Production of $N^*(1535)$ and $N^*(1650)$ in $\Lambda_c\rightarrow\bar{K}^0\eta p$ $(\pi N)$ decay

TL;DR

This paper investigates the properties of the $N^*(1535)$ and $N^*(1650)$ resonances by analyzing mass distributions in $ ext{Lambda}_c$ decays, using chiral unitary and hidden gauge formalisms to identify their signatures.

Contribution

It introduces a detailed calculation of mass distributions in $ ext{Lambda}_c$ decays, incorporating both pseudoscalar-baryon and vector-baryon channels with loop effects, revealing the distinct visibility of resonances.

Findings

$N^*(1535)$ is visible in $ ext{eta} p$ mass distribution.

Both $N^*(1535)$ and $N^*(1650)$ are visible in $ ext{pi} N$ mass distribution.

$K ext{Sigma}$ channel has smaller strength despite strong coupling to $N^*(1650)$.

Abstract

In order to study the properties of the $N^*$(1535) and $N^*$(1650) we calculate the mass distributions of $M B$ in the $\Lambda_c \rightarrow \bar{K}^0 M B$ decay, with $MB=\pi N(I=1/2),\eta p$ and $K\Sigma(I=1/2)$. We do this by calculating the tree-level and loop contributions, mixing pseudoscalar-baryon and vector-baryon channels using the local hidden gauge formalism. The loop contributions for each channel are calculated using the chiral unitary approach. We observe that for the $\eta N$ mass distribution only the $N^*$(1535) is seen, with the $N^*$(1650) contributing to the width of the curve, but for the $\pi N$ mass distribution both resonances are clearly visible. In the case of $MB=K\Sigma$, we found that the strength of the $K\Sigma$ mass distribution is smaller than that of the mass distributions of the $\pi N$ and $\eta p$ in the $\Lambda_c^+\rightarrow\bar{K}^0\pi N$ and $\Lambda_c^+\rightarrow\bar{K}^0\eta p$ processes, in spite of this channel having a large coupling to the $N^*(1650)$. This is because the $K\Sigma$ pair production is suppressed in the primary production from the $\Lambda_c$ decay.