Effective Lagrangian for near-critical technicolor and extended technicolor

At energies small compared to the extended technicolor scale Λ but large compared to the technicolor (TC) scale $A_{TC}$, the light composite scalars generated by the near critical high-energy interactions play an important role in the effective dynamics. In this article we construct the effective Lagrangian of such finely tuned high-energy interactions in terms of these composite scalars. In order to construct $L_{eff}$ we shall use the renormalization group technique to integrate out the high-momentum modes of the technifermions and technigluons. The effect of the running of the TC gauge coupling on the effective dynamics will be taken into account in the weak perturbative limit. We find that for realistic values of $\alpha$ the scalars are relatively broad resonances and for large enough values of $\alpha$ the interaction Lagrangian differs significantly from the canonical $k(\phi^+\phi)^2$ form where κ is the coupling constant for the four-scalar vertex