The BABAR Collaboration searched for the leptonic decay $ B^{+} \rightarrow \mu^{+} \nu_{\mu} $ using data collected at the $ \mathcal{Y}(4S) $ resonance with an integrated luminosity of approximately 81.4 $ fb^{-1} $, corresponding to 88.4 million $ B\overline{B} $ pairs. No significant signal was observed, and a preliminary upper limit on the branching fraction was set at $ \mathcal{B}(B^{+} \rightarrow \mu^{+} \nu_{\mu}) < 6.6 \times 10^{-6} $ at the 90% confidence level. The analysis involved reconstructing the decay products and applying stringent selection criteria to distinguish signal events from background. The signal was identified through kinematic variables $ \Delta E $ and $ m_{ES} $, which were used to define a "signal box" for event selection. Systematic uncertainties in the luminosity, background estimate, and signal efficiency were evaluated. The results were consistent with previous limits from the CLEO and Belle Collaborations. The study provides a conservative upper limit on the branching fraction, considering potential biases and uncertainties in the analysis.The BABAR Collaboration searched for the leptonic decay $ B^{+} \rightarrow \mu^{+} \nu_{\mu} $ using data collected at the $ \mathcal{Y}(4S) $ resonance with an integrated luminosity of approximately 81.4 $ fb^{-1} $, corresponding to 88.4 million $ B\overline{B} $ pairs. No significant signal was observed, and a preliminary upper limit on the branching fraction was set at $ \mathcal{B}(B^{+} \rightarrow \mu^{+} \nu_{\mu}) < 6.6 \times 10^{-6} $ at the 90% confidence level. The analysis involved reconstructing the decay products and applying stringent selection criteria to distinguish signal events from background. The signal was identified through kinematic variables $ \Delta E $ and $ m_{ES} $, which were used to define a "signal box" for event selection. Systematic uncertainties in the luminosity, background estimate, and signal efficiency were evaluated. The results were consistent with previous limits from the CLEO and Belle Collaborations. The study provides a conservative upper limit on the branching fraction, considering potential biases and uncertainties in the analysis.