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We put forward the framework of simplified leptoquark models: simpleextensions of the Standard Model that serve as benchmarks to test theinteractions of leptons with new colored degrees of freedom considered, forinstance, in leptoquark or grand unification models. As a first application ofthe scheme, we analyze the power of precision lepton observables by computinggauge invariant two-loop radiative corrections to the lepton-photon vertex,generated here by Yukawa interactions between the lepton and new coloreddegrees of freedom. The result, detailed in explicit expressions for theinvolved form factors, improves on the literature for the higher loop orderconsidered and highlights the existence of regions in the parameter space ofthe model where two-loop corrections cannot be neglected.

Simplified leptoquark models for precision $l_i \rightarrow l_f \gamma$ experiments: two-loop structure of $O(\alpha_S Y^2)$ corrections