Spectroscopic parameters of $B_c$ meson

Abstract

We study the spectroscopy and decays of the $B_c$ meson in a nonrelativistic quark model in which all observables follow from a single set of wave functions, with spin-dependent effects included directly in the bound-state equation. With parameters calibrated to the measured $B_c(1S)$ and $B_c(2S)$ masses, we predict the $S$-, $P$-, and $D$-wave spectrum up to $n=5$, the pseudoscalar and vector decay constants with one-loop QCD corrections, the E1 and M1 radiative widths, and the radial Regge trajectories of ten spin-parity families. The $1P$ multiplet is predicted at 6692--6746~MeV with the normal fine-structure ordering, compatible with lattice QCD and located in the region of the two structures observed by LHCb in the $B_c^{+}\gamma$ spectrum. The $1D$ states lie near 7008~MeV, below the $BD$ threshold, and all four $D$-wave families are provided. The decay constant $f_{B_c}=507.1$~MeV is consistent with recent QCD sum-rule results and corresponds to $\mathcal{B}(B_c\to \tau {\nu }_{\tau })\approx 3\%$. The E1 widths follow the expected angular weights, while their magnitudes are governed mainly by the radial overlap. The $1P\to 1S$ (81--112~keV) and $1D\to 1P$ (71--93~keV) widths suggest the $1D\to 1P\to 1S$ cascade as a promising route toward the first $D$-wave $B_c$ state. The Regge trajectories are nearly linear, with slopes decreasing from about 5.8~GeV${}^2$ for the $S$-wave to 4.7--4.8~GeV${}^2$ for the $D$-wave states. These results may guide forthcoming measurements at the LHC and future $e^{+}{e}^{-}$ facilities.

arXiv comment18 pages,, 10 figures, 10 tables; new references added