$\Lambda \left(1405\right)$ production in the ${\pi }^{-}p\to K^0\pi \Sigma$ reaction

We discuss the mechanisms that lead to $\Lambda \left(1405\right)$ production in the ${\pi }^{-}p\to K^0\pi \Sigma$ reaction. The problem has gained renewed interest after different works converge to the conclusion that there are two resonances around the region of $1400\text{MeV}$, rather than one, and that they couple differently to the $\pi \Sigma$ and $\overline{K}N$ channels. We look at the dynamics of that reaction and find two mechanisms which eventually filter each one of the resonances, leading to very different shapes of the $\pi \Sigma$ invariant mass distributions. The combination of the two mechanisms leads to a shape of this distribution compatible with the experimental measurements.

Figure 1

Diagrams entering the production of the $\Lambda \left(1405\right)$ in the ${\pi }^{-}p\to K^0\Lambda \left(1405\right)\to K^0\pi \Sigma$. In the figure, $M$ and $B$ stand for the meson and baryon of the ten possible coupled channels. The $\Lambda \left(1405\right)$ resonance is dynamically generated by the final state interaction of $M$ and $B$.

Figure 2

Basic terms entering the threshold production of pions in $\pi N\to \pi \pi N$. (a) meson pole term and (b) contact term.

Figure 3

One loop functions for $MB\to MMB$.

Figure 4

Contribution of the meson pole and contact terms (Fig. 1) to the $\pi \Sigma$ invariant mass obtained averaging ${\pi }^{+}{\Sigma }^{-}$ and ${\pi }^{-}{\Sigma }^{+}$. The histogram shows the experimental data taken from Ref. 15.

Figure 5

Resonant mechanisms for $\Lambda \left(1405\right)$ production in the ${\pi }^{-}p\to K^0\pi \Sigma$ reaction.

Figure 6

Invariant mass distribution of $\pi \Sigma$ obtained by averaging ${\pi }^{+}{\Sigma }^{-}$ and ${\pi }^{-}{\Sigma }^{+}$ with parameter set I. The histogram shows the experimental data taken from Ref. 15

Figure 7

Same as in Fig. 6 but with set II.