Magnetized pole-mass of neutral $\rho$ meson within full RPA evaluation

Abstract

In this work we calculate the pole-mass of the ${\rho }^0$ meson with different spin projections $s_z=0,\pm 1$ 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 ${\rho }^0$ meson mass with spin projection $s_z=\pm 1$ is always catalysed with the magnitude of the magnetic field, showing good agreement with Lattice QCD results. The mass projection $s_z=0$ has a non-monotonic behavior, decreasing until the minimum at $eB\lesssim 0.15$ GeV${}^2$, which is in contrast with available LQCD data.

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Cited by in corpus (5)

• Neutral pseudoscalar and vector meson masses under strong magnetic fields in an extended NJL model: mixing effects
• Masses of magnetized pseudoscalar and vector mesons in an extended NJL model: the role of axial vector mesons
• Magnetic field dependence of the neutral pion longitudinal screening mass in the linear sigma model with quarks
• Strongly interacting matter in extreme magnetic fields
• Thermomagnetic effects on light pseudo-scalar meson masses within the SU(3) Nambu-Jona--Lasinio model