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

TL;DR

This paper studies the stability of Yang-Lee zeros derived from truncated grand partition functions in heavy ion collisions and lattice QCD, revealing stable zeros near phase transitions and instability in non-critical distributions.

Contribution

It demonstrates that the closest Yang-Lee zeros are stable against truncation in models with phase transitions, providing a new method to identify critical behavior from limited data.

Findings

Stable Yang-Lee zeros near phase transition points.

Instability of zeros in non-critical distributions like Skellam.

Comparison of truncation effects with higher order cumulants.

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 $N \leq N_{\text{max}}$. 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.