W-exchange contribution to the decays $\Xi_{cc}^{++}\to\Xi_{c}^{+(\prime)}\pi^{+}$ using light-cone sum rules

We calculate the W-exchange contribution to the $\Xi_{cc}^{++}\to\Xi_{c}^{+(\prime)}\pi^{+}$ decay using light-cone sum rules. The two-particle light-cone distribution amplitudes of the pion are used as non-perturbative input for the sum rules calculation, and the perturbative kernel is calculated at the leading order. We obtain the corresponding decay branching fractions by combining our W-exchange amplitudes with the factorizable amplitudes given by various theoretical methods from the literature. It is shown that with the factorizable amplitudes from heavy quark effective theory, we obtain the branching fraction ratio ${\cal B}(\Xi_{cc}^{++}\to\Xi_{c}^{+\prime}\pi^{+})/{\cal B}(\Xi_{cc}^{++}\to\Xi_{c}^{+}\pi^{+})= 1.42\pm 0.78$, which is consistent with the experimental value of $1.41\pm 0.17\pm 0.1$.