Coupling constant for $\Lambda(1405)\bar{K}N$

TL;DR

This paper determines the $ ext{Lambda}(1405)ar{K}N$ coupling constant using experimental cross section data within an effective Lagrangian framework, highlighting the importance of background contributions and comparing results with previous studies.

Contribution

It provides a new extraction of the $ ext{Lambda}(1405)ar{K}N$ coupling constant considering background effects, challenging previous higher estimates and aligning with recent measurements.

Findings

Initial coupling constant estimate: 1.51 ± 0.10

Adjusted coupling constant considering backgrounds: 0.77 ± 0.07

Results suggest smaller coupling than previous calculations

Abstract

The value of the $\Lambda(1405){\bar K}N$ coupling constant $g_{\Lambda(1405)\bar{K}N}$ is obtained by fitting it to the experimental data on the total cross sections of the $K^-p \to \pi^0\Sigma^0$ reaction. On the basis of an effective Lagrangian approach and isobar model, we show that the value $|g_{\Lambda(1405)\bar{K}N}| = 1.51 \pm 0.10$ could be extracted from the available experimental data by assuming that the $s-$channel $\Lambda(1405)$ resonance plays a dominant role, whereas, the background contributions from the $s-$channel $\Lambda(1115)$, $t-$channel $K^*$ and $u-$channel nucleon pole processes are small and can be neglected. However, the $u-$channel nucleon pole diagram may also give an important contribution in the present calculations. After the background contributions are taken into account, the above value of $g_{\Lambda(1405)\bar{K}N}$ is reduced to $|g_{\Lambda(1405)\bar{K}N}| = 0.77 \pm 0.07$, which is not supported by the previous calculations and the recent CLAS measurements. The theoretical calculations on differential cross sections are also presented, which can be checked by future experiments.