Electroweak chiral Lagrangian from one-doublet and topcolor-assisted technicolor models

Abstract

Based on previous studies deriving the chiral Lagrangian for pseudoscalar mesons from the first principle of QCD, we derive an electroweak chiral Lagrangian and build up a formulation for computing its coefficients from a one-doublet technicolor model and a schematic topcolor-assisted technicolor model. We find that coefficients of the electroweak chiral Lagrangian for the topcolor-assisted technicolor model are divided into three parts: direct TC2 interaction part, TC1 and TC2 induced effective ${Z}^{\ensuremath{'}}$ particle contribution part, and ordinary quarks contribution part. The first two parts are computed in this paper. We show that the direct TC2 interaction part is the same as that in the one-doublet technicolor model, while effective ${Z}^{\ensuremath{'}}$ contributions are at least proportional to the ${p}^{2}$ order parameter ${\ensuremath{\beta}}_{1}$ in the electroweak chiral Lagrangian. Typical features of the topcolor-assisted technicolor model are that it only allows positive $T$ and $U$ parameters, the $T$ parameter varies in the range $0\ensuremath{\sim}1/(25\ensuremath{\alpha})$, and the upper bound of $T$ parameter will decrease as long as ${Z}^{\ensuremath{'}}$ mass become large. The $S$ parameter can be either positive or negative depending on whether the ${Z}^{\ensuremath{'}}$ mass is large or small. The ${Z}^{\ensuremath{'}}$ mass is bounded above and the upper bound depends on the value of the $T$ parameter. We obtain the values for all coefficients of the electroweak chiral Lagrangian up to the order of ${p}^{4}$.