Two-Pion Intermediate States in the DecayKS0→2γ

The unitarity relations for the two-pion intermediate state in the decay $K_S^0\to 2\gamma$ are solved using a recently derived form for the amplitude for the process $2\gamma \to 2\pi$, which keeps the exact one-pion-exchange contribution but neglects the left-hand cut and inelastic cuts in the $\pi -\pi$ scattering amplitude. The resulting amplitude shows no direct enhancement of the decay rate from strong interactions, and the rate could be zero if the cross section for $2\gamma \to 2\pi$ were zero at the $K$ mass. A plausible choice of the amplitude for $2\gamma \to 2\pi$ gives a contribution which has exactly the magnitude that would be calculated using perturbation theory for pointlike pions with no strong interactions, but is shifted by the $\pi -\pi$ scattering phase leading to a unitarity lower bound that is smaller by about a factor of two.