Vector-like Strong Coupling theory with small S and T parameters

We propose a mechanism which can reduce the Peskin and Takeuchi’s S, T and U parameters in dynamical electroweak symmetry breaking models. It is interesting that not only S but also T parameter can become small even if there exists large isospin violation in fermion condensation. For example, when we take the SU(2)L × U(1)Y breaking mass of up-type fermion mU = 1 TeV and that of down-type mD = 0, we get S∼ 0.001N and T∼ 0.05N for the SU(2)L × U(1)Y invariant masses M = 10 TeV. The point is that these parameters are suppressed by SU(2)L × U(1)Y invariant masses which the vector-like fermions can have. Fellow of the Japan Society for the Promotion of Science. ‡ N. Maekawa will be in SLAC in this summer. Dynamical electroweak symmetry breaking is one of the most attractive mechanism which can solve the naturalness problem in the standard model [1]. However recent precision measurements on S and T parameters give these models rather severe constraints [2]. S parameter gives a severe constraint to the number of new SU(2)L doublets, which limits the dynamical models like ‘Walking Technicolor’ [3]. T parameter makes it difficult to break isospin symmetry in dynamical breaking sector [4] in spite of the fact that the Nature has very large isospin violation such as mb/mt << 1. Top condensation [5] is attractive as a point that no new particle exists. But unfortunately it requires strong fine tuning , therefore it does not solve the naturalness problem. If one introduces 4-th generation fermion condensation [6], one should introduce degenerate masses of the 4-th up and down-type quarks, which is not so natural because the Nature has large isospin violation. S, T and U parameters are non-decoupling parameters in terms of SU(2)L ×U(1)Y breaking masses m. On the other hand, they must be suppressed by SU(2)L × U(1)Y invariant masses M in the limit M → ∞ because of decoupling theorem [8]. Therefore even if one introduces new particles which have the SU(2)L × U(1)Y breaking masses m, S, T and U parameters can be reduced if they have also SU(2)L × U(1)Y invariant masses M >> m. By these facts, we can expect that if the condensation of massive vector-like fields ( i.e. they have SU(2)L×U(1)Y invariant masses M ) [9, 10, 11, 12] can break the standard gauge symmetry, S, T and U parameters can become small at least in the limit M >> m. In this paper, we would like to discuss dynamical electroweak symmetry breaking by vector-like fields’ condensation which is induced mainly by 4fermi interactions. First, let us discuss the dynamical symmetry breaking by vector-like fields. Here we introduce 2 pairs of vector-like fields QL,R = (Q U , Q)L,R = (2, Y )L,R and UR,L = (1, Y + 1 2 )R,L, in which the numbers are quantum numbers of SU(2)L and U(1)Y respectively, and L and R represent the chirality. Here we adopt the following lagrangian; L4 = Q̄(iDγμ −MQ)Q+ Ū(iDγμ −MU)U § This is because the T parameter must be made small. In order to decrease the composite scale Λ very heavy top quark is needed [5, 7].