Electromagnetic contribution to the lepton-pair decay of the K10 meson

If we assume that there is no anomalously large CP-violating K_S⁰→μ⁺μ⁻ decay mode, then a possible conflict with a unitarity bound could arise similar to the present situation with K_L⁰→μ⁺μ⁻. It is therefore important to have a reliable estimate of the electromagnetic contribution for K_S⁰→μ⁺μ⁻. In this paper, we assume CP invariance (so K_S⁰≡K₁⁰) and give the results of a detailed calculation of both the real and imaginary parts of the K₁⁰→μ⁺μ⁻ amplitude based on contributions from 2γ, π⁺π⁻, and π⁺π⁻γ states.