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 axionlike 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 $m_X=2.1_{-0.1}^{+0.2}\mathrm{GeV}$ and the product $\mathcal{B}(B^{+}\to K^{+}X)\cdot {\mathcal{P}}_{X,\mathrm{inv}}=9.2_{-3.4}^{+1.8}\cdot 10^{-6}$, where ${\mathcal{P}}_{X,\mathrm{inv}}$ is the probability that $X$ (and its decay products) are undetected. Bayes's 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.