Towards quantitative precision in the chiral crossover: masses and fluctuation scales

TL;DR

This paper explores the relationship between pion masses and fluctuation scales in low-energy QCD, emphasizing the importance of correctly identifying physical scales for understanding phase transitions and modeling QCD accurately.

Contribution

It clarifies the connection between mesonic masses and fluctuation scales, highlighting their agreement at zero temperature and divergence at finite temperature for effective QCD models.

Findings

All scales agree at zero temperature.

Scales deviate at finite temperature.

Proper scale definition is crucial for accurate phase structure modeling.

Abstract

We investigate the relation between the physical pion pole and screening masses and the mesonic fluctuation scale in low-energy QCD, which relates to the curvature of the mesonic effective potential. This relation is important for the correct relative weight of quantum, thermal and density fluctuations. Hence, it governs the location of phase boundaries as well as the phase structure of QCD. The identification of the correct physics scales is also primarily important for the correct adjustment of the parameters of effective models for low-energy QCD. It is shown that subject to an appropriate definition of the latter, all these scales agree at vanishing temperature, while they deviate from each other at finite temperature.