The static quark-antiquark potential in QCD to three loops

Markus Peter

RECORD

The static quark-antiquark potential in QCD to three loops

Markus Peter

High Energy Physics - Phenomenology · Submitted 1 Oct 1996

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The static potential between an infinitely heavy quark and antiquark is derived in the framework of perturbative QCD to three loops by performing a full calculation of the two-loop diagrams and using the renormalization group.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. 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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,255 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The static potential between an infinitely heavy quark and antiquark is derived in the framework of perturbative QCD to three loops by performing a full calculation of the two-loop diagrams and using the renormalization group. The contribution of massless fermions is included.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The static potential between an infinitely heavy quark and antiquark is derived in the framework of perturbative QCD to three loops by performing a full calculation of the two-loop diagrams and using the renormalization group.	contribution 0.78	0.93	0.69	asserted 1.00
s1	The contribution of massless fermions is included.	method 0.62	0.72	0.05	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

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

The paper

Original abstract

The static potential between an infinitely heavy quark and antiquark is derived in the framework of perturbative QCD to three loops by performing a full calculation of the two-loop diagrams and using the renormalization group. The contribution of massless fermions is included.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 12 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
hep-ph 2015-10 accept novelty 7.0 of 10

The authors compute the angle-dependent cusp anomalous dimension to three loops in QCD and supersymmetric Yang-Mills theories, and show it takes a universal form when expressed in terms of an effective coupling set by...
Toponia at the HL-LHC and FCC-ee
hep-ph 2025-06 conditional novelty 6.0 of 10

Toponium ηt and ψt states have promising discovery channels at HL-LHC (ηt b bbar, about 6σ) and FCC-ee (ψt interference in b bbar, about 14σ), while P-wave states remain out of reach.
Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
hep-ph 2019-02 accept novelty 6.0 of 10

Small-angle four-loop QCD calculations confirm a conjecture for the full angle dependence of five fermionic color structures but disprove it for the two structures that receive fermion-box contributions.
The bottom quark mass from the $\Upsilon(1S)$ system at NNNLO
hep-ph 2014-07 conditional novelty 6.0 of 10

Using the full NNNLO Upsilon(1S) mass expression and an improved leading-renormalon normalization Nm = 0.563(26), the bottom MS-bar mass is determined to be 4201(43) MeV.
Three-loop static potential
hep-ph 2009-11 accept novelty 6.0 of 10

The gluonic three-loop coefficient of the static heavy-quark potential is computed as 502.24 C_A^3 minus 136.39 d_F d_A / N_A, completing the three-loop static potential.

Show 7 more citing papers

The MSR Mass and the ${\cal O}(\Lambda_{\rm QCD})$ Renormalon Sum Rule
hep-ph 2017-04 accept novelty 5.0 of 10

An analytic sum rule extracts the O(Lambda_QCD) renormalon normalization of any perturbative series from its known coefficients, giving N_1/2 = 0.526, 0.492, 0.446 for 3, 4, 5 massless flavors.
Third-order correction to top-quark pair production near threshold I. Effective theory set-up and matching coefficients
hep-ph 2013-12 accept novelty 5.0 of 10

The paper assembles the complete set of NRQCD matching coefficients and PNRQCD potentials, including previously unpublished order-epsilon terms, required for a third-order QCD calculation of the top-antitop threshold ...
Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations
hep-ph 2013-04 conditional novelty 5.0 of 10

A generalized dimensional-regularization scheme exposes the beta-function terms in perturbative QCD series, allowing them to be resummed into order-by-order coupling scales and yielding scheme-independent predictions.
The static potential in QCD to two loops
hep-ph 1998-12 conditional novelty 5.0 of 10

An independent two-loop calculation of the static QCD potential finds the pure-gluon coefficient a2 is smaller than the prior published value by 2 pi squared times C_A squared, traced to a discarded contact term.
The QCD Running Coupling
hep-ph 2016-04 accept novelty 2.0 of 10

A comprehensive review of the QCD running coupling across perturbative and nonperturbative regimes, closing with a proposal that effective charges defined directly from observables give the most unified definition of alpha_s.
QCD forces and heavy quark bound states
hep-ph 2000-01 accept novelty 2.0 of 10

A 2000 survey of lattice determinations of the QCD static potential and its excitations, and of how effective field theory turns those potentials into a quarkonium Hamiltonian.
Renormalisation
hep-ph 2025-11 unverdicted novelty 1.0 of 10

An introductory review of renormalisation procedures, the renormalisation group, and scale-setting optimisation in gauge theories such as QCD.

How the literature uses it

38 arXiv papers cite this in 44 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 3 papers

The three-loop corrections to the potential of two heavy quarks are computed.

Full result for the three-loop static quark potential · 0.98
Using a renormalization group improvement, the ``three-loop'' potential in momentum space is thus derived and the third coefficient of the $\beta$-function for the V-scheme is given.

The static potential in QCD - a full Two-Loop Calculation · 0.98
We present analytic results for the three-loop static potential of two heavy quarks.

Analytic three-loop static potential · 0.96

Papers citing it · 27 sentences without a confident label

Uses its data or values 7 papers

The one- and two-loop coefficients $a_1$ [ref] and $a_2$ [ref] are given in Eq. (4) of Ref. [ref] where also the higher order terms in $ϵ$, necessary for the three-loop calculation, are presented.

Three-loop static potential · Introduction · 0.92
The constants $a_1$ [ref] and $a_2$ [ref] are known analytically.

Lambda_msbar from the static potential for QCD with n_f=2 dynamical quark flavors · The static potential in momentum space · 0.90
All the constants as $a_1$, $a_2$, $b_1$, $β_i (i=1,2,3)$ are given in Ref. [ref] (also see [ref] ).

Phenomenological study on the significance of the scalar potential and Lamb shift · The mass spectrum as the Lamb shift is taken into account · 0.91

Cites it as background 10 papers

The two-loop corrections have only been evaluated towards the end of the nineties by two groups [ref] and about five years ago the three-loop corrections have been considered in Refs. [ref] , again in two independent calculations.

Colour octet potential to three loops · Introduction · 0.95
It took almost 20 years until the next order became available [ref] which, at that time, was a heroic enterprize.

Three-loop static potential · Introduction · 0.93
In the 1990ies the two-loop corrections have been computed in the works [ref] and shortly afterwards the coefficient of the three-loop divergence has been evaluated indirectly by examining the ultra-soft contribution to the energy of two heavy quarks [ref] .

Full result for the three-loop static quark potential · Introduction · 0.95

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.