$\Delta F=1$ constraints on composite Higgs models with LR parity

Abstract

We analyze the bounds on the spectrum of composite Higgs models (CHM) that come from flavor observables, by means of simple two-site effective Lagrangians, which incorporate a custodial symmetry and a Left-Right parity and which could also be adopted in further phenomenological studies on CHM. We derive, in particular, an important constraint on the masses of the $(t_L, b_L)$ partners, which does not depend on the flavor structure of the sector beyond the SM. This bound is obtained from the "infrared" contribution to $b \to s\gamma$ induced by the flavor-conserving effective vertex $Wt_Rb_R$. We find that the presence of a custodial symmetry can play a role in protecting this effective coupling and, as a consequence, in attenuating the constraint, which, however, remains of the order of 1 TeV. In addition to this bound, we calculate the constraints from the "ultraviolet" contribution to $b \to s \gamma$, induced by loops of heavy fermions, and to $\epsilon^{'}/\epsilon_K$.