Prediction of the $B_c^{*}$ Mass in Full Lattice QCD

By using the highly improved staggered quark formalism to handle charm, strange, and light valence quarks in full lattice QCD, and NRQCD to handle bottom valence quarks, we are able to determine accurately ratios of the $B$ meson vector-pseudoscalar mass splittings, in particular, $[m(B_c^{*})-m(B_c)]/[m(B_s^{*})-m(B_s)]$. We find this ratio to be 1.15(15), showing the “light” quark mass dependence of this splitting to be very small. Hence we predict $m(B_c^{*})=6.330(7)(2)(6)\mathrm{GeV}$, where the first two errors are from the lattice calculation and the third from existing experiment. This is the most accurate prediction of a gold-plated hadron mass from lattice QCD to date.

Figure 1

The ratio $R_c$ of the $B_c$ and $B_s$ hyperfine splittings [Eq. (3)] as a function of lattice spacing, $a$, from full lattice QCD. Our continuum extrapolation is also given and the result at $a=0$. The lighter points and line give the equivalent points for $R_l$ along with the experimental value [12].

Figure 2

The spectrum of “gold-plated” mesons from HPQCD calculations. Results are divided into those used to fix the parameters of QCD (4 quark masses and a coupling constant); those which are postdictions [2, 11, 15] and those, like the $B_c^{*}$ described here, which are predictions [2, 3]. The calculation of masses of non-gold-plated mesons are also of interest, particularly that of the flavor-singlet ${\eta }^{\prime }$ meson. Calculation of its mass is very hard, but is underway [20].