B -meson decay constants from 2+1 -flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks

We calculate the $B$-meson decay constants ${f}_{B}$, ${f}_{{B}_{s}}$, and their ratio in unquenched lattice QCD using domain-wall light quarks and relativistic $b$ quarks. We use gauge-field ensembles generated by the RBC and UKQCD collaborations using the domain-wall fermion action and Iwasaki gauge action with three flavors of light dynamical quarks. We analyze data at two lattice spacings of $a\ensuremath{\approx}0.11$, 0.086 fm with unitary pion masses as light as ${M}_{\ensuremath{\pi}}\ensuremath{\approx}290\text{ }\text{ }\mathrm{MeV}$; this enables us to control the extrapolation to the physical light-quark masses and continuum. For the $b$ quarks we use the anisotropic clover action with the relativistic heavy-quark interpretation, such that discretization errors from the heavy-quark action are of the same size as from the light-quark sector. We renormalize the lattice heavy-light axial-vector current using a mostly nonperturbative method in which we compute the bulk of the matching factor nonperturbatively, with a small correction, that is close to unity, in lattice perturbation theory. We also improve the lattice heavy-light current through $\mathcal{O}({\ensuremath{\alpha}}_{s}a)$. We extrapolate our results to the physical light-quark masses and continuum using SU(2) heavy-meson chiral perturbation theory, and provide a complete systematic error budget. We obtain ${f}_{{B}^{0}}=199.5(12.6)\text{ }\text{ }\mathrm{MeV}$, ${f}_{{B}^{+}}=195.6(14.9)\text{ }\text{ }\mathrm{MeV}$, ${f}_{{B}_{s}}=235.4(12.2)\text{ }\text{ }\mathrm{MeV}$, ${f}_{{B}_{s}}/{f}_{{B}^{0}}=1.197(50)$, and ${f}_{{B}_{s}}/{f}_{{B}^{+}}=1.223(71)$, where the errors are statistical and total systematic added in quadrature. These results are in good agreement with other published results and provide an important independent cross-check of other three-flavor determinations of $B$-meson decay constants using staggered light quarks.