Impact of background effects on the inclusive $V_{cb}$ determination

TL;DR

This paper calculates the theoretical contributions of background processes, specifically $b o u$ and tauonic modes, to improve the precision of inclusive $V_{cb}$ determinations in semileptonic $b$ decays.

Contribution

It provides high-precision theoretical predictions for background processes affecting inclusive $V_{cb}$ measurements, enabling their uncertainties to be minimized.

Findings

Good agreement between theory and Monte-Carlo for lepton energy moments.

Less agreement observed for hadronic mass moments.

Uncertainties from background processes can be effectively eliminated with proper inclusion.

Abstract

The determination of the CKM element $V_{cb}$ from inclusive semileptonic $b\to c \ell \bar\nu$ decays has reached a high precision thanks to a combination of theoretical and experimental efforts. Aiming towards even higher precision, we discuss two processes that contaminate the inclusive $V_{cb}$ determination; the $b\to u$ background and the contribution of the tauonic mode: $b\to c(\tau \to \mu\nu\bar{\nu})\bar{\nu}$. Both of these contributions are dealt with at the experimental side, using Monte-Carlo methods and momentum cuts. However, these contributions can be calculated with high precision within the Heavy-Quark Expansion. In this note, we calculate the theoretical predictions for these two processes. The $b\to u$ results are compared with generator-level Monte-Carlo results used at Belle and Belle II. We have good agreement between theory and Monte-Carlo for lepton energy moments, but less for hadronic mass moments. Based on our results the uncertainties due to these backgrounds processes can basically be eliminated by properly including them into the analyses.