Photoproduction of $\Lambda (1405)$ with the two-pole structure

Abstract

We investigate the $\Lambda (1405,1/2^{-})\equiv {\Lambda }^{\ast }$ photoproduction off the proton target, i.e. $\gamma p\to K^{+}{\Lambda }^{\ast }$, considering explicitly its two-pole structure, the higher (${\Lambda }_H^{\ast }:1430\mathrm{MeV}$) and lower (${\Lambda }_L^{\ast }:1390\mathrm{MeV}$) mass-pole contributions, suggested by the chiral-unitary model (ChUM) approaches. For this purpose, we construct a two-body process model, which mimics the Dalitz process, $\gamma p\to K^{+}\pi \Sigma$, assuming that the mass of ${\Lambda }^{\ast }$ as the invariant mass of $\pi$ and $\Sigma$, i.e. $M_{{\Lambda }^{\ast }}\sim M_{\pi \Sigma }$. We employ the effective Lagrangian method with the tree-level Born approximation, using the gauge-invariant prescription for the phenomenological form factors. We provide the numerical results for the energy and angular dependences, $\pi$-$\Sigma$ invariant-mass distribution, and so on. It turns out that the model parameters determined from ChUM reproduce the experimental data qualitatively well, supporting the two-pole structure. Moreover, the nucleon resonance contribution near the threshold plays an important role to describe the data.

Comments: 13 pages, 25 figures