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. 41. 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) 2. 2\, GeV, obtaining ΔB (B Xᵤν_) = (2. 720. 050. 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.