New Sum Rules for the $B_c\to J/\psi$ Form Factors

Abstract

We derive new sum rules for the form factors of the $B_c\to J/\psi \ell {\bar{\nu }}_{\ell }$ semileptonic transitions, employing the vacuum-to-$B_c$ correlation function of the $J/\psi$-interpolating and $b\to c$ weak currents. In the heavy quark limit and at a space-like momentum transfer to the weak current, a local operator-product expansion is valid for this correlation function. As a result, in the leading power, the non-perturbative input is reduced to the decay constant of $B_c$ meson. Furthermore, applying hadronic dispersion relation in the $J/\psi$ channel, we find that a non-vanishing OPE spectral density in the duality interval of $J/\psi$ emerges only at $\mathcal{O}({\alpha }_s)$. We calculate this density in the relevant kinematic regime. The $B_c\to J/\psi$ form factors at space-like momentum transfer are then calculated from the new sum rules.

30 pages, 3 figures. v2: version accepted in JHEP

References in corpus (2)

• Form Factors from Light-Cone Sum Rules with B-Meson Distribution Amplitudes
• $B\to D^{(\ast )}$ Form Factors from QCD Light-Cone Sum Rules

Cited by in corpus (3)

• $B_c^{-}\to J/\psi (\to {\mu }^{+}{\mu }^{-}){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau },{\rho }^{-}{\nu }_{\tau },{\ell }^{-}{\bar{\nu }}_{\ell }{\nu }_{\tau }){\bar{\nu }}_{\tau }$ decays with visible final-state kinematics
• Systematic analysis of the transition form factors of $B_c$ to $D$-wave charmonia and corresponding semileptonic decays
• Systematic analysis of the form factors of $B_c$ to $P$-wave charmonia and corresponding weak decays