$b \to c$ semileptonic sum rule: Current status and prospects

TL;DR

This paper revisits the $b o c$ semileptonic sum rule, analyzing theoretical corrections and uncertainties, and discusses its usefulness for testing the Standard Model and guiding future experimental measurements.

Contribution

It provides an updated derivation of the sum rule, evaluates the impact of realistic corrections, and highlights its potential for cross-checking experimental data and probing new physics.

Findings

Corrections from realistic hadron masses are negligible compared to experimental uncertainties.

The sum rule remains a valuable tool for consistency checks and Standard Model tests.

Future precise form factor measurements are essential for detailed comparisons.

Abstract

The $b \to c$ semileptonic sum rules provide relations between the decay rates of $B \to D^{(*)} \tau\bar\nu$ and $\Lambda_b \to \Lambda_c \tau\bar\nu$. Starting from the heavy quark and zero-recoil limits, we revisit the derivation of the sum rule for total decay rates. We then examine deviations from the limits and investigate corrections arising from realistic hadron masses and higher-order contributions to form factors, taking account of uncertainties. We show that these corrections are negligible compared to current experimental uncertainties, indicating that the sum rule is useful for cross-checking experimental consistency and testing the validity of the Standard Model predictions. In future, precise determinations of the form factors particularly for the tensor operator will be necessary to compare the sum rule predictions with $\Lambda_b \to \Lambda_c \tau\bar\nu$ data from the LHCb experiment and the Tera-Z projects.