Can we extract short-distance information from B(K_L -> mu^+ mu^-)?

A new analysis of the long-distance two-photon dispersive amplitude of K_L -> mu^+ mu^- is presented. We introduce a phenomenological parameterization of the K_L -> gamma^* gamma^* form factor, constrained at low energies by K_L -> gamma l^+ l^- (l = e,mu) data and at high energies by perturbative QCD. Using this form factor we provide a reliable estimate of magnitude and relative uncertainty of the two-photon dispersive contribution to K_L -> mu^+ mu^-. We finally discuss the implications of this analysis for the extraction of short-distance information from B(K_L -> mu^+ mu^-).