Learning about flavour structure from tau to ell gamma and mu to e gamma?

Current and upcoming experiments should improve the sensitivity to radiative lepton decays by an order of magnitude. This paper assumes that one of the tau --> (e, mu) gamma decays is observed, and explores the structure and consequences of the required new flavoured couplings. In simple models (a low-scale seesaw, leptoquarks) it is shown that the dipole vertex function is proportional to a product of flavoured matrices from the Lagrangian (a "Jarlskog-like" invariant), provided that the loop particles are weakly coupled to the Higgs. Secondly, if the dipole vertex function has a hierarchical structure, this can imply that only some of the tau --> (e, mu) gamma modes can be observed, due to the "approximate zero" implied by the bound on mu --> e gamma. The assumptions underlying this potential test of a hierarchical structure are discussed.