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We report the first measurement of the absolute branching fraction for$\Lambda^+_{c}\rightarrow \Lambda \mu^+\nu_{\mu}$. This measurement is based ona sample of $e^+e^-$ annihilation data at a center-of-mass energy of$\sqrt{s}=4.6$ GeV collected with the BESIII detector at the BEPCII storagerings. The sample corresponds to an integrated luminosity of 567 pb$^{-1}$. Thebranching fraction is determined to be $\mathcal B({\Lambda^+_c\rightarrow\Lambda \mu^+\nu_{\mu}})=(3.49\pm0.46({\rm stat})\pm0.27({\rm syst}))\%$. Inaddition, we calculate the ratio $\mathcal{B}(\Lambda^+_c\rightarrow \Lambda\mu^+\nu_{\mu})/\mathcal{B}(\Lambda^+_c\rightarrow \Lambda e^+\nu_{e})$ to be$0.96\pm0.16({\rm stat})\pm0.04({\rm syst})$.

Measurement of the Absolute Branching Fraction for $\Lambda_c^+\rightarrow \Lambda \mu^+\nu_{\mu}$