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Based on previous studies deriving the chiral Lagrangian for pseudo scalarmesons from the first principle of QCD, we derive the electroweak chiralLagrangian and build up a formulation for computing its coefficients fromone-doublet technicolor model and a schematic topcolor-assisted technicolormodel. We find that the coefficients of the electroweak chiral Lagrangian forthe topcolor-assisted technicolor model are divided into three parts: directTC2 interaction part, TC1 and TC2 induced effective Z' particle contributionpart, and ordinary quarks contribution part. The first two parts are computedin this paper and we show that the direct TC2 interaction part is the same asthat in the one-doublet technicolor model, while effective Z' contributions areat least proportional to the p^2 order parameter \beta_1 in the electroweakchiral Lagrangian and typical features of topcolor-assisted technicolor modelare that it only allows positive T and U parameters and the T parameter variesin the range 0\sim 1/(25\alpha), the upper bound of T parameter will decreaseas long as Z' mass become large. The S parameter can be either positive ornegative depending on whether the Z' mass is large or small. The Z' mass isalso bounded above and the upper bound depend on value of T parameter. Weobtain the values for all the coefficients of the electroweak chiral Lagrangianup to order of p^4.

Dynamical Computation on Coefficients of Electroweak Chiral Lagrangian from One-doublet and Topcolor-assisted Technicolor Models