The chiral condensate in a constant electromagnetic field at O(p^6)

TL;DR

This paper calculates the change in the chiral condensate caused by a constant electromagnetic field at the sixth order in chiral perturbation theory, highlighting the importance of realistic pion mass values and uncertainties in low-energy constants.

Contribution

It provides a detailed O(p^6) analysis of the chiral condensate shift in electromagnetic fields using SU(2) chiral perturbation theory with realistic pion mass.

Findings

Significant difference from zero pion mass calculations

Uncertainty in two-loop correction magnitude due to LECs

Highlights importance of realistic pion mass in predictions

Abstract

We examine the shift in the chiral condensate due to a constant electromagnetic field at ${\cal O}(p^6)$ using SU(2) chiral perturbation theory and a realistic $M_\pi = 140 \textrm{MeV}$. We find that this value differs significantly from the value calculated using $M_\pi = 0$, while the magnitude of the two-loop correction is unclear due to the uncertainty in the experimentally determined value of the relevant ${\cal L}_6$ LEC.