Relations among $B_c \to J/\psi, \eta_c$ form factors

TL;DR

This paper studies the form factors in $B_c$ meson decays to $J/9$ and $\u03b7_c$ using nonrelativistic QCD and lattice results, providing a comprehensive analysis of their relations and extrapolations.

Contribution

It introduces a systematic expansion in nonrelativistic QCD to relate various form factors in $B_c$ decays, incorporating lattice QCD data for improved predictions.

Findings

Derived relations among form factors in a specific kinematic range.

Provided extrapolation methods to cover the full kinematic range.

Enhanced understanding of heavy quark spin symmetry breaking effects.

Abstract

We analyze the form factors parametrizing the $B_c \to J/\psi, \eta_c$ matrix elements of the operators in a generalized low-energy $b \to c$ semileptonic Hamiltonian. We consider an expansion in nonrelativistic QCD, classifying the heavy quark spin symmetry breaking terms and expressing the form factors in terms of universal functions in a selected kinematical range. Using as an input the lattice QCD results for the $B_c \to J/\psi$ matrix element of the SM operator, we obtain information on other form factors. The extrapolation to the full kinematical range is also presented.