Open bottom mesons in a hot asymmetric hadronic medium

The in-medium masses and optical potentials of $B$ and $\overline{B}$ mesons are studied in an isospin asymmetric, strange, hot, and dense hadronic environment using a chiral effective model. The chiral $\text{SU}\left(3\right)$ model originally designed for the light-quark sector, is generalized to include the heavy-quark sector ($c$ and $b$) to derive the interactions of the $B$ and $\overline{B}$ mesons with the light hadrons. Owing to the large mass of bottom quark, we use only the empirical form of these interactions for the desired purpose, while treating the bottom degrees of freedom to be frozen in the medium. Hence, all medium effects are attributable to the in-medium interaction of the light-quark content of these open bottom mesons. Both $B$ and $\overline{B}$ mesons are found to experience net attractive interactions in the medium, leading to lowering of their masses in the medium. The mass degeneracy of particles and antiparticles, ($B^{+}, B^{-}$) as well as ($B^0, {\overline{B}}^0$), is observed to be broken in the medium, owing to equal and opposite contributions from a vectorial Weinberg-Tomozawa interaction term. Addition of hyperons to the medium lowers further the in-medium mass for each of these four mesons, while a nonzero isospin asymmetry is observed to break the approximate mass degeneracy of each pair of isospin doublets. These medium effects are found to be strongly density dependent and bear a considerably weaker temperature dependence. The results obtained in the present investigation are compared to predictions from the quark-meson coupling model, heavy meson effective theory, and the QCD sum rule approach.

Figure 1

The various contributions to the energy at $\vec{k}=0$, for the $B$ and $\overline{B}$ mesons in isospin-symmetric matter ($\eta =0$), at different temperatures. Subplots (a), (c), and (e) correspond to the degenerate $B$ mesons ($B^{+}, B^0$), while (b), (d), and (f) correspond to the degenerate $\overline{B}$ mesons ($B^{-}, {\overline{B}}^0$). For each case, the individual contributions in hyperonic matter (with $f_s=0.5$), as described in the legend, are also compared against the nuclear-matter situation ($f_s=0$), represented by dotted curves.

Figure 2

The various contributions to the energy at $\vec{k}=0$ for the $B$ meson doublet ($B^{+}, B^0$) in isospin-asymmetric matter ($\eta =0.5$) at different temperatures. Subplots (a), (c), and (e) correspond to the $B^{+}$ meson, while (b), (d), and (f) correspond to the $B^0$ meson. For each case, the individual contributions in hyperonic matter (with $f_s=0.5$), as described in the legend, are also compared against the nuclear matter situation ($f_s=0$), represented by dotted curves.

Figure 3

The various contributions to the energy at $\vec{k}=0$ for the $\overline{B}$ meson doublet ($B^{-}, {\overline{B}}^0$) in isospin-asymmetric matter ($\eta =0.5$) at different temperatures. Subplots (a), (c), and (e) correspond to the $B^{-}$ meson, while (b), (d), and (f) correspond to the ${\overline{B}}^0$ meson. For each case, the individual contributions in hyperonic matter (with $f_s=0.5$), as described in the legend, are also compared against the nuclear-matter situation ($f_s=0$), represented by dotted curves.

Figure 4

A comparison of the energy at $\vec{k}=0$ of the $B^{+}$ [subplots (a), (c), and (e)] and $B^0$ mesons [subplots (b), (d), and (f)] in hyperonic matter (with $f_s=0.3$) at various values of the isospin asymmetry parameter ($\eta$), as described in the legend, and at different temperatures. In each case, this hyperonic matter situation is also compared against the nuclear matter ($f_s=0$) situation, represented by dotted lines.

Figure 5

A comparison of the energy at $\vec{k}=0$ of the $B^{-}$ [subplots (a), (c), and (e)] and ${\overline{B}}^0$ mesons [subplots (b), (d), and (f)] in hyperonic matter (with $f_s=0.3$) at various values of the isospin asymmetry parameter ($\eta$), as described in the legend, and at different temperatures. In each case, this hyperonic matter situation is also compared against the nuclear-matter ($f_s=0$) situation, represented by dotted lines.

Figure 6

A comparison of the energy at $\vec{k}=0$ of the $B^{+}$ [subplots (a), (c), and (e)] and $B^0$ mesons [subplots (b), (d), and (f)] in hyperonic matter (with $f_s=0.5$) at various values of the isospin asymmetry parameter ($\eta$), as described in the legend, and at different temperatures. In each case, this hyperonic matter situation is also compared against the nuclear matter ($f_s=0$) situation, represented by dotted lines.

Figure 7

A comparison of the energy at $\vec{k}=0$ of the $B^{-}$ [subplots (a), (c), and (e)] and ${\overline{B}}^0$ mesons [subplots (b), (d), and (f)] in hyperonic matter (with $f_s=0.5$) at various values of the isospin asymmetry parameter ($\eta$), as described in the legend, and at different temperatures. In each case, this hyperonic matter situation is also compared against the nuclear matter ($f_s=0$) situation, represented by dotted lines.

Figure 8

The optical potentials of the $B$ mesons $[B^{+}$ in subplots (a), (c), and (e) and $B^0$ in subplots (b), (d), and (f)] as a function of momentum $k(\equiv |\vec{k}\left|\right)$ in cold $(T=0)$ hyperonic matter (with $f_s=0.3$) at various values of the isospin asymmetry parameter ($\eta$), as described in the legend, and at different densities. In each case, this hyperonic matter situation is also compared against the nuclear matter ($f_s=0$) situation, represented by dotted lines.

Figure 9

The optical potentials of the $\overline{B}$ mesons $[B^{-}$ in subplots (a), (c), and (e) and ${\overline{B}}^0$ in subplots (b), (d), and (f)] as a function of momentum $k(\equiv |\vec{k}\left|\right)$ in cold $(T=0)$ hyperonic matter (with $f_s=0.3$) at various values of the isospin asymmetry parameter ($\eta$), as described in the legend, and at different densities. In each case, this hyperonic matter situation is also compared against the nuclear matter ($f_s=0$) situation, represented by dotted lines.

Figure 10

The optical potentials of the $B$ mesons $[B^{+}$ in subplots (a), (c), and (e) and $B^0$ in subplots (b), (d), and (f)] as a function of momentum $k(\equiv |\vec{k}\left|\right)$ in cold $(T=0)$ hyperonic matter (with $f_s=0.5$) at various values of the isospin asymmetry parameter ($\eta$), as described in the legend, and at different densities. In each case, this hyperonic matter situation is also compared against the nuclear matter ($f_s=0$) situation, represented by dotted lines.

Figure 11

The optical potentials of the $\overline{B}$ mesons $[B^{-}$ in subplots (a), (c), and (e), and ${\overline{B}}^0$ in subplots (b), (d), and (f)] as a function of momentum $k(\equiv |\vec{k}\left|\right)$ in cold $(T=0)$ hyperonic matter (with $f_s=0.5$) at various values of the isospin asymmetry parameter ($\eta$), as described in the legend, and at different densities. In each case, this hyperonic matter situation is also compared against the nuclear matter ($f_s=0$) situation, represented by dotted lines.