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

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.

Comments: 7 pages, 7 figures, figures changed to pdf format