Next-to-leading order QCD calculation of $B_c$ to charmonium tensor form factors

Abstract

We present a next-to-leading order (NLO) QCD corrections to $B_c\to {\eta }_c$ and $B_c\to J/\psi$ tensor form factors within nonrelativistic QCD (NRQCD) framework. The full analytical results for $B_c$ to S-wave charmonium tensor form factors are obtained. We also studied the asymptotic behaviours of tensor form factors in hierarchy heavy quark limit, i.e. $m_b\to \infty ,m_c\to \infty ,\mathrm{and}{m}_c/m_b\to 0$. A compact expression for tensor form factors are given analytically in the hierarchy heavy quark limit. The relation among different form factors is also analyzed especially at large momentum recoil point. The numerical results for the $B_c$ to charmonium tensor form factors in all the physical region are given in the end.

arXiv commentcomments: 9 pages, 9 figures; some typos corrected, references added; to be published in PRD

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• Next-to-next-to-leading order matching of beauty-charmed meson $B_c$ and $B_c^{\ast }$ decay constants
• Relations among $B_c\to J/\psi ,{\eta }_c$ form factors
• Analyzing the semileptonic and nonleptonic $B_c\to J/\psi ,{\eta }_c$ decays
• Baryonic heavy-to-light form factors induced by tensor current in light-front approach
• $B_c^{-}\to J/\psi (\to {\mu }^{+}{\mu }^{-}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau },{\rho }^{-}{\nu }_{\tau },{\ell }^{-}{\bar{\nu }}_{\ell }{\nu }_{\tau }){\bar{\nu }}_{\tau }$ decays with visible final-state kinematics