Electromagnetic triangle anomaly and neutral pion condensation in QCD vacuum

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.

Comments: V2: 5 pages, 3 figures, published version