Unitarity bounds for semileptonic decays in lattice QCD

In this work we discuss in detail the nonperturbative determination of the momentum dependence of the form factors entering in semileptonic decays using unitarity and analyticity constraints. The method contains several new elements with respect to previous proposals and allows to extract, using suitable two-point functions computed nonperturbatively, the form factors at low momentum transfer q2 from those computed explicitly on the lattice at large q(2), without any assumption about their q(2)-dependence. The approach will be very useful for exclusive semileptonic B-meson decays, where the direct calculation of the form factors at low q(2) is particularly difficult due to large statistical fluctuations and discretization effects. As a testing ground we apply our approach to the semileptonic D -> Kl nu(l) decay, where we can compare the results of the unitarity approach to the explicit direct lattice calculation of the form factors in the full q(2)-range. We show that the method is very effective and that it allows to compute the form factors with rather good precision.

Automated summary

This work discusses the nonperturbative determination of the momentum dependence of form factors in semileptonic decays using unitarity and analyticity constraints. The method allows for the extraction of form factors at low momentum transfer q2 from those computed on the lattice at large q(2) without assumptions about their q(2)-dependence. The approach is particularly useful for exclusive semileptonic B-meson decays where direct calculation of form factors at low q(2) is challenging.