In-medium properties of light vector and axial-vector mesons: effects of Dirac sea

The in-medium masses of the light vector, $\rho^{0, \pm}$, $\omega$ and the light axial-vector, $A_1^{0, \pm}$ mesons, are studied in the magnetized nuclear matter, accounting for the effects of the Dirac sea. The in-medium partial decay widths for the $A_1\rightarrow \rho \pi$ channels, are studied from the in-medium masses of the initial and the final state particles, by applying a phenomenological Lagrangian to account for the $A_1\rho\pi$ interaction vertices. The masses calculated within the QCD sum rule framework, are obtained in terms of the light quark ($\sim \langle \bar{q}q \rangle$) and the scalar gluon condensates ($\sim \langle G^2 \rangle$), as well as the light four-quark condensate ($\sim \langle \bar{q}q\rangle^2 $). The condensates are calculated within the chiral $SU(3)$ model in terms of the medium modified scalar fields. The effects of magnetic fields are incorporated through the Landau energy levels of protons, anomalous magnetic moments (AMMs) of the nucleons in the nuclear matter, in addition to the magnetized Dirac sea contribution, within the chiral effective model. The enhancement (reduction) of the light quark condensates with magnetic field, is called (inverse) magnetic catalysis. The effects of magnetic fields on the in-medium hadronic decay widths of the $A_1$ mesons, are observed to be significant through the Dirac sea effect, accounting for the AMMs of the nucleons. This may affect the light mesons production in the non-central, heavy-ion collision experiments, where estimated magnetic field is very large.