<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>B</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mo>*</mml:mo></mml:msubsup></mml:math> form factors for the full <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>q</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math> range from lattice QCD

Abstract

We compute the Standard Model semileptonic vector and axial-vector form factors for ${B}_{s}\ensuremath{\rightarrow}{D}_{s}^{*}$ decay across the full ${q}^{2}$ range using lattice QCD. We use the highly improved staggered quark (HISQ) action for all valence quarks, enabling us to normalize weak currents nonperturbatively. Working on second-generation MILC ensembles of gluon field configurations which include $u$, $d$, $s$, and $c$ HISQ sea quarks and HISQ heavy quarks with masses from that of the $c$ mass up to that of the $b$ on the ensemble with the smallest lattice spacing, allows us to map out the heavy quark mass dependence of the form factors, and to constrain the associated discretization effects. We can then determine the physical form factors at the $b$ mass. We use these to construct the differential and total rates for $\mathrm{\ensuremath{\Gamma}}({B}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{*\ensuremath{-}}{\ensuremath{\ell}}^{+}{\ensuremath{\nu}}_{\ensuremath{\ell}})$ and find ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\ell}=e}/|{\ensuremath{\eta}}_{\mathrm{EW}}{V}_{cb}{|}^{2}=2.07(17{)}_{\mathrm{latt}}(2{)}_{\mathrm{EM}}\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$, ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\ell}=\ensuremath{\mu}}/|{\ensuremath{\eta}}_{\mathrm{EW}}{V}_{cb}{|}^{2}=2.06(16{)}_{\mathrm{latt}}(2{)}_{\mathrm{EM}}\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$, and ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\ell}=\ensuremath{\tau}}/|{\ensuremath{\eta}}_{\mathrm{EW}}{V}_{cb}{|}^{2}=5.14(37{)}_{\mathrm{latt}}(5{)}_{\mathrm{EM}}\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$, where ${\ensuremath{\eta}}_{\mathrm{EW}}$ contains the short-distance electroweak correction to ${G}_{F}$, the first uncertainty is from our lattice calculation, and the second allows for long-distance QED effects. The ratio $R({D}_{s}^{*\ensuremath{-}})\ensuremath{\equiv}{\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\ell}=\ensuremath{\tau}}/{\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\ell}=\ensuremath{\mu}}=0.2490(60{)}_{\mathrm{latt}}(35{)}_{\mathrm{EM}}$. We also obtain a value for the ratio of decay rates ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\ell}=\ensuremath{\mu}}({B}_{s}\ensuremath{\rightarrow}{D}_{s})/{\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\ell}=\ensuremath{\mu}}({B}_{s}\ensuremath{\rightarrow}{D}_{s}^{*})=0.443(40{)}_{\mathrm{latt}}(4{)}_{\mathrm{EM}}$, which agrees well with recent LHCb results. We can determine ${V}_{cb}$ by combining our lattice results across the full kinematic range of the decay with experimental results from LHCb and obtain $|{V}_{cb}|=42.2(1.5{)}_{\mathrm{latt}}(1.7{)}_{\mathrm{exp}}(0.4{)}_{\mathrm{EM}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. A comparison of our lattice results for the shape of the differential decay rate to the binned, normalized differential decay rate from LHCb shows good agreement. We also test the impact of new physics couplings on angular observables and ratios which are sensitive to lepton flavor universality violation.

Topics & Concepts