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

The radiative decay of $\mathrm{\Lambda }(1405)$ 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 $\mathrm{\Lambda }(1405)$, we observe that the decay to $\mathrm{\Lambda }\gamma$ is dominated by the $K^{-}p$ component inside $\mathrm{\Lambda }(1405)$, because in this decay $\pi ^{+} \Sigma ^{-}$and$\pi ^{-} \Sigma ^{+}$stronglycanceleachotherandthe$\pi \Sigma$componentcancontributetothe$\Lambda \gamma$ decay only through the slight isospin breaking. This means that the decay $\Lambda (1405) \to \Lambda \gamma$issuitableforthestudyofthe$\bar{K} N$componentin$\Lambda (1405)$\mathrm{.}Fixingthe$\Lambda (1405)$-$\pi \Sigma$ coupling constant from the usual decay of $\mathrm{\Lambda }(1405)\to \pi \mathrm{\Sigma }$, we show a relation between the absolute value of the $\bar{K}N$ compositeness for $\mathrm{\Lambda }(1405)$ and the radiative decay width of $\mathrm{\Lambda }(1405)\to \mathrm{\Lambda }\gamma$ and $\Sigma ^{0} \gamma$,andwefindthatlargedecaywidthto$\Lambda \gamma$implieslarge$\bar{K}N$compositenessfor$\Lambda (1405)$. 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 $\Lambda (1405)$\mathrm{.}Wealsodiscussthepolepositiondependenceofourrelationonthe$\Lambda (1405)$ radiative decay width and the effects of the two-pole structure for $\mathrm{\Lambda }(1405)$.