Finding $B_c(3S)$ States via Their Strong Decays

Abstract The experimentally known B c states are all below open bottom-charm threshold, which experience three main decay modes, and all induced by weak interaction. In this work, we investigate the mass spectrum and strong decays of the B c ( 3 S ) states, which just above the threshold, in the Bethe-Salpeter formalism and P 0 3 model. The numerical estimation gives M ( B c ( 3 1 S 0 ) ) = 7273 MeV , M ( B c ⁎ ( 3 3 S 1 ) ) = 7304 MeV , Γ ( B c ( 3 1 S 0 ) → B ⁎ D ) = 26.02 − 2.21 + 2.33 MeV , Γ ( B c ⁎ ( 3 3 S 1 ) → B D ) = 3.39 − 0.26 + 0.27 MeV , Γ ( B c ⁎ ( 3 3 S 1 ) → B ⁎ D ) = 14.77 − 1.33 + 1.40 MeV and Γ ( B c ⁎ ( 3 3 S 1 ) → B D ⁎ ) = 6.14 − 0.54 + 0.58 MeV . Compared with previous studies in non-relativistic approximation, our results indicate that the relativistic effects are notable in B c ( 3 S ) exclusive strong decays. According to the results, we suggest to find the B c ( 3 S ) states in their hadronic decays to B and D mesons in experiment, like the LHCb.