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

Abstract

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 $N\le N_{\text{max}}$. 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 $N_{\text{max}}$ has insufficient statistics, as well as 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 real chemical potential axis is stable against cutting the tail of the multiplicity distribution. The similar behavior is also found in lattice QCD at finite temperature for Roberge-Weiss transition. In contrast, such a stability is found to be absent in the Skellam distribution which does not have phase transition. We compare the number of $N_{\text{max}}$ to obtain the stable Yang-Lee zeros with those of critical higher order cumulants.

15 pages, 9 figures. Version to appear in Phys. Rev. D. Comments on lattice results are added. Typos are corrected

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Cited by in corpus (3)

• Lee-Yang zeros in lattice QCD for searching phase transition points
• Fourier coefficients of the net-baryon number density and chiral criticality
• Condensation of Lee-Yang zeros in scalar field theory