Electromagnetic triangle anomaly and neutral pion condensation in QCD vacuum

TL;DR

This paper investigates how an electromagnetic field with a nonzero second Lorentz invariant can induce neutral pion condensation in the QCD vacuum via the electromagnetic triangle anomaly, using chiral perturbation theory and the NJL model.

Contribution

It demonstrates the mechanism of neutral pion condensation induced by electromagnetic fields in the QCD vacuum and quantifies its dependence on the invariant using two theoretical frameworks.

Findings

Neutral pion condensate depends on the electromagnetic invariant $I_2$.

The stability of the pion-condensed vacuum against Schwinger pair production is analyzed.

The study provides a quantitative description within chiral perturbation theory and NJL model.

Abstract

We study the QCD vacuum structure under the influence of an electromagnetic field with a nonzero second Lorentz invariant $I_2=\vec{E}\cdot{\vec B}$. We show that the presence of $I_2$ can induce neutral pion ($\pi^0$) condensation in the QCD vacuum through the electromagnetic triangle anomaly. Within the frameworks of chiral perturbation theory at leading small-momenta expansion as well as the Nambu--Jona-Lasinio model at leading $1/N_c$ expansion, we quantify the dependence of the $\pi^0$ condensate on $I_2$. The stability of the $\pi^0$-condensed vacuum against the Schwinger charged pair production due to electric field is also discussed.