Weak Decay of $\Lambda$ in Nuclei: Direct Quark Mechanism vs Meson Exchange

Abstract

Nonmesonic decays of $\Lambda$ in nuclear medium and light hypernuclei are studied by using the $\Lambda N \to NN$ weak transition potential derived from the meson exchange mechanism and the direct quark mechanism. The long range part of the transition potential is described by exchanges of the pseudoscalar mesons ($\pi$, $K$, $\eta$), while the vector mesons ($\rho$, $\omega$, $K^\ast$) may be considered as the medium- and short-range part in the meson exchange picture. We propose the direct quark transition potential as the short range part, which is derived from the matrix elements of the $\Delta S=1$ effective weak Hamiltonian in the two baryon states. The results indicate that the direct quark contribution is significantly large and its behavior is qualitatively different from the vector meson exchanges. We also find that the decay rate is sensitive to the choice of form factor and that a soft cutoff must be used for the pion-baryon verteces so that the strong tensor transition is suppressed. We find that the $\pi + K + DQ$ results are compatible with experiment although the $n/p$ ratio is still too large. The $\pi^+$ decays of light hypernuclei are related to the $\DI=3/2$ amplitudes of the nonmesonic decay. The role of chiral symmetry for the pionic decays are discussed.