B-meson decay constants: a more complete picture from full lattice QCD

Abstract

We extend the picture of $B$-meson decay constants obtained in lattice QCD beyond those of the $B$, $B_s$ and $B_c$ to give the first full lattice QCD results for the $B^{\ast }$, $B_s^{\ast }$ and $B_c^{\ast }$. We use improved NonRelativistic QCD for the valence $b$ quark and the Highly Improved Staggered Quark (HISQ) action for the lighter quarks on gluon field configurations that include the effect of $u/d$, $s$ and $c$ quarks in the sea with $u/d$ quark masses going down to physical values. For the ratio of vector to pseudoscalar decay constants, we find $f_{B^{\ast }}/f_B$ = 0.941(26), $f_{B_s^{\ast }}/f_{B_s}$ = 0.953(23) (both $2\sigma$ less than 1.0) and $f_{B_c^{\ast }}/f_{B_c}$ = 0.988(27). Taking correlated uncertainties into account we see clear indications that the ratio increases as the mass of the lighter quark increases. We compare our results to those using the HISQ formalism for all quarks and find good agreement both on decay constant values when the heaviest quark is a $b$ and on the dependence on the mass of the heaviest quark in the region of the $b$. Finally, we give an overview plot of decay constants for gold-plated mesons, the most complete picture of these hadronic parameters to date.

20 pages, 9 figures. Minor updates to the discussion in several places and some additional references

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