Determination of compositeness of the Λ(1405) resonance from its radiative decay

The radiative decay of Lambda(1405) is investigated from the viewpoint of compositeness, which corresponds to the amount of two-body states composing resonances as well as bound states. For a (K) over bar N(I = 0) bound state without couplings to other channels, we establish a relation between the radiative decay width and the compositeness. Especially the radiative decay width of the bound state is proportional to the compositeness. Applying the formulation to Lambda(1405), we observe that the decay to Lambda gamma is dominated by the K- p component inside Lambda(1405), because in this decay pi(+)Sigma(-) and pi(-)Sigma(+) strongly cancel each other and the pi Sigma component can contribute to the Lambda gamma decay only through the slight isospin breaking. This means that the decay Lambda(1405) -> Lambda gamma. is suitable for the study of the (K) over bar N component in Lambda(1405). Fixing the Lambda(1405)-pi Sigma coupling constant from the usual decay of Lambda(1405) -> pi Sigma, we show a relation between the absolute value of the (K) over bar N compositeness for Lambda(1405) and the radiative decay width of Lambda(1405) -> Lambda gamma and Sigma(0)gamma, and we find that large decay width to Lambda gamma. implies large (K) over bar N compositeness for Lambda(1405). By using the "experimental" data on the radiative decay widths, which is based on an isobar model fitting of the K- p atom data, we estimate the (K) over bar N compositeness for Lambda(1405). We also discuss the pole position dependence of our relation on the Lambda(1405) radiative decay width and the effects of the two-pole structure for Lambda(1405).