Eur. Phys. J. C 23, 113-120 (2002)
https://doi.org/10.1007/s100520100853

Extracting the CP-conserving and CP-violating form factors of K_L → γγ, K_S → γγ, and π⁰ → γγ from the decays of K_L, K_S and π⁰ into two identical pairs of leptons

Department of Physics, Millersville University, Millersville, PA 17551, USA

Received: 11 September 2001
Published online: 14 December 2001

Abstract

The extractions of the CP-conserving and CP-violating form factors of the decays of the long-lived kaon K_L and the short-lived kaon K_S into two photons from the branching ratios of K_SL → γγ and K_SL → γγ → l^-l⁺l^-l⁺, where l represents either an electron or a muon, are described. Using the currently available measurements of the branching ratios of K_L → γγ and K_L → e^-e⁺e^-e⁺ and assuming that the form factors are constants, the ratio of the CP-violating decay rate to the CP-conserving decay rate for K_L → γγ is calculated to be 2.51% and the predicted branching ratio for K_L → γγ → μ^- μ⁺ μ^- μ⁺ is 6.07 × 10^-13. For K_S → γγ, a measurement of the branching ratio of K_S → γγ → e^-e⁺e^-e⁺ is needed to determine the ratio of the CP-violating decay rate to the CP-conserving decay rate and to accurately predict the branching ratio of K_S → γγ → μ^- μ⁺ μ^- μ⁺. In the limit of complete CP-conservation the branching ratios are evaluated to be 4.39 × 10^-10 for K_S → γγ → e^-e⁺e^-e⁺ and 6.96 × 10^-15 for K_S → γγ → μ^- μ⁺ μ^- μ⁺. In a similar model where the form factors of π⁰γγ vertex are constants, the CP-violating decay rate component in π⁰ → γγ is shown, based on current available experimental data, to be less than 1% of the total decay rate.The magnitudes of the form factors are obtained by correlating the processes π⁰ → γγ and π⁰ → γγ → e^-e⁺e^-e⁺.