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Transport coefficients in high temperature gauge theories: (I) Leading-log results

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Peter Arnold, Guy D. Moore, Laurence G. Yaffe

High Energy Physics - Phenomenology · Submitted 16 Oct 2000 · 43 references

Pith's verdict: A careful, reimplementable leading-log calculation whose numbers supersede a demonstrably error-prone literature; the one real gap is a deferred IR-cutoff argument for two diagram classes.

T0 · AI review

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arXiv IDhep-ph/0010177 (version 1)
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CitationGuy D. Moore, Laurence G. Yaffe, Peter Arnold. "Transport coefficients in high temperature gauge theories: (I) Leading-log results." arXiv:hep-ph/0010177 (2000). https://pith.science/paper/XUONGMMP
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The paper

The paper claims

The paper derives the leading-log coefficients of shear viscosity, electrical conductivity, and flavor diffusion in hot gauge theories and argues that earlier leading-log calculations were mostly wrong.

The reading

The paper sets out to compute the coefficients that multiply the leading logarithm in three transport properties of a weakly coupled hot gauge theory, Abelian or non-Abelian: shear viscosity, electrical conductivity, and flavor diffusion. These coefficients control how quickly momentum, charge, or particle number relaxes in a quark-gluon plasma or an early-universe plasma, so they matter for hydrodynamic and baryogenesis estimates. The authors use a linearized kinetic theory for hard quasiparticles, keep two-to-two scattering, and isolate the small-momentum-transfer region that produces the logarithm. They turn the resulting integral equation into a variational problem and solve it with a small basis, obtaining numerical tables and compact approximate formulas. They also argue that earlier leading-log calculations missed annihilation and Compton scattering or made algebraic errors, which can shift answers by factors of order two.

What carries the argument

The load-bearing device is the variational functional $Q[χ]=(χ,S)-½(χ,Cχ)$, built from the linearized collision operator $C$ and the driving source $S$. Because $C$ is Hermitian and positive semidefinite in the inner product (2.20), maximizing $Q$ is equivalent to solving the linearized Boltzmann equation, and the maximum value is proportional to the transport coefficient. The leading-log simplification reduces the collision integral to a one-dimensional integral times $ln(1/g)$: for small exchanged momentum $q$, the matrix elements factor into a universal vertex, the difference of the $χ$ functions supplies a $q²$ suppression when species are unchanged, and hard-thermal-loop self-energies cut off the infrared at $q∼gT$. Expanding $χ$ in a handful of basis functions turns the problem into a small matrix inversion, which is how the numerical tables are produced.

Extended reading notes

Core claim

The central claim is that the leading-log coefficients of shear viscosity, electrical conductivity, and flavor diffusion in a hot gauge theory can be extracted reliably from a linearized Boltzmann equation for hard quasiparticles, and that doing so gives the values in Tables I–III and the approximate closed forms (1.11), (1.15), (1.22), and (1.23). The logarithm comes from small momentum transfer, where the collision integral is dominated by $t$-channel gauge exchange and by annihilation/Compton processes; the authors keep diagrams (A)–(E) and drop only terms that are finite or higher order. They formulate the transport problem as maximizing a quadratic functional $Q[χ]$, equivalent to solving the linearized collision equation but numerically stable. The paper uses this to compare with earlier work and concludes that almost all previous leading-log evaluations are wrong, sometimes by factors of two or more.

Load-bearing premise

The load-bearing premise is that the coefficient of $ln(1/g)$ is unchanged when the vacuum $2→2$ amplitudes are evaluated at small momentum transfer and the hard-thermal-loop self-energies are used only to cut off the infrared; for the annihilation and Compton diagrams (D) and (E) the paper asserts this cutoff and defers the demonstration to a companion paper in preparation (Sec. III.B).

