Status of Chiral-Scale Perturbation Theory

Crewther, R. J.; Tunstall, Lewis C.

doi:10.48550/arxiv.1510.01322

Cited by 7 publications

(32 citation statements)

References 14 publications

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“…Gauge theories are then considered in Section 3. For quantum chromodynamics (QCD), there is only a type-I theory, chiral-scale perturbation theory χPT σ [2][3][4], where the dilaton at the IRFP corresponds to the light resonance f 0 (500). The TC analogue of this is crawling TC, where the Higgs boson is the type-I TC analogue of f 0 .…”

Section: Introductionmentioning

confidence: 99%

Genuine Dilatons in Gauge Theories

Crewther

2020

Preprint

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A genuine dilaton σ allows scales to exist even in the limit of exact conformal invariance. In gauge theories, these may occur at an infrared fixed point (IRFP) α IR through dimensional transmutation. These large scales at α IR can be separated from small scales produced by θ µ µ , the trace of the energy-momentum tensor. For quantum chromodynamics (QCD), the conformal limit can be combined with chiral SU(3) × SU(3) symmetry to produce chiral-scale perturbation theory χPT σ , with f 0 (500) as the dilaton. The technicolor (TC) analogue of this is crawling TC: at low energies, the gauge coupling α goes directly to (but does not walk past) α IR , and the massless dilaton at α IR corresponds to a light Higgs boson at α α IR . Unlike crawling TC, in walking TC, θ µ µ produces all scales, large and small, so it is hard to argue that its "dilatonic" candidate for the Higgs boson is not heavy.

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Section: Introductionmentioning

confidence: 99%

Genuine Dilatons in Gauge Theories

Crewther

2020

Preprint

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“…For recent investigations, see for example Refs. [7][8][9][10][11][12][13][14] and references cited therein. This interesting idea has again attracted attention recently as it might provide a natural understanding on the appearance of a flavorsinglet parity-even light meson in the N f = 8 SU (3) gauge theory [15,16].…”

Section: Introductionmentioning

confidence: 99%

A dilaton-pion mass relation

Kasai,

Okumura,

Suzuki

2016

Preprint

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“…eq. 3.7 in [41]) discussed above. The remaining kinetic terms are absent in the case where the low energy constants c 1,2 (µ) → 1 for m q , µ → 0 which is the chiral-scale limit advocated in [41].…”

Section: Spontaneous Broken Chiral Symmetry In the Infraredmentioning

confidence: 82%

“…3.7 in [41]) discussed above. The remaining kinetic terms are absent in the case where the low energy constants c 1,2 (µ) → 1 for m q , µ → 0 which is the chiral-scale limit advocated in [41]. In summary in χPT σ the EMT can be improved in the dilaton sector which in principle allows for the elimination of the previously discussed and dangerous π 2 -term.…”

Section: Spontaneous Broken Chiral Symmetry In the Infraredmentioning

confidence: 82%

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Flow of the □R Weyl anomaly

Prochazka

Zwicky

2017

Phys. Rev. D

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An important aspect of Weyl anomalies is that they encode information on the irreversibility of the renormalisation group flow. We consider, ∆b =b UV −b IR , the difference of the ultraviolet and infrared value of the R-term of the Weyl anomaly. The quantity is related to the fourth moment of the trace of the energy momentum tensor correlator for theories which are conformal at both ends. Subtleties arise for non-conformal fixed points as might be the case for infrared fixed points with broken chiral symmetry. Provided that the moment converges, ∆b is then automatically positive by unitarity. Written as an integral over the renormalisation scale, flowindependence follows since its integrand is a total derivative. Furthermore, using a momentum subtraction scheme (MOM) the 4D Zamolodchikov-metric is shown to be strictly positive beyond perturbation theory and equivalent to the metric of a conformal manifold at both ends of the flow. In this schemeb(µ) can be extended outside the fixed point to a monotonically decreasing function. The ultraviolet finiteness of the fourth moment enables us to define a scheme for the δL ∼ b 0 R 2term, for which the R 2 -anomaly vanishes along the flow. In the MOM-and the R 2 -scheme,b(µ) is shown to satisfy a gradient flow type equation. We verify our findings in free field theories, higher derivative theories and extend ∆b and the Euler flow ∆β a for a Caswell-Banks-Zaks fixed point for QCD-like theories to nextto-next-to leading order using a recent G 2 G 2 -correlator computation.

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Status of Chiral-Scale Perturbation Theory

Cited by 7 publications

References 14 publications

Genuine Dilatons in Gauge Theories

Genuine Dilatons in Gauge Theories

A dilaton-pion mass relation

Flow of the □R Weyl anomaly

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