Photo- and electroproduction of $\Lambda(1405)$ via $\gamma^{(*)}p\to K^+\pi^+\Sigma^-$

Abstract

In this work, we perform a \textit{toy-model} analysis for the unpolarized photo- and electroproduction of $\Lambda(1405)\equiv\Lambda^*$ via $\gamma^{(*)}p\to K^+\pi^+\Sigma^-$ by employing the effective Lagrangian approach at the tree level only. We consider that $\Lambda^*$ consists of the high-mass ($H$) and low-mass ($L$) poles as suggested by the chiral unitary model (ChUM). We determine all the model parameters including coupling constants and cutoff parameters for the phenomenological strong form factors by using the theoretical information from ChUM and available experimental data. The electromagnetic (EM) form factors for the two poles are parameterized appropriately being similar to that for the neutron by employing the ChUM estimates for the EM root-mean-squared (rms) radii for the two poles. We observe from the numerical calculations that, for the photoproduction of $\Lambda^*$, the interference between the two poles turns out to be destructive, resulting in the single-peak line at $M_{\pi^+\Sigma^-}\approx1405$ MeV in the invariant-mass distribution. On the contrary, there appear two peaks in the distribution for the electroproduction as observed in the CLAS/Jlab electroproduction data, due to the constructive interference, which is mainly caused by the Dirac form factors for the two poles. From this observation, we conclude that, in order to explain the photo- and electroproduction data simultaneously, i.e., \textit{single} and \textit{double} peaks, respectively, in the invariant-mass distribution, the interference patterns for the two poles should follow those suggested by ChUM. In turn, it is a strong theoretical and experimental supports for the two-pole structure scenario for $\Lambda^*$.