Anarchy with linear and bilinear interactions

Composite Higgs models with anarchic partial compositeness require a scale of new physics ${\cal O}(10-100)$ TeV, with the bounds being dominated by the dipole moments and $\epsilon_K$. The presence of anarchic bilinear interactions can change this picture. We show a solution to the SM flavor puzzle where the electron and the Right-handed quarks of the first generation have negligible linear interactions, and the bilinear interactions account for most of their masses, whereas the other chiral fermions follow a similar pattern to anarchic partial compositeness. We compute the bounds from flavor and CP violation and show that neutron and electron dipole moments, as well as $\epsilon_K$ and $\mu\to e\gamma$, are compatible with a new physics scale below the TeV. $\Delta F=2$ operators involving Left-handed quarks and $\Delta F=1$ operators with $d_L$ give the most stringent bounds in this scenario. Their Wilson coefficients have the same origin as in anarchic partial compositeness, requiring the masses of the new states to be larger than ${\cal O}(6-7)$ TeV.