The $B_c$ mass up to order ${\alpha }_s^4$

Abstract

We evaluate in perturbative QCD, up to order ${\alpha }_s^4$, the mass of the $B_c$. We use the so-called 1S-mass in order to improve the convergence of the perturbative series. Our result is $E(B_c{)}_{pert}=6326_{-9}^{+29}$ MeV. Non-perturbative effects are discussed. A comparison with potential models seems to be consistent with non-perturbative contributions of the order $-(40÷100)$ MeV.

Comments: 14 pages, revtex, 2 figures, minor changes, discussion on the non-perturbative corrections added, final version to appear in Phys. Rev. D