Modification of the masses of the lightest neutral mesons in a hadronic medium under an external magnetic field

The effective masses of the neutral mesons in a hadronic medium and under an external magnetic field are evaluated as functions of the baryonic density and the field intensity. For this purpose, the meson polarization is evaluated in the one-loop approximation using a quantum hadrodynamics model which includes $\pi$, $\sigma$, $\omega$, and $\rho$ mesons. The propagators of the baryons include the full effect of the coupling to the magnetic field through their charges and their anomalous magnetic moments. Within the range of magnetic intensities considered here $10^{17}\mathrm{G}<B<{10}^{19}\mathrm{G}$, the dependence on $B$ is moderate for the pion and the longitudinal component of the $\omega$ meson and negligible for the remaining mesons.

Figure 1

The diagrams considered in our Dyson-Schwinger calculations. Solid lines represent fermion propagators, and dashed or dotted lines, the meson ones.

Figure 2

The effective meson masses as functions of the baryonic number density for several magnetic intensities corresponding to isospin symmetric nuclear matter.

Figure 3

The effective meson masses as functions of the baryonic number density for several magnetic intensities corresponding to neutral stellar matter.

Figure 4

The effective meson masses as functions of the magnetic intensity for isospin symmetric nuclear matter at the fixed baryonic number density $n=n_0$.

Figure 5

The same as in Fig. 4, but for a wider magnetic range and an extended scale for the meson masses.