# Locating the QCD critical endpoint through finite-size scaling

## TL;DR

This paper uses finite-size scaling and universal effective actions within the 3d Ising universality class to narrow down the location of the QCD critical endpoint based on experimental fluctuation data.

## Contribution

It introduces a universal effective action approach to analyze baryon density fluctuations and constrains the QCD critical endpoint's location using experimental fluctuation measurements.

## Key findings

- Critical region is narrow in chemical potential direction.
- Experimental data restricts the critical endpoint to a specific phase diagram domain.
- Baryon density fluctuations in Si+Si collisions show non-conventional behavior.

## Abstract

Considering the 3d Ising universality class of the QCD critical endpoint we use a universal effective action for the description of the baryon-number density fluctuations around the critical region. Calculating the baryon-number multiplicity moments and determining their scaling with system's size we show that the critical region is very narrow in the direction of the baryon chemical potential $\mu$ and wide in the temperature direction $T$ for $T > T_c$. In this context, published experimental results on local proton density-fluctuation measurements obtained by intermittency analysis in transverse momentum space in NA49 central A+A collisions at $\sqrt{s_{NN}}=17.2$ GeV (A=C,Si,Pb), restrict significantly the location $(\mu_c,T_c)$ of the QCD critical endpoint. The main constraint is provided by the freeze-out chemical potential of the Si+Si system, which shows non-conventional baryon density fluctuations, restricting $(\mu_c,T_c)$ within a narrow domain, $119~\textrm{MeV} \leq T_c \leq 162~\textrm{MeV}$, $252~\textrm{MeV} \leq \mu_c \leq 258~\textrm{MeV}$, of the phase diagram.