Lepton flavour violation in composite Higgs models

We discuss in detail the constraints on the partial compositeness coming from flavour and CP violation in the leptonic sector. In the first part we present a formulation of partial compositeness in terms of a flavour symmetry group and a set of spurions, whose background values specify the symmetry breaking pattern. In such a framework we construct the complete set of dimension-six operators describing lepton flavour violation and CP violation. By exploiting the existing bounds, we derive limits on the compositeness scale in different scenarios, characterised by increasing restrictions on the spurion properties. We confirm that in the most general case the compositeness scale should lie well above 10 TeV. However, if in the composite sector the mass parameters and Yukawa couplings are universal, such a bound can be significantly lowered, without necessarily reproducing the case of minimal flavour violation. The most sensitive processes are decays of charged leptons either of radiative type or into three charged leptons, [Formula: see text] conversion in nuclei and the electric dipole moment of the electron. In the second part we explicitly compute the Wilson coefficients of the relevant dimension-six operators in the so-called two-site model, embodying the symmetry breaking pattern discussed in our first part, and we compare the results with those of the general spurion analysis.