We calculate the electromagnetic (EM) decay widths of the $B^{ \pm}_c(2S)$ meson, which is observed recently by the ATLAS Collaboration. The main EM decay channels of this particle are $1{ ^3S_1}\gamma$ and $1{ P}\gamma$, which, in literature, are estimated to have the branching ratio of about $1/10$. In this work, we get the partial decay widths: $\Gamma(2{ ^1S_0}\rightarrow 1{ ^3S_1}\gamma)=0.192$ keV, $\Gamma(2{ ^1S_0}\rightarrow 1{ P_1}\gamma) = 2.24$ keV and $\Gamma(2{ ^1S_0}\rightarrow 1{ P_1^\prime}\gamma) = 11.4$ keV. In the calculation, the instantaneous approximated Bethe-Salpeter method is used. For the $P$-wave $B_c$ mesons, the wave functions are given by mixing the $^3P_1$ and $^1P_1$ states. Within the Mandelstam formalism, the decay amplitude is given, which includes the relativistic corrections.
Categories: hep-ph hep-ex