$b \to c$ semileptonic sum rule: SU(3)$_{\rm{F}}$ symmetry violation

TL;DR

This paper extends a semileptonic sum rule for heavy meson decays to include baryons, assesses SU(3) symmetry violation, and finds the violation is smaller than experimental uncertainties, supporting the sum rule's robustness.

Contribution

It generalizes the $b o c$ sum rule to include baryonic decays and evaluates SU(3) symmetry breaking effects to validate the sum rule's applicability.

Findings

SU(3) symmetry violation is moderate and smaller than experimental uncertainties.

The extended sum rule remains a useful consistency check for semileptonic decays.

New sum rules are proposed to test for potential new physics effects.

Abstract

To clarify possible deviations in $b\to c\tau\overline\nu$ processes, the $b\to c$ semileptonic sum rule provides a valuable tool. This relation, derived based on heavy quark symmetry (HQS), offers a powerful consistency check among experimental results. In this work, we extend the previously proposed sum rule for $\{B\to D^{(*)} l\overline\nu,\,\Lambda_b\to \Lambda_c l\overline\nu\}$ to include $\{B_s\to D_s^{(*)} l\overline\nu,\,\Xi_b\to \Xi_c l\overline\nu\}$, thereby enabling more useful cross-checks. Although the relation is supported by HQS and SU(3) flavor symmetry, both symmetries are broken in reality, and the size of the violation needs to be quantified to assess the validity of the sum rule. While the violation is expected to be moderate based on chiral perturbation theory, we perform a numerical evaluation and compare it with future experimental sensitivities. We find that the violation remains smaller than the expected experimental uncertainty. Therefore another new physics agnostic and predictive sum rules are constructed to check the consistency.