Relations among $B_c\to J/\psi ,{\eta }_c$ form factors

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.

arXiv comment32 pages, 4 figures. To appear in JHEP

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• Semileptonic $B_c$ decays to $P-$wave charmonium and the nature of ${\chi }_{c1}(3872)$
• $B_c^{-}\to J/\psi (\to {\mu }^{+}{\mu }^{-}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau },{\rho }^{-}{\nu }_{\tau },{\ell }^{-}{\bar{\nu }}_{\ell }{\nu }_{\tau }){\bar{\nu }}_{\tau }$ decays with visible final-state kinematics
• Correlated study on some $B_c\to P$ and $B_c\to S$ wave channels in light of new inputs
• Nonleptonic $B_c$ decay rates from model independent relations