Magnetized pole-mass of neutral ρ meson within full RPA evaluation - Sidney S. Avancini; Ricardo L.S. Farias; William R. Tavares; Varese S. Timóteo (Nuclear Physics B, 2022)
In this work we calculate the pole-mass of the ρ0 meson with different spin projections sz=0,±1 in the context of the magnetized two-flavor Nambu–Jona–Lasinio model. Making use of the mean field approximation to obtain the effective quark mass as a function of the magnetic field, we apply the random phase approximation (RPA) to the vector channel in order to calculate the polarization function for each spin component. We adopt the magnetic field independent regularization (MFIR) in our evaluations as a method of separating divergences and the Pauli-Villars regularization for the vacuum contributions. The ρ0 meson mass with spin projection sz=±1 is always catalyzed with the magnitude of the magnetic field, showing good agreement with Lattice QCD results. The mass projection sz=0 has a non-monotonic behavior, decreasing until the minimum at eB≲0.15 GeV2, which is in contrast with available LQCD data.