Probing the $B^{0}$ meson in a hot medium with finite baryon chemical potential

RESUMO

We perform a quantitative analysis of the $B^{0}$ meson spectroscopic parameters in a hot and dense medium. Within the framework of QCD two-point sum rules, we calculate the mass and decay constant of the $B^{0}$ meson with the help of the perturbative spectral density and nonperturbative contributions up to mass dimension five as functions of temperature $T$ and baryon chemical potential $\mu_B$. For various fixed values of the baryon chemical potential, our numerical results indicate that both the mass and decay constant of the $B^{0}$ meson initially increase with temperature, reach a maximum, and then gradually decrease before eventually vanishing at sufficiently high temperatures. The corresponding vanishing points are found to be in the temperature intervals $(0.182-0.273)~\mathrm{GeV}$ and $(0.118-0.173)~\mathrm{GeV}$, for the mass and decay constant, respectively. Moreover, these temperatures move toward lower values as the baryon chemical potential increases. On the other hand, for various fixed temperatures, both the mass and decay constant exhibit a slight initial increase with increasing baryon chemical potential, followed by a subsequent decrease, eventually vanishing at sufficiently high chemical potentials. The vanishing points for the decay constant is determined to be in baryon chemical potential interval $(0.23-0.83)~\mathrm{GeV}$. For the mass, the decrease at $T=0$ is much weaker than at finite temperatures; excluding this case, the vanishing points for the mass are determined to be in baryon chemical potential interval $(0.38-1.43)~\mathrm{GeV}$ for different fixed temperatures. It is further observed that the baryon chemical potential values corresponding to the vanishing of both the mass and decay constant move to lower values as the temperature increases. In the $T \to 0$ and $\mu_B \to 0$ limit ...