The $B^+ \to K^+ ν\bar ν$ decay as a search for the QCD axion

Abstract

We reinterpret the $B^+ \to K^+ ν\bar ν$ measurement as a probe of the decay $B^+ \to K^+ a$, where $a$ denotes an axion or axion-like particle. This is possible in the kinematic regions where the di-neutrino invariant mass squared, $q^2$, can be identified with the assumed $m_a^2$. While $q^2$ is reconstructed only in the Hadronic Tag Analysis (HTA), it is not directly accessible in the Inclusive Tag Analysis (ITA), which provides much larger statistics and hence higher sensitivity. In ITA, $q^2$ is proxied by a reconstructed variable, $q^2_{\text{rec}}$, usually modeled through Belle II simulations. We show that the mapping between $q^2$ and $q^2_{\text{rec}}$ can be accurately derived from kinematic arguments alone -- without relying on internal experimental inputs. Using this relation and publicly available efficiencies, we obtain the strongest existing bounds on the coupling-rescaled Peccei-Quinn scale, $|(F_V)_{sb}| \ge 0.9 \times 10^9$ GeV, improving the latest bound in the literature by an order of magnitude. We further show that the bound depends only marginally on the assumed value of the di-neutrino signal strength $μ_{ν{\barν}}$, whether fixed or floated. This establishes $B^+ \to K^+ ν\bar ν$ as a double probe -- of new short-distance physics in the $B^+ \to K^+ ν\barν$ amplitude, and of new light, elusive particles produced via $B^+ \to K^+ a$ -- the two probes working independently to an excellent approximation.

Figures (5)

• Figure 1: Correlation between the true ($q^2$) and the reconstructed ($q^2_{{\rm rec}}$) di-neutrino invariant mass squared. The plot is normalised to $10^5$ observed events.
• Figure 2: Upper limit on $\mathcal{B}_a$ (upper row) and lower limit on the coupling-rescaled Peccei-Quinn scale $(F_V)_{sb}$ (lower row) at 90% CL as a function of the mass $m_a$, and with $\mu_{\nu \bar{\nu}}$ set to unity (blue line) or left floating (red).
• Figure 3: Twice the negative profile log-likelihood ratio as a function of $\mu_{\nu \bar{\nu}}$ for the ITA (red), HTA (blue) or combined (black) analyses. The solid line refers to our results while the dashed line are the results from Belle II in Fig. 16 of Ref. Belle-II:2023esi. The grey dashed lines refer to $1,2,3\sigma$$\chi^2$ values with 1 degree of freedom.
• Figure 4: Regions $\mathcal{B}_a$ at 68% (green), 95% (yellow) and 99% (orange) CL and best fit value (solid green line) of $\mathcal{B}_a$ as a function of the mass with $\mu_{\nu \bar{\nu}}$ fixed to 1 (upper row) or left floating (lower row).
• Figure 5: Upper limit at 90% CL on $\mathcal{B}_a$ for fixed values of $\mu_{\nu \bar{\nu}}$.