New sum rules for the B$_{c}$→ J/ψ form factors

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-B$_{c}$ 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 B$_{c}$ 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} $(α$_{s}$). We calculate this density in the relevant kinematic regime. The B$_{c}$ → J/ψ form factors at space-like momentum transfer are then calculated from the new sum rules.