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 ${B}^{*}$, ${B}_{s}^{*}$ and ${B}_{c}^{*}$. 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 ${f}_{{B}^{*}}/{f}_{B}=0.941(26)$, ${f}_{{B}_{s}^{*}}/{f}_{{B}_{s}}=0.953(23)$ (both $2\ensuremath{\sigma}$ less than 1.0) and ${f}_{{B}_{c}^{*}}/{f}_{{B}_{c}}=0.988(27)$. 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.
Highlights
Lattice QCD calculations are an essential part of B physics phenomenology, providing increasingly precise determinations of decay constants, form factors and mixing parameters needed, along with experiment, in the determination of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements
As the constraints being provided by lattice QCD become more stringent it is increasingly important to expand the range of hadronic matrix elements being calculated to allow tests both against experiment where possible and/or against expectations from other approaches
Decay constants are useful in this respect because they are single numbers expressing the amplitude for a meson to annihilate to a single particle, encapsulating information about its internal structure
Summary
Lattice QCD calculations are an essential part of B physics phenomenology (see for example [1]), providing increasingly precise determinations of decay constants, form factors and mixing parameters needed, along with experiment, in the determination of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements. Decay constants are useful in this respect because they are single numbers expressing the amplitude for a meson to annihilate to a single particle (for example a W boson or a photon), encapsulating information about its internal structure. They are straightforwardly calculated in lattice QCD from the same hadron correlation functions being used to determine the hadron masses. The only additional complication is that normalization of the appropriate operator for the meson creation or annihilation is required In this way we can build up a tested and consistent “big picture” of meson decay constants within which sit the results being used for CKM element determination
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