Study of $B^+ \to μ^+ ν_μ$ decays at Belle and Belle II

TL;DR

This work delivers the most precise search to date for the leptonic decay $B^+ \rightarrow \mu^+ \nu_\mu$, combining Belle and Belle II data to measure a branching fraction of $\mathcal{B}(B^+ \rightarrow \mu^+ \nu_\mu) = (4.4 \pm 1.9 \pm 1.0) \times 10^{-7}$ with a 2.4$\sigma$ significance and setting stringent upper limits. It employs an inclusive tagging strategy to reconstruct the signal-side $B$ and uses a sophisticated background-modeling framework with a multi-category, joint fit to extract the signal in the muon-momentum spectrum $p_\mu^B$, while simultaneously constraining backgrounds from $b \rightarrow u$ and $b \rightarrow c$ transitions and continuum processes. The analysis interprets the result in the context of beyond-Standard-Model scenarios, including type II and type III two-Higgs-doublet models, and performs dedicated searches for sterile neutrinos and weak-annihilation processes, providing updated constraints on $|U_{\mu N}|^2$ and WA contributions. In addition, the paper reports a partial branching fraction for $B \rightarrow X_u \ell \nu_\ell$ at the kinematic endpoint and, via extrapolation, a full-space value that agrees with the current world average, thereby contributing to the broader effort to determine $|V_{ub}|$ and test SM predictions in heavy-flavor decays.

Abstract

We report a measurement of the branching fraction for the leptonic decay $B^+\toμ^+ν_μ$. This work presents the first $B^+\toμ^+ν_μ$ 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 $1076\,\mathrm{fb}^{-1}$ 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 $\mathcal{B}(B^+\toμ^+ν_μ)=(4.4\pm1.9\pm 1.0)\times10^{-7}$, 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 $\mathcal{B}(B^+\toμ^+ν_μ)<6.7\times10^{-7}$ using a frequentist approach and a 90\% credibility level upper limit of $\mathcal{B}(B^+\toμ^+ν_μ)<7.2\times 10^{-7}$ 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 $|U_{μN}|^2$ provides improvement over previous limits. We report a measurement of the partial branching fraction of semileptonic $B\to X_u\ellν_\ell$ decays with $p_μ^B>2.2\,\mathrm{GeV}$, obtaining $Δ\mathcal{B}(B\to X_u\ellν_\ell)=(2.72\pm0.05\pm0.29)\times10^{-4}$. 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 $B\to X_u\ellν_\ell$ decays.

Figures (20)

• Figure 1: Tree-level Feynman diagrams for the $B^+ \rightarrow\xspace \mu^+ \nu_\mu$ decay in the SM (a), and for potential beyond Standard Model contributions mediated by a charged Higgs boson $H^+$ ((b),(c)) or a leptoquark $LQ$ (d). Note the final-state sterile neutrino $N$ in cases (c) and (d).
• Figure 2: Leading-order Feynman diagram for the WA processes $B^+ \overset{\text{WA}}{\rightarrow\xspace} X_u \ell^+ \nu_\ell$. The hadronic system $X_u$ is formed through initial-state gluon radiation, while the charged lepton and neutrino originate from the decay of the virtual $W^+$ boson.
• Figure 3: Distribution of the muon momentum $p_\mu^B$ in the $B$ meson rest frame for the flat, peaking and intermediate $B^+ \overset{\text{WA}}{\rightarrow\xspace} X_u \ell^+ \nu_\ell$ models, with the transition between shapes controlled by the parameter $\alpha$, compared to that of $B^+ \rightarrow\xspace \mu^+ \nu_\mu$ decays.
• Figure 4: Relation between the mean generated and reconstructed values of the momentum component $p_z$ in each bin. The difference between the Belle and Belle II distributions stems from the different mass constraint enforced on the tag-side $B$ meson.
• Figure 5: Muon momenta $p_\mu^B$ and $p_\mu^*$ in the estimated signal-$B$ meson rest frame and in the c.m. frame, respectively, from the Belle (top) and Belle II (bottom) data.