The Standard Model Prediction for the Rare Decay $B \to X_s ν\bar ν$

TL;DR

The paper provides a precise Standard Model prediction for the inclusive decay $B \to X_s \nu\bar{\nu}$, motivated by recent Belle II results and inclusive-rate limits. It combines a NLO QCD and electroweak-corrected short-distance coefficient with a kinetic-scheme treatment of heavy-quark masses and power corrections, and incorporates the Heavy Quark Expansion up to $1/m_b^3$ along with HQET-sum-rule estimates for four-quark matrix elements. The predicted branching fractions are $\mathrm{Br}(B^0 \to X_s \nu\bar{\nu}) = (3.351 \pm 0.102) \times 10^{-5}$ and $\mathrm{Br}(B^+ \to X_s \nu\bar{\nu}) = (3.618 \pm 0.110) \times 10^{-5}$, with partial rates provided for Belle II-relevant $q^2$ cuts, representing a significant improvement in both central value and precision over prior work. These results establish a robust Standard Model baseline for future searches of new physics in $b \to s \nu\bar{\nu}$ transitions and help integrate inclusive and exclusive rare decays within the broader flavor-anomaly landscape.

Abstract

We present updated and comprehensive Standard Model predictions for the inclusive rare decay $B \to X_s ν\barν$. 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 $\mathcal{O}(α_s^3)$, 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_sν\barν) = (3.35 \pm 0.10)\times 10^{-5} $ and $ \text{Br}(B^+ \to X_sν\barν) = (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 $B \to Kν\barν$ and the first upper limits on inclusive $B \to X_sν\barν$, and they offer a robust baseline for future searches for physics beyond the Standard Model in $b\to sν\barν$ transitions.

Figures (1)

• Figure 1: The dependence of the branching ratio $\mathrm{Br}(B^0 \to X_s \nu \bar{\nu})$ on the renormalization scale $\mu_s \simeq m_b$ at the low scale (the scale of $C_\nu$ is kept fixed at $M_Z$). In the plot, we compare two predictions at different values of the Wilsonian cutoff $\mu$ in the kinetic scheme: $\mu=1$ GeV and $\mu=0.75$ GeV.