Electromagnetic triangle anomaly and neutral pion condensation in QCD vacuum

We study the QCD vacuum structure under the influence of an electromagnetic field with a nonzero second Lorentz invariant I2=E⋅BI2=E⋅B. We show that the presence of I2I2 can induce neutral pion (π0π0) 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/Nc1/Nc expansion, we quantify the dependence of the π0π0 condensate on I2I2. The stability of the π0π0-condensed vacuum against the Schwinger charged pair production due to electric field is also discussed.