Extracting V_{ub} Without Recourse to Structure Functions

TL;DR

This paper derives a model-independent formula to extract |V_{ub}| from inclusive B decay spectra, reducing systematic errors associated with heavy quark structure function modeling.

Contribution

It provides a closed-form expression for |V_{ub}|^2/|V_{tb} V_{ts}^*|^2 based on endpoint spectra, including next-to-leading order resummation, independent of B meson structure functions.

Findings

Derived a formula linking |V_{ub}| to measurable spectra

Includes next-to-leading order resummation of endpoint logs

Eliminates systematic errors from Fermi motion modeling

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_s\gamma and B -> X_u\ell\nu, 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.