  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 $\Lambda^*$.

High Energy Physics - Phenomenology;Nuclear Theory