arXiv2019
We analyze the Callan-Symanzik equations when scale invariance at a nontrivial infrared (IR) fixed point $α^{}_{\mathrm{IR}}$ is realized in the Nambu-Goldstone (NG) mode. As a result, Green's functions at $α^{}_{\mathrm{IR}}$ 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 $α$ "crawls" towards (but does not pass) $α^{}_{\mathrm{IR}}$ in the exact IR limit. The NG mechanism at $α^{}_{\mathrm{IR}}$ implies the existence of a massless dilaton $σ$, which becomes massive for IR expansions in $ε\equiv α^{}_{\mathrm{IR}} - α$ 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 $εβ'(4+β')F_σ^{-2} \langle\hat{G}^2\rangle_{\text{vac}}$, where $β'$ is the (positive) slope of the beta function at $α^{}_{\mathrm{IR}}$, $F_σ$ 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 $β'$-dependent deviations from that of the Standard Model. Flavor-changing neutral currents are suppressed if the crawling region $α\lesssim α^{}_{\mathrm{IR}}$ 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.