Preprint number: CP3-Origins-2015-35 DNRF90 and DIAS-2015-35
We construct effective Lagrangians, and corresponding counting schemes, valid to describe the dynamics of the lowest lying large N stable massive composite state emerging in strongly coupled theories. The large N counting rules can now be employed when computing quantum corrections via the effective Lagrangian. The framework allows for systematic investigations of composite dynamics of non-Goldstone nature. Relevant examples are
the lightest glueball state emerging in any Yang-Mills theory. We further apply the effective approach to composite models at the electroweak scale. To illustrate the formalism we consider: the possibility that the Higgs emerges as the lightest glueball of a new composite theory; as a large N scalar meson in models of dynamical electroweak symmetry breaking, and finally we consider it to be a large N pseudodilaton useful also for models of near-conformal dynamics. For each of these realisations we determine the leading N corrections to the electroweak precision parameters. The results nicely elucidate the underlying large N dynamics and can be confronted with first principle lattice simulations.