The electromagnetic decays of B _c ^± (2S)

Abstract: We calculate the electromagnetic (EM) decay widths of the B_c ^±(2S) meson, which is observed recently by the ATLAS Collaboration. The main EM decay channels of this particle are 1³S₁γ and 1Pγ, which, in literature, are estimated to have the branching ratio of about 1/10. In this work, we get the partial decay widths: Γ(2¹S₀ → 1³S₁γ) = 0.192 keV, Γ(2¹S₀ → 1P₁γ) = 2.24 keV and Γ(2¹S₀ → 1P₁ ^′γ) = 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 ³P₁ and ¹P₁ states. Within the Mandelstam formalism, the decay amplitude is given, which includes the relativistic corrections.