The $a_0(980)$ and $\Lambda(1670)$ in the $\Lambda^+_c \to \pi^+ \eta \Lambda$ decay

TL;DR

This paper investigates the production of the $a_0(980)$ and $ ext{Lambda}(1670)$ resonances in the decay $ ext{Lambda}_c^+ o ext{pi}^+ ext{eta} ext{Lambda}$, using final state interactions modeled by the chiral unitary approach to understand their nature.

Contribution

It introduces a novel decay process analysis to study the $a_0(980)$ and $ ext{Lambda}(1670)$ resonances through invariant mass distributions in $ ext{Lambda}_c^+$ decay, providing insights into their structure.

Findings

Invariant mass distributions show cusp and peak structures associated with the resonances.

The decay process can serve as an ideal probe for the nature of the $a_0(980)$ and $ ext{Lambda}(1670)$.

Results are testable at facilities like BEPCII.

Abstract

We propose to study the $a_0(980)$ and the $\Lambda(1670)$ resonances in the $\Lambda^+_c \to \pi^+ \eta \Lambda$ decay via the final state interactions of the $\pi^+ \eta$ and $\eta \Lambda$ pairs. The weak interaction part proceeds through the $c$ quark decay process: $c(ud) \to (s + u + \bar d)(ud)$, while the hadronization part takes place in two different mechanisms. In the first mechanism, the $sud$ cluster picks up a $q\bar{q}$ pair from the vacuum to form the $\eta\Lambda$ meson-baryon pair while the $u\bar{d}$ pair from the weak decay hadronizes into a $\pi^+$. In the second, the $sud$ cluster turns into a $\Lambda$, while the $u\bar{d}$ pair from the $c$ decay picks up a $q\bar{q}$ pair and hadronizes into a meson-meson pair ($\pi\eta$ or $K\bar{K}$). Because the final $\pi^+ \eta$ and $\eta \Lambda$ states are in pure isospin $I = 1$ and $I=0$ combinations, the $\Lambda^+_c \to \pi^+ \eta \Lambda$ decay can be an ideal process to study the $a_0(980)$ and $\Lambda(1670)$ resonances. Describing the final state interaction in the chiral unitary approach, we find that the $\pi^+ \eta$ and $\eta \Lambda$ invariant mass distributions, up to an arbitrary normalization, show clear cusp and peak structures, which can be associated with the $a_0(980)$ and $\Lambda(1670)$ resonances, respectively. The proposed mechanism can provide valuable information on the nature of these resonances and can in principle be test by facilities such as BEPCII.