The radiative decay of the $Λ(1405)$ and its two-pole structure

Abstract

We evaluate theoretically the radiative decay widths into $γΛ$ and $γΣ^0$ of the two poles of the $Λ(1405)$ 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 $Λ(1405)$ radiative decays, one gives more weight to one or the other pole, resulting in quite different shapes in the $γΛ(Σ^0)$ invariant mass distributions. Our results for the high-energy pole agree with those of the empirical determination of the $γΛ$ and $γΣ^0$ 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 $K^-p\toπ^0γΛ(Σ^0)$ and $π^-p\to K^0γΛ(Σ^0)$ reactions and have shown that they, indeed, lead to different shapes for the $γΛ(Σ^0)$ invariant mass distributions.