The Oblique and Non-Oblique Corrections in Technicolor Model without Exact Custodial Symmetry

Abstract

We study the possibility whether the technicolor model can satisfy the constraints of the oblique corrections and non-oblique correction at once. To avoid the difficulty for the explanation of the present data of the oblique corrections, the model without exact custodial symmetry was proposed by Appelquist and Terning. We construct the effective lagrangian for the technicolor model and calculate the oblique correction by using the effective lagrangian approach. For the non-oblique correction, the effects of diagonal extended technicolor inter­ action was studied by Wu. We study the effect of the diagonal extended technicolor (ETC) interaction on the oblique parameters. It is shown that the T parameter is unacceptably large when the Zbb vertex correction is consistent with the experiments in the ETC model. The oblique corrections, S and T parameters, severely put constraint on QCD­ like technicolor models and the present data shows that the models cannot satisfy the constraints. l) In the QCD-like model, S is about 0.1 X Ndoublet x Nrc > 0 and T vanishes because of exact custodial symmetry (chiral symmetry SU(Nd)L®SU(Nd)R)· However, S parameter that has been obtained from many experimental data is negative. From the recently experimental data, 1-family technicolor model(Nd = 8) is completely ruled out and !-doublet model may be also. Accordingly, we need to modify the technicolor model to satisfy the constraints of the oblique parameters. It is shown that if these models have the splitting of the masses between up-type and down-type particles (isospin breaking), they may be able to satisfy the constraints from oblique correction S by considering one-loop approximation. In Ref. 2) Appelquist and Terning show that the one-family technicolor model with isospin breaking in technilepton sector. This model has the following features. (1) isospin breaking oftechnilepton doublet, (2) the existence of two scales. Because of the feature (1) S is reduced and because of (2) T is also reduced. In our work, 3 ) we construct the effective lagrangian on this technicolor model without exact custodial symmetry and calculate the oblique corrections by considering the effects of the (axial)vectormeson that are composed by the technifermions. While, for the vertex corrections of Zbb, which is called non-oblique correction, there is the discrepancy between the prediction of the standard model (SM) and the experimental data at LEP. The experimental value Rb = 0.2202 ± 0.0020 was different from the value R~M = 0.2157 predicted by SM with top quark mass mt = 175 GeV. In the extended technicolor model (ETC), the contribution from sideways ETC interaction was first studied by the authors of Ref. 4). However, this discrepancy could not be explained by the effects of the sideways ETC interaction. The discrepancy becomes