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.
$\Lambda_b\to\Lambda^{(*)}\nu{\bar\nu}$ and $b\to s$ $B$ decays
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abstract
The baryonic $b\to s$ transition $\Lambda_b\to\Lambda^{(*)}\nu{\bar\nu}$ is analyzed. We combine the mesonic counterpart $B^+\to K^+\nu{\bar\nu}$ and $B^0\to K^{*0}\nu{\bar\nu}$ as well as other observables involving $B$ mesons like $R(K^{(*)})$, ${\rm Br}(B_s\to\mu^+\mu^-)$, ${\rm Br}(B^+\to K^+\mu^+\mu^-)$, and $P_5'(B^+\to K^{*+}\mu^+\mu^-)$. Using the constraints from mesonic sector, we present predictions for the currently unobserved baryonic decay modes, which is very complementary to mesonic modes for probing new physics. We find that the new physics scale $M_{\rm NP}$ to be $2.04~{\rm TeV}\le M_{\rm NP} \le 11.76~{\rm TeV}$ (at $1\sigma$) for ordinary heavy new mediators. Our predictions for the branching ratios ${\rm Br}(\Lambda_b\to\Lambda^{(*)}\nu{\bar\nu})$ are $2.07 (1.07)$ times the standard model estimations, which could be verified at future colliders. We also find a sum rule for ${\rm Br}(\Lambda_b\to\Lambda \nu{\bar\nu})$ and ${\rm Br}(B\to K^{(*)}\nu{\bar\nu})$ that is very similar to that for $b\to c$ semi-leptonic decays.
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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.
A tauphilic leptoquark model with S1 explaining R(D(*)), ~R2 fitting B to K nu nu via right-handed coefficients, and S3 satisfying Delta m_Bs via mixing predicts subdominant negative C_VL, dominant positive C_SL, C9^LQ approx +1, and masses below 3 TeV.
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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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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.
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$B$ anomalies and the tauphilic leptoquark model
A tauphilic leptoquark model with S1 explaining R(D(*)), ~R2 fitting B to K nu nu via right-handed coefficients, and S3 satisfying Delta m_Bs via mixing predicts subdominant negative C_VL, dominant positive C_SL, C9^LQ approx +1, and masses below 3 TeV.