Constraints on invisible $B^{+}\to K^{+} X$ decays from the Belle II $B^{+} \to K^{+} \nu \bar{\nu}$ measurement

Abstract

The Belle II measurement of the branching fraction for $B^+\to K^+ \nu \bar \nu$ shows a $2.7\sigma$ excess over the Standard Model prediction and motivates new-physics explanations such as axion-like particles, Higgs-like scalars, or beyond Standard Model gauge bosons. A two-body decay $B^+\to K^+ X$ with an invisible $X$ provides a natural candidate explanation. This work provides a comprehensive test of this hypothesis using Belle II's public model-agnostic likelihood. Posterior distributions are derived for the resonance mass $m_X$ and the branching fraction, and a modified frequentist upper-limit mass scan is performed. The data favor a resonance with mass $m_X = 2.1^{+0.2}_{-0.1}$ GeV and the product $\mathcal{B}(B^+\to K^+ X) \cdot \mathcal{P}_{X,\rm inv} = 9.2^{+1.8}_{-3.4} \cdot 10^{-6}$, where $\mathcal{P}_{X,\rm inv}$ is the probability that $X$ (and its decay products) are undetected. Bayes factors indicate a very strong preference for the Standard Model plus resonance over the Standard Model-only hypothesis. A frequentist likelihood-ratio test favors the Standard Model plus resonance hypothesis by $3.0\sigma$. A light invisible resonance plus the Standard Model therefore provides a compelling description of the Belle II data.