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QCD with an Infrared Fixed Point and a Dilaton
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abstract
Following previous work we further explore the possibility that the chirally broken phase of gauge theories admits an infrared fixed point interpretation. The slope of the $\beta$ function, $\beta'_*$, is found to vanish at the infrared fixed point which has several attractive features such as logarithmic running. We provide a more in-depth analysis of our previous result that the mass anomalous assumes $\gamma_* = 1$ at the fixed point. The results are found to be consistent with ${\cal N}=1$ supersymmetric gauge theories. In a second part the specific properties of a dilaton, the (pseudo) Goldstone, due to spontaneous symmetry breaking are investigated. Dilaton soft theorems indicate that a soft dilaton mass can only originate from an operator of scaling dimension two. In the gauge theory this role is taken on by the $\bar qq$-operator. The QCD dilaton candidate, the $\sigma = f_0(500)$ meson is investigated. Singlet-octet mixing is found to be important. We briefly discuss the dilaton as a candidate for the Higgs boson, which relies on the ratio of dilaton to pion decay constant being close to unity. In QCD this is approximately satisfied but it is remains unclear if this is accidental or whether there is unknown reason behind it.
Forward citations
Cited by 7 Pith papers
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Light dilaton from top-down holographic confinement with magnetic fluxes
In a two-flux family of top-down holographic confining theories, the lightest scalar is an approximate dilaton with mass about one tenth of the lightest spin-2 confinement scale, over a wide, untuned region of paramet...
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The Potential of HEFT and the scale of New Physics
From a geometric recursion, the authors compute leading high-energy amplitudes with arbitrary multiplicities, resum them into unitarity bounds and cut-offs, and show that a dilaton HEFT reaches the SM as Δ→2 without p...
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Dilaton Effective Field Theory across the Conformal Edge
Fitting a dilaton EFT with a free exponent Δ to lattice spectra indicates SU(3) N_f=8 is confining (Δ<4) and SU(2) adjoint is infrared conformal (Δ>4).
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Gluon Gravitational $ D$-Form Factor: The $\sigma$-Meson as a Dilaton Confronted with Lattice Data II
σ-pole residues in gluon D-form factors for π, N, ρ and Δ are consistent with dilaton effective theory predictions within large uncertainties.
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Gravitational form factors of the nucleon in the Skyrme model based on scale-invariant chiral perturbation theory
A Skyrme model with a dilaton field attributes the proton's negative internal pressure and confining force to the gluonic scale anomaly, and reproduces the lattice QCD D(t) form factor.
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From Nuclear Matter with Quenched $g_A$ to Compact-Star Matter with a Signal for Emergent Hidden Scale Symmetry
The paper argues that quenched g_A ≈ 1 in nuclei and the pseudo-conformal sound speed v_s^2/c^2 ≈ 1/3 in compact stars are parallel signals of one emergent hidden scale symmetry.
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Dilatonic states, phase transitions, and criticality in holography
A review of holographic examples indicating that a light dilaton appears near critical endpoints of first-order zero-temperature phase transitions, with explicit but lower-dimensional demonstrations.
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