High Energy Physics - Lattice · arXiv:1307.6997 v2 · submitted 26 Jul 2013
Running coupling constant and mass anomalous dimension of six-flavor SU(2) gauge theory
The paper says
“We find that the running slows down and comes to a stop at 0.06 ≲ 1/g2 ≲ 0.15 where the mass anomalous dimension is estimated to be 0.26 ≲ γ*m ≲ 0.74.”
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Abstract
In the exploration of viable models of dynamical electroweak symmetry breaking, it is essential to locate the lower end of the conformal window and know the mass anomalous dimensions there for a variety of gauge theories. We calculate, with the Schrödinger functional scheme, the running coupling constant and the mass anomalous dimension of SU(2) gauge theory with six massless Dirac fermions in the fundamental representation. The calculations are performed on 64 - 244 lattices over a wide range of lattice bare couplings to take the continuum limit. The discretization errors for both quantities are removed perturbatively. We find that the running slows down and comes to a stop at 0.06 ≲ 1/g2 ≲ 0.15 where the mass anomalous dimension is estimated to be 0.26 ≲ γ*m ≲ 0.74.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.23 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.05 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| In the exploration of viable models of dynamical electroweak symmetry breaking, it is essential to locate the lower end of the conformal window and know the mass anomalous dimensions there for a variety of gauge theories. | background 0.99 | 0.04 | 0.03 | asserted 0.98 |
| We calculate, with the Schr\"odinger functional scheme, the running coupling constant and the mass anomalous dimension of SU(2) gauge theory with six massless Dirac fermions in the fundamental representation. | contribution 0.99 | 0.98 | 0.06 | asserted 1.00 |
| The calculations are performed on $6^4$ - $24^4$ lattices over a wide range of lattice bare couplings to take the continuum limit. | method 1.00 | 0.95 | 0.02 | asserted 0.99 |
| The discretization errors for both quantities are removed perturbatively. | method 1.00 | 0.91 | 0.02 | asserted 1.00 |
| We find that the running slows down and comes to a stop at $0.06 \lesssim 1/g^2 \lesssim 0.15$ where the mass anomalous dimension is estimated to be $0.26 \lesssim \gamma^*_m \lesssim 0.74$. | result 1.00 | 0.97 | 0.92 | asserted 1.00 |
What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,432 input tokens, $0.0002 reported.
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Cited by 2 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
How the literature uses it
12 arXiv papers cite this in 18 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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We establish an infrared stable fixed point at strong coupling and measure also the anomalous dimension of the fermion mass operator at the fixed point.
Infrared fixed point of SU(2) gauge theory with six flavors · 0.85
Papers citing it · 13 sentences without a confident label
Compares with it 1 paper
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This indicates [equation] which is not inconsistent with that found in the study of the running coupling constant defined in the Schrödinger functional scheme [ref] ; [equation]
Lattice study on chiral dynamics of two-color six-flavors QCD · Chiral Condensate · 0.98
Cites it as background 4 papers
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These theories have been studied on the lattice by several groups [ref] .
From chiral symmetry breaking to conformality in SU(2) gauge theory · Introduction · 0.93
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The measurement of the anomalous dimension $γ$ using the mass step scaling method described in section [ref] is well established and has been applied to many theories which may have an infrared fixed point, e.g. to SU(2) with fundamental fermions in Refs. [ref] .
The gradient flow running coupling in SU(2) gauge theory with $N_f=8$ fundamental flavors · Mass step scaling · 0.86
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Since then, the formalism has been successfully applied to study the renormalized gauge coupling and a number of other physical quantities in QCD [ref] and, more recently, has also been used to investigate the dynamics of other strongly coupled non-supersymmetric gauge theories with dynamical fermionic fields [ref] .
Strong coupling from non-equilibrium Monte Carlo simulations · Conclusions · 0.88
What it cites · 16 sentences without a confident label
Uses the method or tool of 5 papers
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The scale dependence of the gauge coupling and the mass is calculated in the SF scheme [ref] .
The Schr\"odinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories · Simulation details · 1.00
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The scale dependence of the gauge coupling and the mass is calculated in the SF scheme [ref] .
The running quark mass in the SF scheme and its two-loop anomalous dimension · Simulation details · 1.00
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The running of the coupling is analyzed with the discrete $β$ function (DBF) [ref] [equation] where [equation] where $s> 1$ denotes the change of the renormalization scale.
Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions · Discrete $β$ function · 1.00
Compares with 3 papers
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After the continuum extrapolation linear in $a^2$, it is found that the running of the renormalized coupling begins to slow down at $g^2∼5$ compared to the two-loop perturbation theory and the $β$ function eventually becomes consistent with zero at $g^2∼$12, which is obviously larger than that of Ref. [ref] .
Mass anomalous dimension in SU(2) with six fundamental fermions · Introduction · 0.86
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The discretization errors are improved perturbatively and the improvement turns out to decrease the DBF, which explains the discrepancy between Ref. [ref] and Ref. [ref] qualitatively.
Determining the conformal window: SU(2) gauge theory with N_f = 4, 6 and 10 fermion flavours · Summary and discussion · 0.92
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The same is observed in the improvement coefficient in ten-flavor QCD [ref] .
Running coupling constant of ten-flavor QCD with the Schr\"odinger functional method · Improving discretization errors · 0.92
Cites as support 1 paper
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The same argument is derived in our recent study on spectroscopy [ref] .
Lattice Study on quantum-mechanical dynamics of two-color QCD with six light flavors · Introduction · 0.97
Cites as background 38 papers
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The lattice determination of the running coupling of this theory was performed by three groups [ref] , all of which adopt the Schrödinger functional (SF) scheme [ref] .
Two-Color Schrodinger Functional with Six-Flavors of Stout-Smeared Wilson Fermions · Introduction · 0.91
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The lattice determination of the running coupling of this theory was performed by three groups [ref] , all of which adopt the Schrödinger functional (SF) scheme [ref] .
The Schr\"odinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories · Introduction · 0.91
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The lattice determination of the running coupling of this theory was performed by three groups [ref] , all of which adopt the Schrödinger functional (SF) scheme [ref] .
Mass anomalous dimension in SU(2) with six fundamental fermions · Introduction · 0.91
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