Restricting q2l2 operators from charged lepton flavour violation

In this paper, we consider dimension-6 semileptonic lepton flavor violating operators with two quarks and two leptons of the type [Formula: see text] within low-energy effective theory (LEFT). At the chiral scale, we match these operators to chiral perturbation theory ([Formula: see text]PT) and place constraints from the neutral pion and kaon decays to [Formula: see text] ([Formula: see text] and [Formula: see text]). These bounds are indeed shown to be depended on the chiral nature of the operators. The scalar operators are significantly more constrained compared to the vector operators. We then compare the limits from [Formula: see text] conversion in Nuclei and show that the dominant constraint on scalar operators arises from kaon decay and they are an order of magnitude stronger than the corresponding limits from [Formula: see text] conversion in Ti. On the other hand, the limits on vector operators from [Formula: see text] conversion process are stronger than the ones obtained from the pion and kaon decays. Toward the end, we match these LEFT operators to the Standard Model effective field theory (SMEFT) operators, at W-boson mass scale and further to relevant leptoquark models at tree-level. We, then, derive the constraints on the parameter space of the leptoquarks using the obtained results.