Magnetic Dipole Transitions of $B_c$ and $B_c^{\ast }$ mesons in the Relativistic Independent Quark Model

Abstract

We study M1-transitions involving mesons: $B_c(1s)$, $B_c^{\ast }(1s)$, $B_c(2s)$, $B_c^{\ast }(2s)$, $B_c(3s)$ and $B_c^{\ast }(3s)$ in the relativistic independent quark (RIQ) model based on a flavor independent average potential in the scalar-vector harmonic form. The transition form factor for $B_c^{\ast }\to B_c\gamma$ is found to have analytical continuation from spacelike to physical timelike region. Our predicted coupling constant $g_{B_c^{\ast }{B}_c}$ = 0.34 Ge$V^{-1}$ and decay width $\Gamma (B_c^{\ast }\to B_c\gamma )$ = 23 eV agree with other model predictions. In view of possible observation of $B_c$ and $B_c^{\ast }$ s-wave states at LHC and Z-factory and potential use of theoretical estimate on M1-transitions, we investigate the allowed as well as hindered transitions of orbitally excited $B_c$-meson states and predict their decay widths in overall agreement with other model predictions. We consider the typical case of $B_c^{\ast }(1s)\to B_c(1s)\gamma$, where our predicted decay width which is found quite sensitive to the mass difference between $B_c^{\ast }$ and $B_c$ mesons may help in determining the mass of $B_c^{\ast }$ experimentally.