2010/09/30 by Michio Hashimoto, Koichi Yamawaki · 70 citations
Physics and Astronomy · #Atomic and Subatomic Physics Research #Cold Atom Physics and Bose-Einstein Condensates #Coupling (piping) #Particle physics #Physics #Quantum, superfluid, helium dynamics #hep-lat #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.83.015008
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 83(1) (American Physical Society) · 17 pages, 14 figures; discussions clarified, references added, to appear in Phys.Rev.D
arxiv created 2011/01/02 · openalex publication_date 2011/01/21 · arxiv updated 2013/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Technidilaton (TD) was proposed long ago in the technicolor near criticality/conformality. To reveal the critical behavior of TD, we explicitly compute the nonperturbative contributions to the scale anomaly ⟨\ensuremathθ_\ensuremathμ^\ensuremathμ⟩ and to the technigluon condensate ⟨\ensuremathαG_\ensuremathμ\ensuremathν2⟩, which are generated by the dynamical mass m of the technifermions. Our computation is based on the (improved) ladder Schwinger-Dyson equation, with the gauge coupling \ensuremathα replaced by the two-loop running coupling \ensuremathα(\ensuremathμ) having the Caswell-Banks-Zaks infrared fixed point \ensuremathα*: \ensuremathα(\ensuremathμ)\ensuremath≃\ensuremathα=\ensuremathα* for the infrared region m<\ensuremathμ<\ensuremathΛTC, where \ensuremathΛTC is the intrinsic scale (analogue of \ensuremathΛQCD of QCD) relevant to the perturbative scale anomaly. We find that \ensuremath-⟨\ensuremathθ_\ensuremathμ^\ensuremathμ⟩/m4\ensuremath→const\ensuremath≠0 and ⟨\ensuremathαG_\ensuremathμ\ensuremathν2⟩/m4\ensuremath→(\ensuremathα/\ensuremathαcr\ensuremath-1)^\ensuremath-3/2\ensuremath→\ensuremath∞ in the criticality limit m/\ensuremathΛTC\ensuremath∼exp(\ensuremath-\ensuremathπ/(\ensuremathα/\ensuremathαcr\ensuremath-1)1/2)\ensuremath→0 (\ensuremathα=\ensuremathα*\ensuremath\searrow\ensuremathαcr, or Nf\ensuremath\nearrowNfcr) (``conformal edge''). Our result precisely reproduces the formal identity ⟨\ensuremathθ_\ensuremathμ^\ensuremathμ⟩=(\ensuremathβ(\ensuremathα)/4\ensuremathα2)⟨\ensuremathαG_\ensuremathμ\ensuremathν2⟩, where \ensuremathβ(\ensuremathα)=\ensuremathΛTC\frac\ensuremath∂\ensuremathα\ensuremath∂\ensuremathΛTC=\ensuremath-(2\ensuremathαcr/\ensuremathπ)\ifmmode⋅\else\textperiodcentered\fi(\ensuremathα/\ensuremathαcr\ensuremath-1)3/2 is the nonperturbative beta function corresponding to the above essential singularity scaling of m/\ensuremathΛTC. Accordingly, the partially conserved dilatation current implies (MTD/m)2(FTD/m)2=\ensuremath-4⟨\ensuremathθ_\ensuremathμ^\ensuremathμ⟩/m4\ensuremath→const\ensuremath≠0 at criticality limit, where MTD is the mass of TD and FTD the decay constant of TD. We thus conclude that at criticality limit the TD could become a ``true (massless) Nambu-Goldstone boson'' MTD/m\ensuremath→0, only when m/FTD\ensuremath→0, namely, getting decoupled, as was the case of ``holographic technidilaton'' of Haba-Matsuzaki-Yamawaki. The decoupled TD can be a candidate of dark matter.