b->c semileptonic sum rule

概要

Measurements of $R_{D^{(*)}}={\rm{BR}}(B\to D^{(*)} \tau\bar\nu)/{\rm{BR}}(B\to D^{(*)} \ell\bar\nu)$ have shown deviations from the SM predictions at the 3.8$\sigma$ level. These results may suggest contributions from new physics, leading to an excess of the tau lepton modes. In contrast, the recent measurement of $R_{\Lambda_c} ={\rm{BR}}(\Lambda_b\to\Lambda_c\tau\bar\nu)/{\rm{BR}}(\Lambda_b\to\Lambda_c\ell\bar\nu)$ is consistent with the SM prediction. Such a situation motivates investigations into potential shortcomings in the experimental data and SM predictions. In this talk, we propose $b \to c$ semileptonic sum rules that 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 outline the derivation of the sum rule. We then examine deviations from these limits and study corrections arising from realistic hadron masses and higher-order contributions to form factors, while taking account of uncertainties. It is shown 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 SM predictions. We also discuss future prospects.

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