Study of $B^+ \to \mu^+ \nu_\mu$ decays at Belle and Belle II

Abstract

We report a measurement of the branching fraction for the leptonic decay $B^+\to\mu^+\nu_\mu$. This work presents the first $B^+\to\mu^+\nu_\mu$ result using Belle~II data, an updated Belle measurement that supersedes the previous result, and their combination, which yields the most precise search to date. The analysis is based on $1076\,\mathrm{fb}^{-1}$ of $e^+e^-$ collision data collected at a center-of-mass energy of $10.58\,\mathrm{GeV}$ with the Belle and Belle~II detectors at the KEKB and SuperKEKB colliders, respectively. We measure $\mathcal{B}(B^+\to\mu^+\nu_\mu)=(4.4\pm1.9\pm 1.0)\times10^{-7}$, where the first uncertainty is statistical and the second systematic. The observed significance relative to the background-only hypothesis is 2.4 standard deviations. We set a 90\% confidence level upper limit of $\mathcal{B}(B^+\to\mu^+\nu_\mu)<6.7\times10^{-7}$ using a frequentist approach and a 90\% credibility level upper limit of $\mathcal{B}(B^+\to\mu^+\nu_\mu)<7.2\times 10^{-7}$ using a Bayesian approach. These are the most stringent limits to date. The result is interpreted as an exclusion region in the parameter space of type~II and type~III two-Higgs-doublet models. We search for stable sterile neutrinos with masses $m_N\in[0,1.5]\,\mathrm{GeV}$. No signal is observed, and the resulting exclusion on the squared mixing parameter $|U_{\mu N}|^2$ provides improvement over previous limits. We report a measurement of the partial branching fraction of semileptonic $B\to X_u\ell\nu_\ell$ decays with $p_\mu^B>2.2\,\mathrm{GeV}$, obtaining $\Delta\mathcal{B}(B\to X_u\ell\nu_\ell)=(2.72\pm0.05\pm0.29)\times10^{-4}$. We present a model-dependent study of weak annihilation decays using the muon momentum spectrum. We observe a signal of 2.4 standard deviations above the background-only hypothesis in regions where the distribution resembles that of $B\to X_u\ell\nu_\ell$ decays.