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 GeV with the Belle and Belle II detectors at the KEKB and SuperKEKB colliders, respectively. We measure $\mathcal{B}(B^{+}\to {\mu }^{+}{\nu }_{\mu })=(4.4\pm 1.9\pm 1.0)\times {10}^{-7}$, 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 $\mathcal{B}(B^{+}\to {\mu }^{+}{\nu }_{\mu })<6.7\times {10}^{-7}$ 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 $\mathrm{\Delta }\mathcal{B}(B\to X_u\ell {\nu }_{\ell })=(2.72\pm 0.05\pm 0.29)\times {10}^{-4}$. 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.

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• Branching fraction
• Cabibbo–Kobayashi–Maskawa matrix
• Leptonic, semileptonic & radiative decays
• Rare decays