Constraining walking and custodial technicolor

Abstract

We show how to constrain the physical spectrum of walking technicolor models via precision measurements and modified Weinberg sum rules. We also study models possessing a custodial symmetry for the S parameter at the effective Lagrangian level -custodial technicolor -and argue that these models cannot emerge from walking type dynamics. We suggest that it is possible to have a very light spin-one axial vector boson. However, in the walking dynamics the associated vector boson is heavy while it is degenerate with the axial in custodial technicolor.Walking Technicolor (WT) is one of the major frameworks for constructing natural models able to break the electroweak symmetry dynamically [1,2,3,4]. It is hence important to show how to constrain phenomenologically these models using field theoretical tools, a general effective Lagrangian and the LEP data. WT makes use of near conformal dynamics. Hints of such dynamics were observed in [5] for minimal walking technicolor (MWT) theories [6,7]. The phase diagram of strongly coupled theories as function of number of colors, flavors and matter representation has been studied using the all-order (non)supersymmetric beta function in [8,9] as well as the truncated Schwinger-Dyson Equation [7]. All the analysis point to the existence of a critical number of flavors above which asymptotically free gauge theories develop an infrared stable fixed point.A comprehensive low energy Lagrangian describing MWT has been constructed in [10]. It incorporates the knowledge of the underlying gauge theory via dispersion relations. More phenomenological approaches simply assume the existence of an underlying dynamics of WT type [11] and then guess the spectrum of the lightest resonances and couplings. We will show that when WT dynamics is taken into account, via the modified Weinberg sum rules (WSR) [12,13] together with the LEP constraints [14,15,16,17,18] it allows us to relate the spectrum of spin-one resonances with their couplings to the weak gauge bosons. We will argue that it is not possible, within walking dynamics with a small S parameter [14], to achieve the spectrum proposed in [11] and suggest what kind of strongly coupled dynamics can accommodate instead a degenerate and very light vector spectrum not at odds with precision measurements.We start from the observation that although WT theories are near an infrared stable fixed point, they develop the Fermi scale nonperturbatively. This implies a well defined low energy spectrum with the lightest resonances affecting directly the electroweak observables. This fact does not mean that the heavier resonances, or more generally the walking dynamics, is not relevant. Via dispersion relations the entire spectrum of the underlying theory will still affect the spectrum and couplings of the lightest ones. Our low energy spectrum consists of the lightest spin-one resonances, besides the Goldstones. The effect of walking on the lightest spin-one resonances is modeled via modified WSRs [12,13]. The three basic ingredients we use are: i) Asymptot...

Unnatural origin of fermion masses for technicolor

“…These new findings are compatible with the conjectured form of the beta function proposed in [7,8]; for recent extensions, see [11]. The models with higher representation matter fields have been shown to be compatible with the current precision data [5,14,15]. Their phenomenological implications for LHC experiments [16,17,18,19,20,21] as well as for cosmology [22,23,24] are being investigated.…”

Electroweak phase transition in nearly conformal technicolor

“…The effective theory contains composite scalars and spin-one vectors. Compatibility between the electroweak precision constraints and tree-level unitarity of W W -scattering was demonstrated in [64].…”

“…A key realization that enabled further progress was that gauge theories with fermions in two-index (symmetric or adjoint) representations of the underlying gauge group have interesting features [26,27,28,29,36], such as the possibility of the existence of a nonperturbative infrared fixed point for a very low number of flavors [26], naturally reducing the tension with precision data [26,36,37,38]. These properties make them intriguing candidates for walking technicolor type models [26,36] (related studies can be found in [39]).…”

“…The study of longitudinal WW scattering unitarity versus precision measurements within the effective Lagrangian approach demonstrated that it is possible to pass the precision tests while simultaneously delaying the onset of unitarity [64].…”

The effect of composite resonances on Higgs decay into two photons

“…In this regard, it is important to explore the consequences of this new constraint on composite models, in conjunction with those previously known from electroweak precision measurements. Given the recent evidence of the Higgs boson, a strongly interacting sector that is phenomenologically viable nowadays should include this scalar boson in its low energy spectrum, but it is also assumed that vector and axial-vector resonances should appear as well, in a way that the so called Weinberg sum rules [6] are satisfied [7][8][9].…”