New sum rules for the Bc→ J/ψ form factors

Abstract

We derive new sum rules for the form factors of the {B}_cto 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.