Microscopic approach to the proton asymmetry in the non-mesonic weak decay of Lambda-hypernuclei

TL;DR

This paper presents a microscopic theoretical framework for analyzing the proton asymmetry in the non-mesonic weak decay of polarized Lambda-hypernuclei, incorporating various decay mechanisms and final state interactions, and compares results with experimental data.

Contribution

It introduces a comprehensive microscopic diagrammatic approach that includes one- and two-nucleon induced decay mechanisms, final state interactions, and different weak transition potentials, providing new insights into asymmetry behavior.

Findings

Two-nucleon induced decay reduces asymmetry magnitude.

Final state interactions also decrease asymmetry.

Results align with KEK experimental measurements.

Abstract

The non--mesonic weak decay of polarized $\Lambda$-hypernuclei is studied with a microscopic diagrammatic formalism in which one- and two-nucleon induced decay mechanisms, $\vec{\Lambda} N \to NN$ and $\vec{\Lambda} NN \to NNN$, are considered together with (and on the same ground of) nucleon final state interactions. We adopt a nuclear matter formalism extended to finite nuclei via the local density approximation. Our approach adopts different one-meson-exchange weak transition potentials, while the strong interaction effects are accounted for by a Bonn nucleon-nucleon interaction. We also consider the two-pion-exchange effect in the weak transition potential. Both the two-nucleon induced decay mechanism and the final state interactions reduce the magnitude of the asymmetry. The quantum interference terms considered in the present microscopic approach give rise to an opposite behavior of the asymmetry with increasing energy cuts to that observed in models describing the nucleon final state interactions semi-classically via the intranuclear cascade code. Our results for the asymmetry parameter in $^{12}_{\Lambda}$C obtained with different potential models are consistent with the asymmetry measured at KEK.