Interference of Conversion and Bremsstrahlung Amplitudes in the Decay K_L -> mu^+ mu^- gamma

In the region of large mu^+ mu^- invariant mass, the decay spectrum of K_L -> mu^+ mu^- gamma deviates from the Dalitz pair spectrum, as a result of interference between conversion (K_L -> gamma^* gamma -> mu^+ mu^- gamma) and bremsstrahlung amplitudes. The latter is proportional to the K_L -> mu^+ mu^- matrix element, whose 2 gamma-absorptive part appears to dominate the observed K_L -> mu^+ mu^- decay rate. We examine the extent to which a scrutiny of the K_L -> mu^+ mu^- gamma spectrum in the end-point region could provide evidence on the real part of the K_L -> mu^+ mu^- amplitude. As a by-product, we obtain the absorptive part of the K_L -> gamma^* gamma form factor, using data on the K_L -> pi^+ pi^- gamma spectrum.