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

Abstract: 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 $\bar{K}N (I=0)$ 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 $\Lambda (1405)$, 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 $\Lambda (1405) \to \Lambda \gamma$ is suitable for the study of the $\bar{K} N$ component in $\Lambda (1405)$. Fixing the $\Lambda (1405)$-$\pi \Sigma$ coupling constant from the usual decay of $\Lambda (1405) \to \pi \Sigma$, we show a relation between the absolute value of the $\bar{K} N$ compositeness for $\Lambda (1405)$ and the radiative decay width of $\Lambda (1405) \to \Lambda \gamma$ and $\Sigma ^{0} \gamma$, and we find that large decay width to $\Lambda \gamma$ implies large $\bar{K}N$ 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 $\bar{K}N$ 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 $\Lambda (1405)$.