Abstract
We analyze the Callan-Symanzik equations when scale invariance at a nontrivial infrared (IR) fixed point $\alpha^{}_{\mathrm{IR}}$ is realized in the Nambu-Goldstone (NG) mode. As a result, Green's functions at $\alpha^{}_{\mathrm{IR}}$ do not scale in the same way as for the conventional Wigner-Weyl (WW) mode. This allows us to propose a new mechanism for dynamical electroweak symmetry breaking where the running coupling $\alpha$ "crawls" towards (but does not pass) $\alpha^{}_{\mathrm{IR}}$ in the exact IR limit. The NG mechanism at $\alpha^{}_{\mathrm{IR}}$ implies the existence of a massless dilaton $\sigma$, which becomes massive for IR expansions in $\epsilon \equiv \alpha^{}_{\mathrm{IR}} - \alpha$ and is identified with the Higgs boson. Unlike "dilatons" that are close to a WW-mode fixed point or associated with a Coleman-Weinberg potential, our NG-mode dilaton is genuine and hence naturally light. Its (mass)$^2$ is proportional to $\epsilon \beta'(4+\beta')F_\sigma^{-2} \langle\hat{G}^2\rangle_{\text{vac}}$, where $\beta'$ is the (positive) slope of the beta function at $\alpha^{}_{\mathrm{IR}}$, $F_\sigma$ is the dilaton decay constant and $\langle\hat{G}^2\rangle_{\text{vac}}$ is the technigluon condensate. Our effective field theory for this works because it respects Zumino's consistency condition for dilaton Lagrangians. We find a closed form of the Higgs potential with $\beta'$-dependent deviations from that of the Standard Model. Flavor-changing neutral currents are suppressed if the crawling region $\alpha \lesssim \alpha^{}_{\mathrm{IR}}$ includes a sufficiently large range of energies above the TeV scale. In Appendix A, we observe that, contrary to folklore, condensates protect fields from decoupling in the IR limit.
Highlights
CSSM and ARC Centre of Excellence for Particle Physics at the Tera-scale, Department of Physics, University of Adelaide, Adelaide SA 5005, Australia
The resulting effective field theory (EFT) looks like an electroweak chiral Lagrangian [32,33,34] with a generic Higgs-like scalar field h [35,36,37,38,39,40,41,42,43,44,45], but in our theory, the NG mode for exact scale invariance requires us to constrain h and verify that the equivalence theorem permits our change of field variables σ → h
By analogy with quantum chromodynamics (QCD), where at energies below the confinement scale one can use EFT methods to describe pion dynamics, an EFT for dynamical electroweak symmetry is the most efficient way to describe physics at energies ranging from a few GeV to several hundred GeV
Summary
The discovery of the Higgs boson has focussed attention on strongly coupled electroweak theories that can produce a light scalar. The main idea of crawling TC is that there is a conformal limit of dynamical electroweak theory at which the Higgs boson corresponds to a zero-mass dilaton. The resulting EFT looks like an electroweak chiral Lagrangian [32,33,34] with a generic Higgs-like scalar field h [35,36,37,38,39,40,41,42,43,44,45], but in our theory, the NG mode for exact scale invariance requires us to constrain h and verify that the equivalence theorem permits our change of field variables σ → h. The phases of jσiTC;QCD are chosen such that Fσ and fσ are positive
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