Coleman-Weinberg Symmetry Breaking Research Articles

Transformation of scalar couplings between Coleman-Weinberg and MS schemes

The Coleman-Weinberg (CW) renormalization scheme for renormalization-group improvement of the effective potential is particularly valuable for CW symmetry-breaking mechanisms (including the challenging case of models with multiple scalar fields). CW mechanism is typically studied using models with classical scale invariance which not only provide a possibility for an alternative symmetry breaking mechanism but also partially address the gauge hierarchies through dimensional transmutation. As outlined in our discussion section, when the couplings are not large, models with CW symmetry-breaking mechanisms have also been shown to naturally provide the strong first-order phase transition necessary for stochastic gravitational wave signals. A full understanding of the CW-MS scheme transformation of couplings thus becomes important in the era of gravitational wave detection and precision coupling measurements. A generalized Coleman-Weinberg (GCW) renormalization scheme is formulated and methods for transforming scalar self-couplings between the GCW and MS (minimal-subtraction) renormalization schemes are developed. Scalar $\ensuremath{\lambda}{\mathrm{\ensuremath{\Phi}}}^{4}$ theory with global $O(4)$ symmetry is explicitly studied up to six-loop order to explore the magnitude of this scheme transformation effect on the couplings. The dynamical rescaling of renormalization scales between the GCW and MS schemes can lead to significant (order of 10%) differences in the coupling at any order, and consequently GCW-MS scheme transformation effects must be considered within precision determinations of scalar couplings in extensions of the Standard Model.

Conformality Loss, Walking, and 4D Complex Conformal Field Theories at Weak Coupling.

Four-dimensional gauge theories with matter can have regions in parameter space, often dubbed conformal windows, where they flow in the infrared to nontrivial conformal field theories. It has been conjectured that conformality can be lost because of merging of two nearby fixed points that move into the complex plane, and that a walking dynamics governed by scaling dimensions of operators defined at such complex fixed points can occur. We find controlled, parametrically weakly coupled, and ultraviolet-complete 4D gauge theories that explicitly realize this scenario. We show how the walking dynamics is controlled by the coupling of a double-trace operator that crosses marginality. The walking regime ends when the renormalization group flow of this coupling leads to a (weak) first-order phase transition with Coleman-Weinberg symmetry breaking. A light dilatonlike scalar particle appears in the spectrum, but it is not parametrically lighter than the other excitations.

Coleman–Weinberg symmetry breaking in SU(8) induced by a third rank antisymmetric tensor scalar field II: the fermion spectrum

We continue our study of Coleman–Weinberg symmetry breaking induced by a third rank antisymmetric tensor scalar, in the context of the SU(8) model (Adler 2014 Int. J. Mod. Phys. A 29 1450130) we proposed earlier. We focus in this paper on qualitative features that will determine whether the model can make contact with the observed particle spectrum. We discuss the mechanism for giving the spin field a mass by the BEH mechanism, and analyze the remaining massless spin fermions, the global chiral symmetries, and the running couplings after symmetry breaking. We note that the smallest gluon mass matrix eigenvalue has an eigenvector suggestive of U(1)B−L, and conjecture that the theory runs to an infrared fixed point at which there is a massless gluon with 3 to −1 ratios in generator components. Assuming this, we discuss a mechanism for making contact with the standard model, based on a conjectured asymmetric breaking of Sp(4) to SU(2) subgroups, one of which is the electroweak SU(2), and the other of which is a ‘technicolor’ group that binds the original SU(8) model fermions, which play the role of ‘preons’, into composites. Quarks can emerge as 5 preon composites and leptons as 3 preon composites, with consequent stability of the proton against decay to a single lepton plus a meson. A composite Higgs boson can emerge as a two preon composite. Since anomaly matching for the relevant conserved global symmetry current is not obeyed by three fermion families, emergence of three composite families requires formation of a Goldstone boson with quantum numbers matching this current, which can be a light dark matter candidate.

Coleman–Weinberg symmetry breaking in SU(8) induced by a third rank antisymmetric tensor scalar field

We study SU(8) symmetry breaking induced by minimizing the Coleman–Weinberg effective potential for a third rank antisymmetric tensor scalar field in the 56 representation. Instead of breaking , we find that the stable minimum of the potential breaks the original symmetry according to . Using both numerical and analytical methods, we present results for the potential minimum, the corresponding Goldstone boson structure and BEH mechanism, and the group-theoretic classification of the residual states after symmetry breaking.

Radiative symmetry breaking of the minimal left-right symmetric model

Under the assumption of classical conformal invariance, we study the Coleman-Weinberg symmetry breaking mechanism in the minimal left-right symmetric model. This model is attractive as it provides a natural framework for small neutrino masses and the restoration of parity as a good symmetry of nature. We find that, in a large fraction of the parameter space, the parity symmetry is maximally broken by quantum corrections in the Coleman-Weinberg potential, which are a consequence of the conformal anomaly. As the left-right symmetry breaking scale is connected to the Planck scale through the logarithmic running of the dimensionless couplings of the scalar potential, a large separation of the two scales can be dynamically generated. The symmetry breaking dynamics of the model was studied using a renormalization group analysis. Electroweak symmetry breaking is triggered by the breakdown of left-right symmetry, and the left-right breaking scale is therefore expected in the few TeV range. The phenomenological implications of the symmetry breaking mechanism are discussed.

