Inclusive $\bar{B} \to X_s \ell^+ \ell^-$ with a hadronic mass cut

TL;DR

This paper analyzes the inclusive B meson decay spectrum with hadronic mass cuts at next-to-leading order, discussing the validity of theoretical descriptions and proposing interpolation strategies for experimental cuts.

Contribution

It provides a detailed theoretical analysis of the hadronic mass spectrum in B decays with mass cuts and discusses methods to bridge different kinematic regions.

Findings

The heavy quark expansion remains valid for mild mass cuts.

Severe experimental cuts challenge the local operator expansion.

Strategies for interpolating between theoretical and experimental regions are proposed.

Abstract

The hadronic mass spectrum of inclusive $\bar{B} \to X_s \ell^+ \ell^-$ is investigated at next to leading order in the heavy quark expansion. For mild cuts on the hadronic mass, the expansion, which applies when the cut is released, remains convergent. However, the cuts used at BaBar and Belle to reduce backgrounds from charged current semileptonic processes are too severe for a description in terms of matrix elements of local operators to apply. Strategies for interpolating between the two regions are discussed.