Model-independent constraints on leptoquarks from rare $\mu$ and $\tau$ lepton processes

We perform a model-independent analysis so as to constrain the leptoquark (LQ) models from negative searches for $\overrightarrow{\mu }e\gamma ,$ $\overrightarrow{\mu }3e$ 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 $\overrightarrow{\mu }3e.$ In particular we find that the coherent $\mu -e$ conversion in nuclei mediated by the photon-conversion mechanism and the $\overrightarrow{\mu }3e$ 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 $\log {(m}_q^2{/m}_{\mathrm{LQ}}^2)$ terms which are induced by the so-called “photon-penguin” diagrams. These enhancements, which produce a mild Glashow-Iliopoulos-Maiani (GIM) suppression in the amplitudes, have not been taken into account in the previous analyses. We show that the $\overrightarrow{\mu }e\gamma$ decay can set weaker constraints on the LQ models and this is because its amplitude is strongly GIM suppressed by the terms of order ${O(m}_q^2{/m}_{\mathrm{LQ}}^2).\mathrm{}$ We also present the results for the corresponding constraints in the τ sector. Finally, the prospects of the future muon experiments for the improvement of the present bounds are analyzed and discussed.