The BABAR Collaboration has searched for the leptonic decay \( B^+ \rightarrow \mu^+ \nu_\mu \) using data collected at the \( Y(4S) \) resonance with an integrated luminosity of approximately 81.4 fb\(^{-1}\). The analysis focuses on selecting well-identified muon candidates with momentum between 2.25 and 2.95 GeV/c in the CM frame, reconstructing the companion \( B \) meson from the remaining visible energy, and using kinematic variables such as \(\Delta E\) and \( m_{\text{ES}} \) to identify signal decays. Backgrounds from \( B \) semi-leptonic decays and non-resonant \( q\bar{q} \) events are suppressed using event shape variables and cuts on muon candidate momentum. The background estimate is determined using an Argus function fit to the data. Systematic uncertainties are evaluated, including luminosity, background estimate, and signal efficiency. The final result sets a preliminary upper limit on the branching fraction \(\mathcal{B}(B^+ \rightarrow \mu^+ \nu_\mu) < 6.6 \times 10^{-6}\) at the 90% confidence level.The BABAR Collaboration has searched for the leptonic decay \( B^+ \rightarrow \mu^+ \nu_\mu \) using data collected at the \( Y(4S) \) resonance with an integrated luminosity of approximately 81.4 fb\(^{-1}\). The analysis focuses on selecting well-identified muon candidates with momentum between 2.25 and 2.95 GeV/c in the CM frame, reconstructing the companion \( B \) meson from the remaining visible energy, and using kinematic variables such as \(\Delta E\) and \( m_{\text{ES}} \) to identify signal decays. Backgrounds from \( B \) semi-leptonic decays and non-resonant \( q\bar{q} \) events are suppressed using event shape variables and cuts on muon candidate momentum. The background estimate is determined using an Argus function fit to the data. Systematic uncertainties are evaluated, including luminosity, background estimate, and signal efficiency. The final result sets a preliminary upper limit on the branching fraction \(\mathcal{B}(B^+ \rightarrow \mu^+ \nu_\mu) < 6.6 \times 10^{-6}\) at the 90% confidence level.