Excited $B_c$ States via Continuum QCD

Abstract

We study the most recently observed excited $B_c$ states with the Dyson-Schwinger equation and the Bethe-Salpeter equation approach of continuum QCD. The obtained $M_{B_c^{+}(2S)}=6.813(16)\text{GeV}$, $M_{B_c^{\ast +}(2S)}=6.841(18)\text{GeV}$ and the mass splitting $M_{B_c^{+}(2S)}-M_{B_c^{\ast +}(2S)}^{\text{rec}}\approx 0.039\text{GeV}$ agree with the observations very well. Moreover we predict the leptonic decay constant $f_{B_c^{+}(2S)}=-0.165(10)\text{GeV}$, $f_{B_c^{\ast +}(2S)}=-0.161(7)\text{GeV}$ respectively.

5 pages, 2 figures