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

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.