Extracting V_{ub} Without Recourse to Structure Functions

TL;DR

The paper proposes a method to extract the CKM element ratio |V_{ub}|^2/|V_{ts}^*V_{tb}|^2 from inclusive B decays without modeling the B meson structure function. It develops a framework that resums endpoint perturbative logs for both semileptonic and radiative decays, and incorporates nonperturbative effects via a universal B-meson structure function, which is then eliminated from the final ratio through a carefully constructed convolution and inverse Mellin transform. The key result is a closed-form, model-independent relation between measured endpoint spectra and the desired CKM ratio, with quantified perturbative and nonperturbative uncertainties. The approach leverages HQET, Sudakov resummation, and the universality of the leading-twist structure function to suppress modeling errors from Fermi motion, potentially improving the precision of |V_{ub}| extraction in CP-violation studies.

Abstract

We present a closed form expression for |V_{ub}|^2/ |V_{tb} V_{ts}^*|^2 in terms of the endpoint photon and lepton spectra from the inclusive decays B -> X_sγand B -> X_u\ellν, respectively, which includes the resummation of the endpoint logs at next to leading order and is completely independent of the B meson structure function. The use of this expression for extracting V_{ub} would eliminate the large systematic errors usually incurred due to the modeling of the heavy quarks' Fermi motion.