Improved Lattice QCD $B_c\to J/\psi$ Vector, Axial-Vector, and Tensor Form Factors

We present an update of HPQCD's lattice QCD determination of the $B_c\to J/\psi$ vector and axial-vector form factors, and provide new results for the tensor form factors. We use the Highly Improved Staggered Quark action for all valence quarks, together with the second generation MILC $n_f=2+1+1$ HISQ gluon field configurations. This calculation includes two additional ensembles, one with physically light up and down quarks and $a\approx 0.06 \mathrm{fm}$ and one with $a\approx 0.03\mathrm{fm}$ on which we are able to reach the physical bottom quark mass. Our calculation uses nonperturbatively renormalised current operators and covers the full kinematical range of the decay. We use our recent results for the heavy-charm susceptibilities, as a function of $u=m_c/m_h$, in order to employ the full dispersive parameterisation for $B_c\to J/\psi$ in our physical-continuum extrapolation. We give updated SM predictions $R(J/\psi)=0.2597(27)$, $A_{\lambda_\tau}=0.5093(42)$, $F_L^{J/\psi}=0.4421(55)$, and $\mathcal{A}_\mathrm{FB}=-0.0567(61)$, reducing uncertainties by $29\%$, $45\%$, $40\%$ and $50\%$ respectively. Since our lattice form factors cover the full kinematic range we can use them to test extrapolations using data in a truncated range, at low-recoil. We investigate different physical continuum parameterisation schemes, with lattice results in the first $1/3$ of the kinematic range near $q^2_\mathrm{max}$. We find that unexpectedly large systematic uncertainties near $q^2=0$ can emerge when extrapolating synthetic data in the high-$q^2$ region if higher order kinematical terms are omitted from the physical continuum extrapolation. This suggests a potentially underestimated systematic uncerainty entering extrapolations of synthetic lattice QCD data for the related $B\to D^*\ell\bar{\nu}$ decay from the high-$q^2$ region into the low-$q^2$ region.