Non-Perturbative Bounds for Semileptonic Decays in Lattice QCD

Abstract

We present a new method aiming at a non-perturbative, model-independent determination of the momentum dependence of the form factors entering semileptonic decays using unitarity and analyticity constraints. We extend the original proposal and, using suitable two-point functions computed non-perturbatively, we determine the form factors at low-momentum transfer 𝑞 2 from those computed explicitly on the lattice at large 𝑞 2 , without making any assumption about their 𝑞 2 dependence. As a training ground we apply the new method to the analysis of the lattice data of the semileptonic 𝐷 → 𝐾ℓ𝜈 ℓ decays obtained both at finite values of the lattice spacing and at the physical pion point in the continuum limit. We show that, starting from a limited set of data at large 𝑞 2 , it is possible to determine quite precisely the form factors in a model independent way in the full kinematical range, obtaining a remarkable agreement with the direct calculation of the form factors. This finding opens the possibility to obtain non-perturbatively the form factors entering the semileptonic B decays in the full kinematical range.