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 $\Lambda (1405)$.

13 pages, 7 figures; Added references; version accepted for publication in Phys. Rev. C

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• Compositeness of baryonic resonances: Applications to the Delta(1232), N(1535), and N(1650) resonances
• Light-quark contributions to the magnetic form factor of the Lambda(1405)
• Compositeness of $T_{cc}$ and $X(3872)$ by considering decay and coupled-channels effects
• Constituent-counting rule in photoproduction of hyperon resonances
• Singlet baryons in the graded symmetry approach to partially quenched QCD
• Determining Compositeness of Hadronic Resonances: the $\Lambda (1405)$ Radiative Decay and the $a_0(980)$-$f_0(980)$ Mixing
• Exotic hadron production in hard exclusive reactions
• Hadron tomography studies by generalized parton distributions and distribution amplitudes
• Compositeness of Hadrons and Near-Threshold Dynamics
• Internal structure of exotic hadrons by high-energy exclusive reactions