  We evaluate theoretically the radiative decay widths into $\gamma\Lambda$ and
$\gamma\Sigma^0$ of the two poles of the $\Lambda(1405)$ found in chiral
unitary theories and we find quite different results for each of the two poles.
We show that, depending on which reaction is used to measure the
$\Lambda(1405)$ radiative decays, one gives more weight to one or the other
pole, resulting in quite different shapes in the $\gamma\Lambda(\Sigma^0)$
invariant mass distributions. Our results for the high-energy pole agree with
those of the empirical determination of the $\gamma\Lambda$ and
$\gamma\Sigma^0$ radiative widths (based on an isobar model fitting of the
$K^-p$ atom data), which are sometimes referred to as ``experimental data''. We
have made a detailed study of the $K^-p\to\pi^0\gamma\Lambda(\Sigma^0)$ and
$\pi^-p\to K^0\gamma\Lambda(\Sigma^0)$ reactions and have shown that they,
indeed, lead to different shapes for the $\gamma\Lambda(\Sigma^0)$ invariant
mass distributions.

High Energy Physics - Phenomenology