We derive new sum rules for the form factors of the Bc→J/ψℓνˉℓ 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 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.
@article{arxiv.2209.08851,
title = {New Sum Rules for the $B_c \to J/\psi$ Form Factors},
author = {Marzia Bordone and Alexander Khodjamirian and Thomas Mannel},
journal= {arXiv preprint arXiv:2209.08851},
year = {2023}
}