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In this paper we consider semileptonic lepton flavor violating operators ofthe type $q^2l^2$ in low energy effective theory (LEFT). At the chiral scale,we match these operators to chiral perturbation theory ($\chi$PT) and placeconstraints from the process $\pi^0\rightarrow \mu^+ \,\, e^-$. These boundsare shown to depend on the chiral nature of the operators. The scalar operatorsare significantly more constrained compared to the vector operators. We thencompare the limits from $\mu \to e$ conversion in Nuclei and show that thelimits on scalar operators are within an order of magnitude of thecorresponding limits from $\mu \to e$ conversion in Ti. On the other hand, thelimits on vector operators are however much weaker. Towards the end, we evolvethe LEFT operators to W-boson mass scale using RGE, and match them to theStandard Model effective field theory (SMEFT) operators. We, then, derive theconstraints on the parameter space of Leptoquark models that could generatethese SMEFT operators at tree level.

Restricting $q^2 l^2$ operators from $\pi^0 \rightarrow \mu e$