An exact sum rule connects branching fractions of Lambda_b -> Lambda nu nubar and B -> K(*) nu nubar decays with coefficients identical to those in the b->c tau semileptonic sum rule.
$b \to c$ semileptonic sum rule: SU(3)$_{\rm{F}}$ symmetry violation
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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.
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Sum rules for b→cτν transitions to orbitally excited charm hadrons show larger deviations from heavy quark symmetry than ground states, with tensor effects often sizable, but current form factor uncertainties prevent robust lepton-universality predictions.
A sum rule among LFU ratios R^{mu e} for c to d l nu decays holds within 1% under current NP bounds, yielding a prediction for the unmeasured R_n^{mu e} in Lambda_c to n l nu.
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Baryon-Meson Sum Rule for $b \to s \nu\bar\nu$
An exact sum rule connects branching fractions of Lambda_b -> Lambda nu nubar and B -> K(*) nu nubar decays with coefficients identical to those in the b->c tau semileptonic sum rule.
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$b \to c$ semileptonic sum rule: orbitally excited hadrons
Sum rules for b→cτν transitions to orbitally excited charm hadrons show larger deviations from heavy quark symmetry than ground states, with tensor effects often sizable, but current form factor uncertainties prevent robust lepton-universality predictions.
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Semileptonic sum rules in heavy-to-light charm decays
A sum rule among LFU ratios R^{mu e} for c to d l nu decays holds within 1% under current NP bounds, yielding a prediction for the unmeasured R_n^{mu e} in Lambda_c to n l nu.