E2 Strength in the Radiative Charmed Baryon Decay

Abstract

The radiative decay $\Sigma_Q^* \rightarrow \Lambda_Q\gamma$ can have both magnetic dipole (M1) and electric quadrupole (E2) components. In the heavy quark limit $M_Q\rightarrow\infty$ the transition arises from the spin of the light degrees of freedom changing from $s_l=1$ to $s_l=0$ and hence the E2 contribution vanishes. We compute the leading contribution to the E2 strength in chiral perturbation theory and find that the amplitude is enhanced by a small energy denominator in the chiral limit. This enhancement essentially compensates for the $1/M_c$ suppression that is present in the charm system. We find a mixing ratio of order a few percent dependent upon the $\Sigma_c^*--\Sigma_c$ spin symmetry breaking mass difference. The analogous quantity in the b-baryon sector is smaller by a factor of $\sim M_c/M_b$.