Coleman-Weinberg phase transition in extended Higgs models.

In Coleman-Weinberg symmetry breaking, all dimensionful parameters vanish and the symmetry is broken by loop corrections. Before Coleman-Weinberg symmetry breaking in the standard model was experimentally ruled out, it had already been excluded on cosmological grounds. In this Brief Report, the cosmological analysis is carried out for Coleman-Weinberg models with extended Higgs sectors, which are not experimentally ruled out, and general constraints on such models are given.

Calculating the critical temperature for Coleman-Weinberg GUTs

The authors study the finite-temperature effective potential of the Higgs scalar in GUTs with Coleman-Weinberg symmetry breaking. The critical temperature is derived without employing a high-temperature approximation to the effective potential, and the limitations of such approximations are discussed.

Coleman-Weinberg symmetry breaking in the early Universe with an inhomogeneity

The 1-loop renormalized effective potential for a phi 4 theory in the early Universe with a small inhomogeneity is evaluated under the adiabatic approximation. It is used to investigate the Coleman-Weinberg symmetry breaking processes usually leading to inflationary cosmologies in the presence of an inhomogeneity. The result shows that whether the symmetry is radiatively broken or not will crucially depend upon the scalar-gravitational coupling xi and the magnitude of the scalar curvature R. In particular, the author shows how the mode-mixing behaviour resulting from the inhomogeneity of spacetime is naturally replaced by introducing the non-local term into the field equation. This property allows the analysis of other quantum field effects in the inhomogenous spacetime, which will be presented in later papers.

Renormalization group analysis of Coleman-Weinberg symmetry breaking in two-Higgs models

Using renormalization group techniques we investigate Coleman-Weinberg symmetry breaking in the standard model with two Higgs doublets. Bounds on the mass spectrum will be found from the requirement of vacuum stability and finiteness of the quartic couplings up to a unification scale.

Is Coleman-Weinberg symmetry breaking in the standard model ruled out?

In the standard model with Coleman-Weinberg symmetry breaking a symmetric vacuum (〈 φ〉 = 0) always exists at any non-zero temperature; the transition to the symmetry-breaking vacuum can only occur after much supercooling. Witten has shown that this transition occurs when the strong interactions break chiral symmetry; the transition temperature is O(200) MeV and a large (but not fatal) amount of entropy is produced. It is noted here that since the strong coupling grows as the universe cools in the metastable symmetric vacuum, the Yukawa coupling to the top quark will also grow. This causes top quark loops to dominate the effective potential at small scales, drastically altering the nature of the transition. We show that if m t ⪆ 65 GeV , a metastable vacuum at 〈 φ〉 ≈ 0(1) GeV forms which persists to T = 0; the resulting transition would generate far too much entropy to be compatible with the current baryon to entropy ratio, ruling out the CW mechanism. If m t ⪅ 65 GeV, we argue that a metastable vacuum might also exist, but a breakdown of perturbation theory precludes a definitive statement.

Cosmological inflation cries out for supersymmetry

We re-examine the inflationary scenario in the standard SU(5) model with Coleman-Weinberg symmetry breaking and point out difficulties which may be resolved in a broken supersymmetric model. Because of a partial cancellation at the one-loop level, the effective potential in a broken supersymmetric theory may be much flatter than in standard SU(5), thus permitting a greater amount of inflation.

Constraints on GUTS with Coleman-Weinberg symmetry breaking

A popular assumption introduced by Coleman and Weinberg is that the elementary Higgs scalars of a gauge theory are massless at the tree level; the symmetry breakdown is then entirely due to quantum radiative corrections. In grand unified theories (GUTS), this assumption becomes particularly attractive. Many GUTS have “intermediate” mass scales [scales of symmetry breaking between baryon number generation and SU(2) × U(1) breaking], and it is attractive to apply the Coleman-Weinberg assumption to all stages of symmetry breaking after baryon number generation. In this paper, it is shown that most such GUTS are phenomenologically unacceptable. The reason is that as the universe cools, at each scale of symmetry breaking there will be a phase transition; if the symmetry is broken à la Coleman-Weinberg, this transition is strongly first order and thus generates entropy, decreasing the previously generated baryon number to entropy ratio by a large, and perhaps unacceptable amount. The entropy generated in a general intermediate mass scale transition is calculated, and the severe constraints that any Coleman-Weinberg-type GUT with intermediate mass scales must satisfy (in order to avoid excessive entropy generation) are found. Turning to specific models, it is shown that all intermediate mass scale transitions associated with SO(10) do not satisfy these constraints; the Coleman-Weinberg form of these transitions is inconsistent with cosmological observations and is thus phenomenologically unacceptable.