ar X iv : h ep - p h / 02 12 26 2 v 1 1 8 D ec 2 00 2 Interference of Conversion and Bremsstrahlung Amplitudes in the Decay K L → μ + μ − γ

In the region of large μ+μ− invariant mass, the decay spectrum of KL → μ +μ−γ deviates from the Dalitz pair spectrum, as a result of interference between conversion (KL → γ ∗γ → μ+μ−γ) and bremsstrahlung amplitudes. The latter is proportional to the KL → μ +μ− matrix element, whose 2γ-absorptive part appears to dominate the observed KL → μ +μ− decay rate. We examine the extent to which a scrutiny of the KL → μ +μ−γ spectrum in the end-point region could provide evidence on the real part of the KL → μ +μ− amplitude. As a by-product, we obtain the absorptive part of the KL → γ ∗γ form factor, using data on the KL → π +π−γ spectrum. It is customary to interpret the decays KL → e eγ and KL → μ μγ in terms of a Dalitz pair process KL → γ ∗γ → llγ. The branching ratio and the lepton mass spectrum are fitted to an s-dependent KLγ ∗γ vertex fKγγ(s) = fKγγ(0)f(s), where fKγγ(0) is a dimensionless parameter related to the decay width of KL → γγ by |fKγγ(0)| 2 = 64π mK Γ(KL → γγ) (1) and f(s) is a form factor. The spectrum in the invariant mass of the lepton pair (s = (p+ + p−) ) is given by [1] dΓ(KL → l lγ)/ds Γ(KL → γγ) = 2α 3π ( 1− s mK )3 ( 1 + 2ml s )( 1− 4ml s )1/2