# Two-loop master integrals for $q\overline{q}\to VV$ : the planar topologies

Gehrmann, Thomas; Tancredi, Lorenzo; Weihs, Erich (2013). Two-loop master integrals for $q\overline{q}\to VV$ : the planar topologies. Journal of High Energy Physics, 2013(8):1-52.

## Abstract

The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master integrals by solving linear relations among them. We then use differential equations in the external invariants to compute all master integrals that are relevant to planar Feynman amplitudes. Our results are expressed analytically in terms of generalized harmonic polylogarithms. The calculation relies heavily on techniques that exploit the algebraic structure of these functions, which we describe in detail.

The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master integrals by solving linear relations among them. We then use differential equations in the external invariants to compute all master integrals that are relevant to planar Feynman amplitudes. Our results are expressed analytically in terms of generalized harmonic polylogarithms. The calculation relies heavily on techniques that exploit the algebraic structure of these functions, which we describe in detail.

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18 citations in Web of Science®
19 citations in Scopus®

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Physics Institute 530 Physics English June 2013 05 Sep 2013 06:11 05 Apr 2016 16:58 Springer 1029-8479 The final publication is available at link.springer.com Publisher DOI. An embargo period may apply. https://doi.org/10.1007/JHEP08(2013)070
Permanent URL: https://doi.org/10.5167/uzh-80702