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.

7 pages, 7 figures, figures changed to pdf format

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• Roles of $a_0(980)$, $\Lambda (1670)$, and $\Sigma (1385)$ in the ${\Lambda }_c^{+}\to \eta \Lambda {\pi }^{+}$ decay
• Role of the $N^{\ast }(1535)$ in the ${\Lambda }_c^{+}\to {\bar{K}}^0\eta p$ decay
• Theoretical study of $N(1535)$ and ${\Sigma }^{\ast }(1/2^{-})$ in the Cabibbo-favored process ${\Lambda }_c^{+}\to p{\bar{K}}^0\eta$
• Search for the ${\Sigma }^{\ast }$ state in ${\Lambda }_c^{+}\to {\pi }^{+}{\pi }^0{\pi }^{-}{\Sigma }^{+}$ decay by triangle singularity
• Measurement of Branching Fractions of ${\Lambda }_c^{+}\to \eta \Lambda {\pi }^{+}$, $\eta {\Sigma }^0{\pi }^{+}$, $\Lambda (1670){\pi }^{+}$, and $\eta \Sigma (1385{)}^{+}$
• Measurement of the absolute branching fractions of ${\Lambda }_c^{+}\to \Lambda \eta {\pi }^{+}$ and $\Sigma (1385{)}^{+}\eta$
• Production of $N^{\ast }(1535)$ and $N^{\ast }(1650)$ in ${\Lambda }_c\to {\bar{K}}^0\eta p$ $(\pi N)$ decay
• Cabibbo-favored ${\Lambda }_c^{+}\to \Lambda a_0(980{)}^{+}$ decay in the final state interaction
• Structure of the $\mathbf{\Lambda }(1670)$ resonance
• Roles of the scalar $f_0(500)$ and $f_0(980)$ in the process $D^0\to {\pi }^0{\pi }^0{\bar{K}}^0$
• Study of the resonance contributions in the ${\Xi }_b^{-}\to p{K}^{-}{K}^{-}$ decay
• Theoretical study in the ${\bar{B}}^0\to J/\psi {\bar{K}}^{\ast 0}{K}^0$ and ${\bar{B}}^0\to J/\psi f_1(1285)$ decays
• Probing the isospin structure and low-lying resonances in ${\Lambda }_c^{+}\to n{\bar{K}}^0{\pi }^{+}$ decays
• Study $B_{(s)}^0$ decays into $\varphi$ and a scalar or vector meson