The Standard Model Prediction for the Rare Decay $B\to X_s\nu \bar{\nu }$

Abstract

We present updated and comprehensive Standard Model predictions for the inclusive rare decay $B\to X_s\nu \bar{\nu }$. Using a state-of-the-art determination of the short-distance coefficient, including NLO QCD and electroweak effects, and implementing a consistent treatment of heavy-quark masses and power corrections within the kinetic scheme, we compute the total decay rate and the neutrino invariant mass spectrum. We incorporate all known perturbative contributions in the heavy quark limit up to $\mathcal{O}({\alpha }_s^3)$, evaluate non-perturbative corrections through the Heavy Quark Expansion up to $1/m_b^3$, and include estimates of four-quark operator matrix elements from HQET sum rules. We obtain the Standard Model branching ratios $\text{Br}(B^0\to X_s\nu \bar{\nu })=(3.35\pm 0.10)\times 10^{-5}$ and $\text{Br}(B^{+}\to X_s\nu \bar{\nu })=(3.62\pm 0.11)\times 10^{-5},$ representing a significant improvement in both central value and precision compared to previous determinations. We also provide predictions for partial rates with kinematic cuts relevant to Belle II. Our results are timely in view of recent measurements of $B\to K\nu \bar{\nu }$ and the first upper limits on inclusive $B\to X_s\nu \bar{\nu }$, and they offer a robust baseline for future searches for physics beyond the Standard Model in $b\to s\nu \bar{\nu }$ transitions.

Comments: 21 pages, 1 figure