Breaking of isospin symmetry in theories with a dynamical Higgs mechanism.

Abstract

The sensitivity of physical amplitudes to the observed isospin-symmetry breaking in the fermion mass matrix is analyzed in theories where the electroweak symmetry is dynamically broken. As a first step toward discussing dynamical theories in a model-independent way, we consider a strongly interacting Higgs theory. The nonlinear \ensuremath{\sigma} model coupled to an SU(2)\ifmmode\times\else\texttimes\fi{}U(1) Yang-Mills theory and to fermions is used to generate the low-dimensional operators induced by the quantum theory. The strengths of these operators, in particular those that break isospin symmetry, are estimated using the Higgs-boson mass of the linear \ensuremath{\sigma} model as a regulator. Technicolor models are next considered as a specific example of the strong-interaction physics which leads to electroweak symmetry breaking. Emphasis is placed on the effective four-fermion interactions that are natural partners of those which give mass to the ordinary fermions. New sources of isospin-symmetry breaking are found; in particular there is one which contributes directly to the \ensuremath{\rho} parameter with strength that is linear in the effective Yukawa coupling of the heaviest ordinary fermion. This effect is qualitatively different from the quadratic dependence found in Higgs theories.