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Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions
High Energy Physics - Phenomenology · Submitted 21 Apr 2005
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that both the singlet and non-singlet vertex functions satisfy the correct chiral Ward identities.
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The abstract, sentence by sentence
We present closed analytic expressions for the order $\alpha_s^2$ triangle diagram contributions to the matrix elements of the singlet and non-singlet axial vector currents between the vacuum and a quark-antiquark state. We have calculated these vertex functions for arbitrary momentum transfer and for four different sets of internal and external quark masses. We show that both the singlet and non-singlet vertex functions satisfy the correct chiral Ward identities. Using the exact expressions for the finite axial vector form factors, we check the quality and the convergence of expansions at production threshold and for asymptotic energies.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present closed analytic expressions for the order $\alpha_s^2$ triangle diagram contributions to the matrix elements of the singlet and non-singlet axial vector currents between the vacuum and a quark-antiquark state. | contribution 0.74 | 0.97 | 0.52 | asserted 1.00 |
| s1 | We have calculated these vertex functions for arbitrary momentum transfer and for four different sets of internal and external quark masses. | contribution 0.60 | 0.97 | 0.07 | asserted 1.00 |
| s2 | We show that both the singlet and non-singlet vertex functions satisfy the correct chiral Ward identities. | result 0.99 | 0.93 | 0.25 | asserted 1.00 |
| s3 | Using the exact expressions for the finite axial vector form factors, we check the quality and the convergence of expansions at production threshold and for asymptotic energies. | contribution 0.37 | 0.95 | 0.14 | asserted 0.99 |
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The paper
Original abstract
We present closed analytic expressions for the order $\alpha_s^2$ triangle diagram contributions to the matrix elements of the singlet and non-singlet axial vector currents between the vacuum and a quark-antiquark state. We have calculated these vertex functions for arbitrary momentum transfer and for four different sets of internal and external quark masses. We show that both the singlet and non-singlet vertex functions satisfy the correct chiral Ward identities. Using the exact expressions for the finite axial vector form factors, we check the quality and the convergence of expansions at production threshold and for asymptotic energies.
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References
How the literature uses it
32 arXiv papers cite this in 51 sentences
Papers citing it · 29 sentences without a confident label
Contests it 1 paper
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Although we do not present results for the renormalized singlet contributions we like to point out, that we cannot reproduce the result for the singlet axial-vector contribution presented in Ref. [ref] .
The Heavy Quark Form Factors at Two Loops · Results · contest 0.79
Uses its data or values 1 paper
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Its N$^2$LO expression can be extracted from Refs. [ref] , while the logarithmic dependences at third-loop order accuracy can be obtained from the anomalous dimensions.
The $q_T$ and $\Delta\phi$ spectra in W and Z production at the LHC at N$^3$LL'+N$^2$LO · Hard function: non-singlet and singlet contributions · 0.84
Compares with it 3 papers
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We have also confirmed that they correctly describe the IR singularities of the two-loop massive quark form factor calculated in [ref] .
Infrared singularities of QCD amplitudes with massive partons · Two-parton correlations · 0.96
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[ref] and agreement is found.
The complete singlet contribution to the massless quark form factor at three loops in QCD · Results for the finite remainders · 1.00
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At two-loop order we reproduce the massless and massive singlet axial-vector and pseudoscalar results presented in Ref. [ref] .
Massive three-loop form factors: anomaly contribution · Cross checks · 1.00
Cites it as background 13 papers
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A series of papers followed obtaining the two-loop QCD corrections for the vector form factor [ref] , the axial-vector form factor [ref] , the anomaly contributions [ref] and the scalar and pseudo-scalar form factors [ref] .
The Heavy Quark Form Factors at Two Loops · Introduction · 0.84
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Limited to purely massless QCD corrections, the 3-loop results for vector [ref] , scalar [ref] and pseudo-scalar [ref] part of quark FFs were derived in the literature, and there was recently important progress towards the 4-loop corrections to the vector quark FFs [ref] .[We note that massive quark FFs are known to 2-loop order in QCD [ref] , and partially at 3-loop order [ref] .] The three-loop singlet contribution to the axial part of quark FFs in purely massless QCD was determined only very recently in ref.
The complete singlet contribution to the massless quark form factor at three loops in QCD · Introduction · 0.93
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The current state-of-the-art computations in this frontier involve third order QCD $(𝒪(α_s^3))$ corrections [ref] to the HQFF.
Three loop QCD corrections to the heavy-light form factors in the color-planar limit · Introduction · 0.83
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