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

The radiative decay of $Λ(1405)$ 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 $\bar{K}N (I=0)$ 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 $Λ(1405)$, we observe that the decay to $Λγ$ is dominated by the $K^{-}p$ component inside $Λ(1405)$, because in this decay $π^{+} Σ^{-}$ and $π^{-} Σ^{+}$ strongly cancel each other and the $πΣ$ component can contribute to the $Λγ$ decay only through the slight isospin breaking. This means that the decay $Λ(1405) \to Λγ$ is suitable for the study of the $\bar{K} N$ component in $Λ(1405)$. Fixing the $Λ(1405)$-$πΣ$ coupling constant from the usual decay of $Λ(1405) \to πΣ$, we show a relation between the absolute value of the $\bar{K} N$ compositeness for $Λ(1405)$ and the radiative decay width of $Λ(1405) \to Λγ$ and $Σ^{0} γ$, and we find that large decay width to $Λγ$ implies large $\bar{K}N$ compositeness for $Λ(1405)$. 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 $\bar{K}N$ compositeness for $Λ(1405)$. We also discuss the pole position dependence of our relation on the $Λ(1405)$ radiative decay width and the effects of the two-pole structure for $Λ(1405)$.

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