Mass enhancement and critical behavior in technicolor theories.

Quark and lepton masses in technicolor theories can be enhanced if the high energy, extended technicolor (ETC) interactions play an important role in electroweak symmetry breaking. This happens when the ETC coupling and the technicolor gauge coupling at high energies lie close to a certain critical line. The enhancement has been associated with the existence of composite scalars made mainly of technifermions, with masses small compared to the ETC scale. The initial study of these states was carried out with the technicolor gauge coupling neglected. In this paper we investigate the properties of such scalars including the technicolor gauge interactions. We find that for realistic values of the gauge coupling, the scalars will not be narrow resonances. The recent revival of interest in technicolor theories of electroweak symmetry breaking has been stimulated partly by the observation that momentum components well above the confinement scale Λtc can play a more important role than they do in QCD. In particular the higher energy extended technicolor (ETC) interactions, which must be present to generate the masses of ordinary fermions, can play an important direct role, along with the technicolor interactions, in the electroweak breaking, leading to even larger fermion masses. This can take place only if the combination of the ETC coupling and the technicolor coupling at the ETC scale is sufficiently close to a certain critical curve. Here we summarize a study of the light composite scalars generated by near-critical high energy interactions. We conclude that unless the technicolor coupling at the ETC scale is unrealistically weak and the ETC coupling is very close to the critical curve, these light states will have large widths. We consider a single doublet of technifermions Ψ = (U,D) subject to a confining technicolor force and an additional attractive ETC interaction. The latter is approxi∗Presented by John Terning mated by an effective, SU(2)L × U(1) invariant, four-fermion coupling L4f = 8πλ NtcΛ (Ψ̄LUR)(ŪRΨ i L) , (1) where i is a summed SU(2)L index,Ntc is the number of technicolors, Λ is the ETC mass scale, and λ is the interaction strength of the ETC interactions. Implicit technicolor indices are also summed in each fermion bilinear. We begin by recalling some features of dynamical chiral symmetry breaking driven by the combination of gauge and four-fermion interactions. Suppose that the physics of interest takes place at energies well above the confinement scale Λtc. It should be possible to describe this physics in terms of λ and α ≡ α(Λ) (the technicolor coupling at the ETC scale). With the running of α neglected, dynamical mass generation can be studied in linearized ladder approximation. Analysis of the gap equation for the dynamical mass Σ(p) of the U fermion in the α, λ plane reveals that a critical curve separates the broken phase (Σ 6= 0) from the symmetric phase (Σ = 0). For λ ≤ 1/4, the broken phase exists only for α > αc ≡ π/3C2(R), where C2(R) is the Casimir of the fermion representation. For λ ≥ 1/4, the critical curve separating the two phases is defined by