Crawling technicolor

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 $\epsilon {\beta }^{\prime }(4+{\beta }^{\prime })F_{\sigma }^{-2}⟨{\hat{G}}^2{⟩}_{\text{vac}}$, where ${\beta }^{\prime }$ is the (positive) slope of the beta function at ${\alpha }_{\mathrm{IR}}^{}$, $F_{\sigma }$ is the dilaton decay constant and $⟨{\hat{G}}^2{⟩}_{\text{vac}}$ 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 ${\beta }^{\prime }$-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.

arXiv comment42 pages, 4 figures, as in PRD except for the Table of Contents, with Zumino's consistency condition for dilaton Lagrangians highlighted in Sec. 4

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