Mass spectroscopy, decays and mixing parameters of open flavour bottom and bottom strange mesons using instanton induced potential with additional confinement

Abstract

The mass spectra for the heavy-light $(b\bar{q}) ;$ $q = u$ or $d$ and $s$ bottom and bottom strange mesons are computed based on the instanton induced interactions inspired potential along with additional confinement term. Spectroscopic predictions for ground, radial and orbital states are provided. The low-lying states $1S$ and $1P$ are found to be in an excellent agreement with the PDG reported values. The predicted mass spectra strongly support the newly observed $B_J(5840)$ and $B_J(5970)$ by $LHCb$ collaboration as $2^1S_0$ and $1^3D_3$ states respectively. Apart from the mass spectra, the other observables like radiative transitions, decay constant for $1S$ state, the di-leptonic rare decays and the Cabibbo allowed two body hadronic decays are also predicted. The predicted value of branching ratio of rare decay $B_s^0 \rightarrow \mu^+ \mu^-$ as 3.65 $\times 10^{-9}$ is in excellent agreement with the recent measurement of $LHCb$ of $(3.09^{+0.46}_{-0.43}) \times 10^{-9}$. The branching ratios of color favoured decays $B_{(s)} \rightarrow D^{(*)-}_{(s)} \ \pi^+$ and $B_{(s)} \rightarrow D^{(*)-}_{(s)} \ \rho^+$ are found to be exceeding by factor of two as compared to the PDG listed values. The mixing parameters of $B^0_q - \bar{B^0_q}$, $\Delta M_q, x_q$ and $\chi_q$ are obtained as $0.512$, $0.755$ and $0.1877$ respectively which are very close to the PDG listed values of $0.5065 \pm 0.0019$, $0.769 \pm 0.004$ and $0.1858 \pm 0.0011$ respectively.