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

TL;DR

This work reinterprets the Belle II measurement of ${B^{+}\rightarrow K^{+}\nu\bar{\nu}}$ with a model-agnostic likelihood to test a possible two-body decay ${B^{+}\rightarrow K^{+}X}$ where $X$ is invisible. Using a Breit–Wigner resonance in $q^{2}$ and Bayesian as well as frequentist methods, the analysis finds a posterior mode at $m_X\approx2.1$ GeV and a nonzero signal strength ${\mathcal{B}(B^{+}\rightarrow K^{+}X)\mathcal{P}_{X,\rm inv}}\approx 9\times10^{-6}$, with strong model preference over SM-only and background hypotheses. A mass-scan via ${CL_s}$ confirms localization near $m_X\approx2\,$GeV and yields competitive 95% CL upper limits across $m_X$, especially for $\Gamma_X=0.1$ GeV; Bayes factors likewise indicate a very strong to decisive preference for the ${B^{+}\rightarrow K^{+}X}$ scenario. Overall, the results motivate further experimental scrutiny of light invisible resonances in rare $B$ decays and demonstrate the utility of model-agnostic reinterpretations for beyond-SM searches.

Abstract

Belle II measurement of the branching fraction for $B^{+} \to K^{+} ν\barν$ shows a $2.7σ$ 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 \BKX 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 $3.0σ$. A light invisible resonance plus the Standard Model therefore provides a compelling description of the Belle II data.

Figures (4)

• Figure 1: Predicted differential branching fraction from \ref{['eq:bkx-width']} for two resonance widths at $\mu_X=1$, $m_X=2\mathrm{\,Ge V}\xspace$. Bands include hadronic form-factor and $5\%$ SM normalization uncertainties. Form factor uncertainties on the resonance contribution are not considered.
• Figure 2: Marginalized posterior distributions for ${B^{+}\rightarrow\xspace K^{+}X}$ model parameters from \ref{['eq:bkx-width']} for two resonance widths $\Gamma_X = 0.1$ and $0.5 \mathrm{\,Ge V}\xspace$. Diagonal panels show 1-dimensional densities; the off-diagonal panel shows 2-dimensional densities (linear scale). Contours enclose $68\%$ and $95\%$ credible regions. The dash-dotted yellow lines and cross mark the posterior mode.
• Figure 3: Observed and predicted best-fit yields in the highest sensitivity region. Signal predictions are for the unconstrained $B^{+}\rightarrow\xspace K^{+}\nu\bar{\nu}$ SM (left) and ${B^{+}\rightarrow\xspace K^{+}X}$ with $\Gamma_X=0.1\mathrm{\,Ge V}\xspace$ (right). For ${B^{+}\rightarrow\xspace K^{+}X}$, the constrained $B^{+}\rightarrow\xspace K^{+}\nu\bar{\nu}$ SM background is shown separately. Background yields include neutral and charged $B$-meson decays and summed continuum categories. Lower panels show pulls.
• Figure 4: Modified frequentist 95% $CL_s$ upper limit on $\mathcal{B}({B^{+}\rightarrow\xspace K^{+}X}\xspace) \cdot \mathcal{P}_{X,\rm inv}$ as a function of $m_X$ (solid black), compared to the expected SM limit (dashed black) with $\pm 1\sigma$ (green) and $\pm 2\sigma$ (yellow) bands.