Original abstract

Leading-log results are derived for the shear viscosity, electrical conductivity, and flavor diffusion constants in both Abelian and non-Abelian high temperature gauge theories with various matter field content.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,616 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Leading-log results are derived for the shear viscosity, electrical conductivity, and flavor diffusion constants in both Abelian and non-Abelian high temperature gauge theories with various matter field content.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Leading-log results are derived for the shear viscosity, electrical conductivity, and flavor diffusion constants in both Abelian and non-Abelian high temperature gauge theories with various matter field content. contribution 0.64 0.93 0.81 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. FIG. 1. Momentum and species label conventions for 2
Figure 2. FIG. 2. Leading-order diagrams for all 2
Figure 3. FIG. 3. A generic vertex from diagrams (
Figure 4. FIG. 4. Comparison of the exact (leading-log) form for

Figures reproduced from arXiv:hep-ph/0010177 by the authors.

References
How later papers used it

250 later papers cite it

Evidence: substantial. 239 of the citing papers share no author with it, and 63 of those carry a confident label from Pith's citation classifier.

Pith read 38 of the 456 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Builds on it 2 of 4 papers with this label · 1 by the same authors

By the same authors

  • Namely, we extend the Arnold-Moore-Yaffe (AMY) calculations for shear viscosity at leading log [ref] in weakly coupled high-temperature and dense QCD. “High temperature” in this work means the same as in [ref] , that the temperature is much larger than the zero-temperature masses of elementary particles, i.e., we require that $T ≫Λ_QCD$ and $T ≫m_q$, and dense means that $μ≥T$.

    Hot and Dense QCD Shear Viscosity at Leading Log (2022) (same authors) · Introduction · 1.00

Uses its method or tool 4 of 24 papers with this label · 1 by the same authors

  • Expanded χ(p) in the same basis as that used in this paper.

    Hadronic transport coefficients from the linear sigma model at finite temperature (2020) · 0.99 · paraphrased: the licence does not allow quoting

  • Considered the quadratic functional following this paper.

    Re-running the QCD shear viscosity (2017) · 0.98 · paraphrased: the licence does not allow quoting

  • Based on the approach of Arnold, Moore and Yaffe (AMY) [ref] , we study the evolution of the phase-space distribution $f()$, where, after integrating out position space, the kinetic equation is given by [equation] The leading-order QCD elastic scatterings are described by the $2 ↔2$ collision integral $C_a^2↔2[f]$, where we use hard thermal loop propagators for the internal quark and gluon to regulate the divergent small angle scatterings, while the other in-coming and out-going parton lines are assumed to be vacuum like [ref] , with thermal distributions for the partons that emerge from and re-enter the medium.

    Quenching jets increases their flavor (2022) · The effective Boltzmann equation for a jet in a static QGP · 0.98

By the same authors

Uses its data or values 9 of 24 papers with this label
Compares with it 1 of 21 papers with this label
How the literature uses it

219 arXiv papers cite this in 404 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 242 sentences without a confident label

Contests it 5 papers
Builds on it 4 papers
Uses its method or tool 17 papers
Uses its data or values 25 papers
  • Combining Eq. [ref] and [ref] then yields [equation] where we have set $g_* = 106.75$, $α_Y = 0.011$ and $σ_Y = 50 T$ at $10^6$ GeV [ref] .

    A new constraint on primordial lepton flavour asymmetries · Introduction · 0.88

  • In fact, leading-order (LO) perturbative calculations of $η$ [ref] find $η/s ∼0.5$ for coupling values of physical relevance for achievable temperatures.

    QCD Shear Viscosity at (almost) NLO · Introduction · 0.93

  • The equations for $b _ ±≡b _ 1 ±i b _ 2$ decouple, [equation] For [equation] there is an instability with the growth rate [equation] The maximal growth rate is [equation] The linear kinetic equation neglecting the dynamics of the long wavelength hypermagnetic fields is valid as long as the magnetic dynamics happen on longer time scales than the perturbative ones characterized by the equilibration rate $γ$, [equation] In the leading logarithmic approximation the hyperelectric conductivity is [ref] [equation] with $C = 7.05$ in the Standard Model with one Higgs doublet.

    Equilibration of right-handed electrons · Conversion of $$ to hypercharge gauge fields · 0.88

Compares with it 19 papers
Cites it as support 2 papers
Cites it as background 57 papers

Discussion

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