# Calculation of the quark and gluon form factors to three loops in QCD

@article{Gehrmann2010CalculationOT, title={Calculation of the quark and gluon form factors to three loops in QCD}, author={Thomas Gehrmann and E. W. N. Glover and Tobias Huber and N. Ikizlerli and C. Studerus}, journal={Journal of High Energy Physics}, year={2010}, volume={2010}, pages={1-64} }

We describe the calculation of the three-loop QCD corrections to quark and gluon form factors. The relevant three-loop Feynman diagrams are evaluated and the resulting three-loop Feynman integrals are reduced to a small set of known master integrals by using integration-by-parts relations. Our calculation confirms the recent results by Baikov et al. for the three-loop form factors. In addition, we derive the subleading $$ \mathcal{O}\left( \varepsilon \right) $$ terms for the fermion-loop type… Expand

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#### References

SHOWING 1-10 OF 149 REFERENCES

Three-loop results for quark and gluon form-factors

- Physics
- 2005

Abstract We study the photon–quark–quark and Higgs–gluon–gluon form factors for on-shell massless quarks and gluons in perturbative QCD. Previous third-order results for the quark case are extended… Expand

Two-loop quark and gluon form factors in dimensional regularisation

- Physics
- 2005

Abstract We compute the two-loop corrections to the massless quark form factor γ ∗ → q q ¯ and gluon form factor H → g g to all orders in the dimensional regularisation parameter e = ( 4 − d ) / 2 .… Expand

The quark form factor at higher orders

- Physics
- 2005

We study the electromagnetic on-shell form factor of quarks in massless perturbative QCD. We derive the complete pole part in dimensional regularization at three loops, and extend the resummation of… Expand

Large Perturbative Corrections to the Drell-Yan Process in QCD

- Physics
- 1979

The total cross section dσdQ2 for the production of a muon pair of invariant mass Q2 via the Drell-Yan mechanism and the Feynman xF differential cross section d2σdQ2dxF are calculated in QCD… Expand

The Three-loop splitting functions in QCD: The Singlet case

- Physics
- 2004

Abstract We compute the next-to-next-to-leading order (NNLO) contributions to the three splitting functions governing the evolution of unpolarized non-singlet combinations of quark densities in… Expand

Higher-order soft corrections to lepton pair and Higgs boson production

- Physics
- 2005

Abstract Utilizing recent three-loop results on the quark and gluon splitting functions and form factors, we derive the complete threshold-enhanced third-order (N 3 LO) QCD corrections to the total… Expand

Master integrals for fermionic contributions to massless three-loop form-factors

- Physics
- 2008

In this letter we continue the calculation of master integrals for massless three-loop form factors by giving analytical results for those diagrams which are relevant for the fermionic contributions… Expand

Quark and gluon form factors to three loops.

- Physics, Medicine
- Physical review letters
- 2009

This is the first calculation of complete three-loop vertex corrections within massless perturbative quantum chromodynamics and provides building blocks for many third-order cross sections. Expand

Resummation of Threshold Logarithms in Effective Field Theory for DIS, Drell-Yan and Higgs Production

- Physics
- 2006

We apply the effective field theoretic (EFT) approach to resum the large perturbative logarithms arising when partonic hard scattering cross sections are taken to the threshold limit. We consider… Expand

Two-loop anomalous-dimension matrix for soft-gluon exchange.

- Physics, Medicine
- Physical review letters
- 2006

The proportionality of the one- and two-loop matrices makes possible the resummation in closed form of the next-to-next- to-leading logarithms and poles in dimensional regularization for the 2-->n processes. Expand