Model-agnostic likelihood for the reinterpretation of the $B^+\to K^+\nu\bar{\nu}$ measurement at Belle II

TL;DR

This paper presents a model-agnostic likelihood approach for the $B^+ o K^+ uar{ u}$ measurement at Belle II, enabling reinterpretation within the Weak Effective Theory and providing posterior distributions for Wilson coefficients.

Contribution

It introduces a publicly available likelihood framework for the $B^+ o K^+ uar{ u}$ measurement, facilitating reinterpretations under various theoretical models.

Findings

Derived posterior distributions for Wilson coefficients.

Constructed credible intervals for key Wilson coefficients.

Assessed goodness of fit to Belle II data.

Abstract

We recently measured the branching fraction of the $B^{+}\rightarrow K^{+}\nu\bar{\nu}$ decay using 362fb$^{-1}$ of on-resonance $e^+e^-$ collision data under the assumption of Standard Model kinematics, providing the first evidence for this decay. To facilitate future reinterpretations and maximize the scientific impact of this measurement, we publicly release the full analysis likelihood along with all necessary material required for reinterpretation under arbitrary theoretical models sensitive to this measurement. In this work, we demonstrate how the measurement can be reinterpreted within the framework of the Weak Effective Theory. Using a kinematic reweighting technique in combination with the published likelihood, we derive marginal posterior distributions for the Wilson coefficients, construct credible intervals, and assess the goodness of fit to the Belle II data. For the Weak Effective Theory Wilson coefficients, the posterior mode of the magnitudes $|C_\mathrm{VL}+C_\mathrm{VR}|$, $|C_\mathrm{SL}+C_\mathrm{SR}|$, and $|C_\mathrm{TL}|$ corresponds to the point ${(11.3, 0.0, 8.2)}$. The respective 95\% credible intervals are $[1.9, 16.2]$, $[0.0, 15.4]$, and $[0.0, 11.2]$.