Master integrals for four-loop massless propagators up to weight twelve

@article{Lee2012MasterIF,
  title={Master integrals for four-loop massless propagators up to weight twelve},
  author={R. N. Lee and Alexander Valeryevich Smirnov and Vladimir A. Smirnov},
  journal={Nuclear Physics},
  year={2012},
  volume={856},
  pages={95-110}
}

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References

SHOWING 1-10 OF 43 REFERENCES

Analytic epsilon expansion of three-loop on-shell master integrals up to four-loop transcendentality weight

We evaluate analytically higher terms of the ϵ-expansion of the three-loop master integrals corresponding to three-loop quark and gluon form factors and to the three-loop master integrals

On epsilon expansions of four-loop non-planar massless propagator diagrams

We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter ϵ=(4−d)/2 up to transcendentality weight twelve, using a

Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight

We evaluate analytically higher terms of the epsilon-expansion of the three-loop master integrals corresponding to three-loop quark and gluon form factors and to the three-loop master integrals

Analytic results for massless three-loop form factors

We evaluate, exactly in d, the master integrals contributing to massless threeloop QCD form factors. The calculation is based on a combination of a method recently suggested by one of the authors

The Massless Higher-Loop Two-Point Function

We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph G to evaluate to