The weak decay process of varOmega _c to varXi is calculated in the method of QCD light-cone sum rule. The decay width of varOmega _c^0 rightarrow varXi ^- l^+ nu _l and its decay branching ratio are also calculated with the form factors from this work’s calculation. To the twist-6 distribution amplitudes, the form factors f_1=0.66pm 0.02, f_2=-0.76pm 0.03, g_1=0.06pm 0.01 and g_2=-0.44pm 0.01 are given at zero recoil point. The result of the semileptonic decay width of varOmega _c^0 rightarrow varXi ^-l^+nu _l is varGamma =(7.51pm 0.36)times 10^{-15}~mathrm{{GeV}} , and the prediction of the decay branching ratio Br(varOmega _c^0rightarrow varXi ^-l^+nu _l)=(3.06pm 0.15)times 10^{-3}. These results fit well with other works, and the decay width and branching ratio are improved. This not too small branching ratio gives a good direction to explore this decay channel in the future experiments.
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