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

Neutral pseudoscalar and vector meson masses under strong magnetic fields in an extended NJL model: mixing effects

“…In the case of the neutral vector mesons, we consider both states with quantum numbers S z = 0 and S z = ±1, where S z is the spin projection in the direction of the magnetic field (it is worth noticing that only S z = 0 states can mix with pseudoscalar states). Most LQCD results and effective model calculations agree in the finding that the masses of S z = ±1 states get monotonically enhanced with the magnetic field, while results for S z = 0 mesons are still not conclusive [31,45,49,50,52,57,58]. In our framework, which lacks a description of confinement, for large magnetic fields the masses of some of the S z = 0 states are found to grow beyond the q q pair production threshold; therefore our results in this region should be taken just as qualitative ones.…”

“…[22] and Ref. [57]. To carry out a proper comparison, in our model we have taken α = 0.5 and have set to zero the ρ 0⊥ − ρ 3⊥ mixing contributions, as done in those works (in which the ρ 0⊥ state is not included).…”

“…On the other hand, in Ref. [57] the regularization is carried out using the MFIR method, as in the present work. However, to deal with vacuum-like terms the authors of Ref.…”

“…However, to deal with vacuum-like terms the authors of Ref. [57] choose a Pauli-Villars regularization, instead of the 3D-cutoff scheme considered here. From Fig.…”

“…Regarding the ρ meson sector, studies of magnetized ρ meson masses in the framework of effective models and LQCD can be found in Refs. [18,28,31,36,45,[54][55][56][57] and Refs. [49,50,52,58,59], respectively.…”