Study of B⁺ → μ⁺ ν_μ decays at Belle and Belle II

We report a measurement of the branching fraction for the leptonic decay B⁺→μ⁺ν_μ. This work presents the first B⁺→μ⁺ν_μ 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\,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 B(B⁺→μ⁺ν_μ)=(4.4±1.9± 1.0)×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 B(B⁺→μ⁺ν_μ)<6.7×10⁻⁷ using a frequentist approach and a 90% credibility level upper limit of B(B⁺→μ⁺ν_μ)<7.2× 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 mN∈[0,1.5]\,GeV. No signal is observed, and the resulting exclusion on the squared mixing parameter |UμN|² provides improvement over previous limits. We report a measurement of the partial branching fraction of semileptonic B→ Xᵤν_ decays with p_μB>2.2\,GeV, obtaining ΔB(B→ Xᵤν₎=(2.72±0.05±0.29)×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→ Xᵤν_ decays.