Abstract
We derive new sum rules for the form factors of the \( {B}_c\to J/\psi \ell {\overline{\nu}}_{\ell } \) semileptonic transitions, employing the vacuum-to-Bc correlation function of the J/ψ-interpolating and b → 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 Bc meson. Furthermore, applying hadronic dispersion relation in the J/ψ channel, we find that a non-vanishing OPE spectral density in the duality interval of J/ψ emerges only at \( \mathcal{O} \)(αs). We calculate this density in the relevant kinematic regime. The Bc → J/ψ form factors at space-like momentum transfer are then calculated from the new sum rules.
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Bordone, M., Khodjamirian, A. & Mannel, T. New sum rules for the Bc → J/ψ form factors. J. High Energ. Phys. 2023, 32 (2023). https://doi.org/10.1007/JHEP01(2023)032
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DOI: https://doi.org/10.1007/JHEP01(2023)032