Non-mesonic Weak Decays of Light Hypernuclei in the Direct Quark and the One-Pion Exchange Mechanisms

Contributions of the direct quark mechanism are studied in the nonmesonic weak decays of light hypernuclei. The $\Lambda N \to NN$ transition is described by the one pion exchange mechanism and the direct quark mechanism, induced by the four-quark vertices in the effective weak Hamiltonian. By employing a realistic wave function of the $\Lambda$ inside the hypernuclei, nonmesonic decay rates of $^4_{\Lambda}$H, $^4_{\Lambda}$He, and $^5_{\Lambda}$He are calculated. The results show that the direct quark mechanism is significantly large and gives a large $\Delta I =3/2$ contribution in the J=0 channel. The relative phase between the one-pion exchange and the direct-quark contributions is determined so that the effective weak Hamiltonian for quarks give both of them consistently. We find that the sum of these two contributions reproduce the current available experimental data fairly well.