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</script>We analyze the Callan-Symanzik equations when scale invariance at a nontrivial infrared (IR) fixed point $��^{}_{\mathrm{IR}}$ is realized in the Nambu-Goldstone (NG) mode. As a result, Green's functions at $��^{}_{\mathrm{IR}}$ 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 $��$ "crawls" towards (but does not pass) $��^{}_{\mathrm{IR}}$ in the exact IR limit. The NG mechanism at $��^{}_{\mathrm{IR}}$ implies the existence of a massless dilaton $��$, which becomes massive for IR expansions in $��\equiv ��^{}_{\mathrm{IR}} - ��$ 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 $����'(4+��')F_��^{-2} \langle\hat{G}^2\rangle_{\text{vac}}$, where $��'$ is the (positive) slope of the beta function at $��^{}_{\mathrm{IR}}$, $F_��$ 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 $��'$-dependent deviations from that of the Standard Model. Flavor-changing neutral currents are suppressed if the crawling region $��\lesssim ��^{}_{\mathrm{IR}}$ 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.
42 pages, 4 figures, as in PRD except for the Table of Contents, with Zumino's consistency condition for dilaton Lagrangians highlighted in Sec. 4
High Energy Physics - Theory, High Energy Physics - Phenomenology, High Energy Physics - Lattice, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), High Energy Physics - Lattice (hep-lat), FOS: Physical sciences
High Energy Physics - Theory, High Energy Physics - Phenomenology, High Energy Physics - Lattice, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), High Energy Physics - Lattice (hep-lat), FOS: Physical sciences
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