Open bottom mesons in asymmetric nuclear matter in the presence of strong magnetic fields

The modifications of the masses of the $B$ and $\overline{B}$ mesons in asymmetric nuclear matter in the presence of strong magnetic fields are investigated using a chiral effective model. The medium modifications of these open bottom mesons arise due to their interactions with the scalar mesons and the nucleons. In the magnetized nuclear matter, the proton has contributions from the Landau levels. In the chiral effective model, the masses of the $B$ and $\overline{B}$ mesons are calculated from the leading term, namely the vectorial Weinberg-Tomozawa term as well as from the next-to-leading-order contributions, i.e., due to the scalar exchange and the range terms. Due to the Weinberg-Tomozawa term, the $\overline{B}$ mesons experience an attractive interaction in the symmetric nuclear matter, whereas the $B$ mesons have a repulsive interaction. Inclusion of the contributions from the scalar exchange and the range terms as well leads to drop of the masses of both $B$ and $\overline{B}$ mesons. The effect of the isospin asymmetry breaks the mass degeneracy of the $B^{+}$ and $B^0$ (as well as of the $B^{-}$ and $\overline{B^0}$) mesons, and its effect is observed to be large at high densities. The effects of anomalous magnetic moments of the nucleons are taken into account in the present study of the masses of the open bottom mesons in magnetized nuclear matter.

Figure 1

The in-medium masses of the $B$ and $\overline{B}$ mesons plotted as functions of the baryon density (in units of nuclear matter saturation density) for various values of isospin asymmetry parameter, $\eta$, for value of the magnetic field, $eB=2m_{\pi }^2$, accounting for the effects of anomalous magnetic moment. These results are compared to the case when the effects of the anomalous magnetic moment are not taken into account (shown as dotted line).

Figure 2

The in-medium masses of the $B$ and $\overline{B}$ mesons plotted as functions of the baryon density (in units of nuclear matter saturation density) for various values of isospin asymmetry parameter, $\eta$, for value of the magnetic field, $eB=4m_{\pi }^2$, accounting for the effects of anomalous magnetic moment. These results are compared to the case when the effects of the anomalous magnetic moment are not taken into account (shown as dotted line).

Figure 3

The in-medium masses of the $B$ and $\overline{B}$ mesons plotted as functions of the baryon density (in units of nuclear matter saturation density) for various values of isospin asymmetry parameter, $\eta$, for value of the magnetic field, $eB=6m_{\pi }^2$, accounting for the effects of anomalous magnetic moment. These results are compared to the case when the effects of the anomalous magnetic moment are not taken into account (shown as dotted line).

Figure 4

The in-medium masses of the $B$ and $\overline{B}$ mesons plotted as functions of the baryon density (in units of nuclear matter saturation density) for various values of isospin asymmetry parameter, $\eta$, for value of the magnetic field, $eB=8m_{\pi }^2$, accounting for the effects of anomalous magnetic moment. These results are compared to the case when the effects of the anomalous magnetic moment are not taken into account (shown as dotted line).

Figure 5

The effective masses of $B$ ($B^{+},B^0$) and $\overline{B}$ ($B^{-}, \overline{B^0}$) mesons in MeV plotted as functions of $eB/m_{\pi }^2$, for baryon density, ${\rho }_B={\rho }_0$, with different values of isospin asymmetry parameter, $\eta$, accounting for the effects of the anomalous magnetic moments (AMM) for the nucleons. The results are compared with the case of not accounting for the anomalous magnetic moments (shown as dotted lines).

Figure 6

The effective masses of $B$ ($B^{+},B^0$) and $\overline{B}$ ($B^{-}, \overline{B^0}$) mesons in MeV plotted as functions of $eB/m_{\pi }^2$, for baryon density, ${\rho }_B=3{\rho }_0$, with different values of isospin asymmetry parameter, $\eta$, accounting for the effects of the anomalous magnetic moments (AMM) for the nucleons. The results are compared with the case of not accounting for the anomalous magnetic moments (shown as dotted lines).

Figure 7

The effective masses of $B$ ($B^{+},B^0$) and $\overline{B}$ ($B^{-}, \overline{B^0}$) mesons in MeV plotted as functions of $eB/m_{\pi }^2$, for baryon density, ${\rho }_B=5{\rho }_0$, with different values of isospin asymmetry parameter, $\eta$, accounting for the effects of the anomalous magnetic moments (AMM) for the nucleons. The results are compared with the case of not accounting for the anomalous magnetic moments (shown as dotted lines).