baryonic chemical potential.

Figure 2

Behavior of the order parameter ${\varphi }_0$ of a periodic chiral random matrix model in imaginary chemical potential $\theta ={\mu }_I/T$ at ${\mu }_R=0$.

Figure 3

Yang-Lee zeros of the periodic random matrix model in the complex $\omega$ plane for $m=0$ at $T/T_c=0.99$. Open symbols stand for the zeros in different $N_s$ and the solid line indicates the Stokes boundary. The branch point is denoted by closed circles.

Figure 4

Yang-Lee zeros of the periodic random matrix model in complex $\mu$ plane. The left panel corresponds to the case of Fig. 3. Right panel shows the case with a finite but small quark mass, $m=0.05$ at the same temperature.

Figure 5

Distribution of the Yang-Lee zeros from the truncated partition function of the periodic chiral random matrix model for $m=0.05$. Left and right panels stand for $T=T_c$ and $T=T_{\mathrm{CP}}$, respectively.

Figure 6

Same as Fig. 5, but for $T=0.6T_c$.

Figure 7

Distribution of Yang-Lee zeros for a lattice QCD data [54].

Figure 8

Left: $P(N)$ for the random matrix model at $T=T_c$ and $m=0.05$, and the corresponding Skellam distribution. Right: Distribution of Lee-Yang zeros for a truncated Skellam partition function.

Figure 9

Distribution of the zeros for the Skellam partition function for ${\sigma }^2=14.89$.