Do charged-pions condense in a magnetic field with rotation?

We revisit the condensation scenario of charged pions in external magnetic field and rotation, which was first considered by Y. Liu and I. Zahed. Based on the Ginzburg-Landau analysis of the Nambu-Jona-Lasinio model, we find that the charged-pion condensation takes place only when both a strong coupling constant and negatively large baryon chemical potential are applied. Besides, our numerical calculation shows that the chiral restoration induced by the interplay between magnetic field and rotation (i.e., the rotational magnetic inhibition) interrupts the formation of the charged-pion condensate. This suggests that the analysis of such condensation requires a careful treatment of the inner structure of pions, which was not taken into account before. We also discuss the underlying physical mechanism of our finding and the indication of charged-rho condensation.