# Fourier coefficients of the net baryon number density and their scaling properties near a phase transition

## TL;DR

This paper investigates how Fourier coefficients of net baryon density reveal phase transition signatures in QCD, analyzing their behavior near critical points and across different transition types.

## Contribution

It derives the scaling laws of Fourier coefficients near second order phase transitions and explores their relation to the QCD phase diagram.

## Key findings

- Fourier coefficients exhibit distinct asymptotic behavior near phase transitions.
- Scaling properties differ between second order, first order, and crossover transitions.
- The study links Fourier coefficient behavior to the structure of the QCD phase diagram.

## Abstract

We study the Fourier coefficients b(k,T) of the net baryon number density in strongly interacting matter at finite temperature. We show that singularities in the complex chemical potential plane connected with phase transitions are reflected in the asymptotic behavior of the coefficients at large k. We derive the scaling properties of b(k,T) near a second order phase transition in the O(4) and Z(2) universality classes. The impact of first order and crossover transitions is also examined. The scaling properties of b(k,T) are linked to the QCD phase diagram in the temperature and complex chemical potential plane.