The radiative decay of $\Lambda \left(1405\right)$ 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 $\overline{K}N(I=0)$ 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 $\Lambda \left(1405\right)$, we observe that the decay to $\Lambda \gamma$ is dominated by the $K^{-}p$ component inside $\Lambda \left(1405\right)$, 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 $\Lambda \left(1405\right)\to \Lambda \gamma$ is suitable for the study of the $\overline{K}N$ component in $\Lambda \left(1405\right)$. Fixing the $\Lambda \left(1405\right)$-$\pi \Sigma$ coupling constant from the usual decay of $\Lambda \left(1405\right)\to \pi \Sigma$, we show a relation between the absolute value of the $\overline{K}N$ compositeness for $\Lambda \left(1405\right)$ and the radiative decay width of $\Lambda \left(1405\right)\to \Lambda \gamma$ and ${\Sigma }^0\gamma$, and we find that large decay width to $\Lambda \gamma$ implies large $\overline{K}N$ compositeness for $\Lambda \left(1405\right)$. 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 $\overline{K}N$ compositeness for $\Lambda \left(1405\right)$. We also discuss the pole position dependence of our relation on the $\Lambda \left(1405\right)$ radiative decay width and the effects of the two-pole structure for $\Lambda \left(1405\right)$.

• Received 22 November 2013

DOI:https://doi.org/10.1103/PhysRevC.89.025202