The Electromagnetic Decays of $B_c^{\pm }(2S)$

Abstract

We calculate the electromagnetic (EM) decay widths of the $B_c^{\pm }(2S)$ meson, which is observed recently by the ATLAS Collaboration. The main EM decay channels of this particle are $1{}^3{S}_1\gamma$ and $1P\gamma$, which, in literature, are estimated to have the branching ratio of about $1/10$. In this work, we get the partial decay widths: $\Gamma (2{}^1{S}_0\to 1{}^3{S}_1\gamma )=0.192$ keV, $\Gamma (2{}^1{S}_0\to 1P_1\gamma )=2.24$ keV and $\Gamma (2{}^1{S}_0\to 1P_1^{\prime }\gamma )=11.4$ 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 ${}^3{P}_1$ and ${}^1{P}_1$ states. Within the Mandelstam formalism, the decay amplitude is given, which includes the relativistic corrections.

Comments: 9 pages, 3 figures, 3 tables