$B_c\to J/\ddot{I}ˆ$ Form Factors for the full $q^2$ range from Lattice QCD

Abstract

We present the first lattice QCD determination of the $B_c\to J/\ddot{I}ˆ$ vector and axial-vector form factors. These will enable experimental information on the rate for $B_c$ semileptonic decays to $J/\ddot{I}ˆ$ to be converted into a value for $V_{cb}$. Our calculation covers the full physical $q^2$ range of the decay and uses non-perturbatively renormalised 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 $B_c^{-}\to J/\ddot{I}ˆ\hat{I}{¼}^{-}\bar{\hat{I}}{½}_{\hat{I}}¼$ and obtain a total rate with $7\%$ uncertainty: $\hat{I}“(B_c^{-}\to J/\ddot{I}ˆ\hat{I}{¼}^{-}\bar{\hat{I}}{½}_{\hat{I}}¼)/|\hat{I}{\cdot }_{\mathrm{EW}}{V}_{cb}{|}^2=1.73(12)\times 10^{13}{\mathrm{s}}^{-1}$. Including values for $V_{cb}$, $\hat{I}{\cdot }_{\mathrm{EW}}$ and $\ddot{I}{„}_{B_c}$ yields a branching fraction for this decay mode of 0.0150(11)(10)(3) ~with uncertainties from lattice QCD, $\hat{I}{\cdot }_{\mathrm{EW}}{V}_{cb}$ and $\ddot{I}{„}_{B_c}$ respectively.

23 pages, 14 Figures, Version accepted for publication in Phys. Rev. D