Crawling technicolor

Abstract: We analyze the Callan-Symanzik equations when scale invariance at a nontrivial infrared (IR) fixed point $\alpha<sup>{}_{\mathrm{IR}}$ is realized in the Nambu-Goldstone (NG) mode. As a result, Green's functions at $\alpha<sup>{}_{\mathrm{IR}}$ 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) $\alpha<sup>{}_{\mathrm{IR}}$ in the exact IR limit. The NG mechanism at $\alpha<sup>{}_{\mathrm{IR}}$ 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)$<sup>2$ is proportional to $\epsilon \beta&#39;(4+\beta&#39;)F_\sigma^{-2} \langle\hat{G}<sup>2\rangle_{\text{vac}}$, where $\beta&#39;$ is the (positive) slope of the beta function at $\alpha<sup>{}_{\mathrm{IR}}$, $F_\sigma$ is the dilaton decay constant and $\langle\hat{G}<sup>2\rangle_{\text{vac}}$ 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 $\beta&#39;$-dependent deviations from that of the Standard Model. Flavor-changing neutral currents are suppressed if the crawling region $\alpha \lesssim \alpha<sup>{}_{\mathrm{IR}}$ 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.