<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi></mml:mrow></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
Judd Harrison, C. T. H. Davies, Andrew Lytle
Abstract
We present the first lattice QCD determination of the ${B}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}$ vector and axial-vector form factors. These will enable experimental information on the rate for ${B}_{c}$ semileptonic decays to $J/\ensuremath{\psi}$ to be converted into a value for ${V}_{cb}$. Our calculation covers the full physical ${q}^{2}$ range of the decay and uses nonperturbatively renormalized lattice currents. We use the highly improved staggered quark (HISQ) action for all valence quarks on the second generation MILC ensembles of gluon field configurations including $u$, $d$, $s$ and $c$ HISQ sea quarks. Our HISQ heavy quarks have masses ranging upwards from that of $c$; we are able to reach that of the $b$ on our finest lattices. This enables us to map out the dependence on heavy quark mass and determine results in the continuum limit at the $b$. We use our form factors to construct the differential rates for ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}$ and obtain a total rate with 7% uncertainty: $\mathrm{\ensuremath{\Gamma}}({B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}})/|{\ensuremath{\eta}}_{\mathrm{EW}}{V}_{cb}{|}^{2}=1.73(12)\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. Including values for ${V}_{cb}$, ${\ensuremath{\eta}}_{\mathrm{EW}}$ and ${\ensuremath{\tau}}_{{B}_{c}}$ yields a branching fraction for this decay mode of 0.0150(11)(10)(3) with uncertainties from lattice QCD, ${\ensuremath{\eta}}_{\mathrm{EW}}{V}_{cb}$ and ${\ensuremath{\tau}}_{{B}_{c}}$ respectively.