Speaker
Description
We present a new method aiming at a non-perturbative, model-independent determination of the momentum dependence of the form factors entering hadronic semileptonic decays using unitarity and analyticity constraints. We extend the original proposal of Ref. [1] 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 $D \to K \ell \nu_\ell$ decays obtained in Ref. [2] 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 of Ref. [2]. This finding opens the possibility to obtain non-perturbatively the form factors entering the semileptonic $B$ decays in their full kinematical range.
References
[1] L. Lellouch, Nucl. Phys. B 479(1996), 353-391 doi:10.1016/0550-3213(96)00443-9 [arXiv:hep-ph/9509358 [hep-ph]]
[2] V. Lubicz et al. [ETM],Phys. Rev. D 96 (2017) no.5, 054514 [erratum: Phys. Rev. D 99 (2019) no.9, 099902; erratum: Phys. Rev. D 100 (2019) no.7, 079901] doi:10.1103/PhysRevD.96.054514 [arXiv:1706.03017 [hep-lat]].
