The $Lambda Lambda to YN$ Weak Transition in Double-$Lambda$ Hypernuclei

We calculate the $Lambda Lambda to YN$ transition rate of ${^{phantom{Lambda}6}_{Lambda Lambda}}$He by the hybrid picture, the $pi$ and $K$ exchanges plus the direct quark processes. It is found that the hyperon-induced decay is weaker than the nucleon-induced decay, but the former may reveal the short-range mechanism of the weak transition and also give a clear signal of the strong $Delta I=3/2$ transition. The $Lambda Lambda to Y N$ transition in double-$Lambda$ hypernucleus is complement to the $Lambda N to NN$ transition as it occurs only in the J=0 channel, while the J=1 transition is dominant in the $Lambda N to NN$ case.