Model independent constraints on leptoquarks from MU and TAU lepton rare processes

We perform a model independent analysis so as to constrain the leptoquark (LQ) models from negative searches for $\mu \to e \gamma$, $\mu \to 3e$ decays (and analogous processes in the $\tau$ sector), and coherent $\mu-e$ conversion in nuclei. We considerably improve some constraints obtained by analyses known in the literature, analyses which we show have by far underestimated the LQ contributions to the $\mu\to 3e$. In particular we find that the coherent $\mu-e$ conversion in nuclei mediated by the photon--conversion mechanism and the $\mu \to 3e$ decay are golden plates where the flavor changing leptoquark couplings, involving the second and third quark generations, can be strongly constrained. This is due to the fact that these processes get the enhancements by large $\log(m_q^2/m^2_{LQ})$ terms which are induced by the so-called ``photon-penguin'' diagrams. These enhancements, which produce a mild GIM suppression in the amplitudes, have not been taken into account in the previous analyses. We show that the $\mu \to e \gamma$ decay can set weaker constraints on the LQ models and this is because its amplitude is strongly GIM suppressed by the terms of order $O(m_q^2/m^2_{LQ})$. We also present the results for the corresponding constraints in the $\tau$ sector. Finally the prospects of the future muon experiments for the improvement of the present bounds are analyzed and discussed.