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We evaluate the $\Lambda_c\Sigma_c\pi$ coupling constant ($G_{\Lambda_c\Sigma_c \pi}$) and the width of the strong decay $\Sigma_c\rightarrow\Lambda_c \pi$ in 2+1 flavor lattice QCD on four different ensembleswith pion masses ranging from 700 MeV to 300 MeV. We find $G_{\Lambda_c\Sigma_c \pi}=18.332(1.476)_{\rm{stat.}}(2.171)_{\rm{syst.}}$ and the decaywidth $\Gamma(\Sigma_c \rightarrow\Lambda_c\pi)=1.65(28)_{\rm{stat.}}(30)_{\rm{syst.}}$~MeV on the physical quark-masspoint, which is in agreement with the recent experimental determination.

$\Lambda_c\Sigma_c\pi$ coupling and $\Sigma_c \rightarrow\Lambda_c \pi$ decay in lattice QCD