QED vertex form factors at two loops

Bologna); E. Remiddi (Bologna U.; INFN; ITT); Karlsruhe U.; P. Mastrolia (Bologna U.; R. Bonciani (Freiburg U.)

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QED vertex form factors at two loops

R. Bonciani (Freiburg U.), P. Mastrolia (Bologna U., Karlsruhe U., ITT), E. Remiddi (Bologna U., INFN, Bologna)

High Energy Physics - Phenomenology · Submitted 23 Jul 2003

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

The authors' main claim We present the closed analytic expression of the form factors of the two-loop QED vertex amplitude for on-shell electrons of finite mass $m$ and arbitrary momentum transfer $S=-Q^2$.

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arXiv IDhep-ph/0307295 (version 1)

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CitationBologna), E. Remiddi (Bologna U., INFN, ITT), Karlsruhe U., P. Mastrolia (Bologna U., R. Bonciani (Freiburg U.). "QED vertex form factors at two loops." arXiv:hep-ph/0307295 (2003). https://pith.science/paper/OAAHSP3A

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.25 · compares with prior results 0.04 · mentions code or data availability 0.02.

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We present the closed analytic expression of the form factors of the two-loop QED vertex amplitude for on-shell electrons of finite mass $m$ and arbitrary momentum transfer $S=-Q^2$. The calculation is carried out within the continuous $D$-dimensional regularization scheme, with a single continuous parameter $D$, the dimension of the space-time, which regularizes at the same time UltraViolet (UV) and InfraRed (IR) divergences. The results are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present the closed analytic expression of the form factors of the two-loop QED vertex amplitude for on-shell electrons of finite mass $m$ and arbitrary momentum transfer $S=-Q^2$.	contribution 0.62	0.96	0.89	asserted 1.00
s1	The calculation is carried out within the continuous $D$-dimensional regularization scheme, with a single continuous parameter $D$, the dimension of the space-time, which regularizes at the same time UltraViolet (UV) and InfraRed (IR) divergences.	method 1.00	0.89	0.04	asserted 1.00
s2	The results are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.	result 0.88	0.92	0.17	asserted 1.00

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

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The paper

Original abstract

We present the closed analytic expression of the form factors of the two-loop QED vertex amplitude for on-shell electrons of finite mass $m$ and arbitrary momentum transfer $S=-Q^2$. The calculation is carried out within the continuous $D$-dimensional regularization scheme, with a single continuous parameter $D$, the dimension of the space-time, which regularizes at the same time UltraViolet (UV) and InfraRed (IR) divergences. The results are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.

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References

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Cited by 9 Pith papers

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The paper computes the O(alpha_s) soft-limit constants that interpolate between massive and massless scheme resummations, raising the accuracy of heavy-flavour fragmentation predictions from NLL to NLL'.
Singlet and non-singlet three-loop massive form factors
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Three-loop massive quark form factors for all four QCD currents are computed across the whole kinematic range, with at least seven digits of precision and a public evaluation package.
Magnus and Dyson Series for Master Integrals
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A Magnus-series algorithm constructs the transformation that puts linear-in-epsilon systems of differential equations for Feynman master integrals into canonical form, with explicit results for two-loop QED vertices a...
Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data
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The working group finds that the leading luminosity Monte Carlo generators agree to about 0.1 percent and assigns a total theoretical uncertainty of 0.11 to 0.18 percent to large-angle Bhabha scattering at meson factories.

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HPL, a Mathematica implementation of the harmonic polylogarithms
hep-ph 2005-07 accept novelty 4.0 of 10

A Mathematica implementation of harmonic polylogarithms is presented, covering product algebra, derivatives, series expansion, numerical evaluation, and analytic continuation with user-controlled branch-cut signs.
Theory for muon-electron scattering @ 10ppm: A report of the MUonE theory initiative
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The MUonE theory initiative reports that a 10 ppm prediction for elastic muon-electron scattering is reachable via massive NLO QED, partial NNLO, and resummation, but the full NNLO calculation is not yet finished.
Standard Model Theory for the FCC-ee Tera-Z stage
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The report argues that, with dedicated investment, Standard Model predictions for Z-boson observables can be made precise enough not to limit the FCC-ee Tera-Z physics programme.
Feynman Diagrams and Differential Equations
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A pedagogical review showing how integration-by-parts identities turn Feynman master integrals into differential equations that are solved exactly in D or Laurent-expanded around D = 4.

How the literature uses it

33 arXiv papers cite this in 55 sentences

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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 1 paper

We evaluate the on shell form factors of the electron for arbitrary momentum transfer and finite electron mass, at two loops in QED, by integrating the corresponding dispersion relations, which involve the imaginary parts known since a long time.

Two-Loop Form Factors in QED · 0.97

Papers citing it · 28 sentences without a confident label

Contests it 1 paper

Those contributions have been obtained earlier in Refs. [ref] , however, the printed expressions contain several typos.

Electron-positron annihilation into heavy leptons at two loops · Results and ancillary files · contest 0.91

Uses its method or tool 3 papers

This critically reduced the complexity of the problem and made it solvable by the method of [ref] .[When this work was in preparation a numerical result for the two-loop heavy-flavor contribution was obtained by means of the dispersion relation approach [ref] .]

Calculation of the Two-Loop Heavy-Flavor Contribution to Bhabha Scattering · Introduction · 0.86
The pure electronic and muonic two-loop amplitudes can be calculated with full mass dependence based on the heavy quark form factor [ref] .

Muon-Electron Scattering at NNLO · Validation · 0.80
These form factors are evaluated by employing a set of techniques which are by now standard in multiloop calculations (see for instance [ref] ).

Two-Loop QCD Corrections to the Heavy-to-Light Quark Decay · Introduction · 0.92

Uses its data or values 1 paper

As a last input to the LBK theorem [ref] we have calculated the non-radiative two-loop amplitude using the known expression for the heavy-quark form factor [ref] .

The LBK theorem to all orders · Real-virtual-virtual corrections for muon-electron scattering · 0.86

Compares with it 5 papers

With these conventions in mind, we now compare the sum of the momentum regions as given in Sec. [ref]-[ref] to the expansion in $m^2/ŝ$ up to NLP of the full result of [ref] and [ref] .

Region analysis of QED massive fermion form factor · Cross-checks · 1.00
We have found an agreement with the results of Refs. [ref] .

Electron-positron annihilation into heavy leptons at two loops · Form factors · 1.00
The result was checked against the small mass limit of [ref] and with [ref] .

Bridging massive and massless schemes for soft gluon resummation in heavy-flavour production in $e^+e^-$ collisions · Virtual · 0.99

Cites it as background 11 papers

The massive form factor at two-loop was first computed in QED in [ref] , followed by [ref] , which considered its generalization to QCD.

Region analysis of QED massive fermion form factor · Massive form factors · 0.97
The corrections involving a closed electron loop were obtained in [ref] by direct diagrammatic calculation, retaining the full dependence on $m_e$.

Calculation of the Two-Loop Heavy-Flavor Contribution to Bhabha Scattering · Introduction · 0.88
Massive quark form factors are known at two-loop order from Refs. [ref] .

Massive vector form factors to three loops · Introduction · 0.87

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