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The Two-Loop Master Integrals for $q \bar{q} \to V V$

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arxiv 1404.4853 v2 pith:GVEO5OKG submitted 2014-04-18 hep-ph hep-th

Thomas Gehrmann , Andreas von Manteuffel , Lorenzo Tancredi , Erich Weihs This is my paper · ORCID
classification hep-phhep-th
keywords integralstwo-loopallowcomputeemployingfunctionsmasterresults
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes for vector boson pair production at hadron colliders, $q \bar{q} \to V V$, and thus to compute this process to next-to-next-to-leading order accuracy in QCD. The master integrals are derived using the method of differential equations, employing a canonical basis for the integrals. We obtain analytical results for all integrals, expressed in terms of multiple polylogarithms. We optimize our results for numerical evaluation by employing functions which are real valued for physical scattering kinematics and allow for an immediate power series expansion.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Analytic two-loop amplitudes for $q\bar{q}\to \gamma \gamma$ and $gg \to \gamma \gamma$ mediated by a heavy-quark loop

    hep-ph 2025-01 accept novelty 8.0 of 10

    The two-loop amplitudes for q qbar -> gamma gamma and gg -> gamma gamma with a heavy-quark loop are computed analytically in terms of elliptic iterated integrals, with validated fast series expansions for numerical ev...

  2. Dihadron Angular Correlations in the $e^+e^-$ Collision

    hep-ph 2025-06 conditional novelty 7.0 of 10

    The paper derives the first complete O(alpha_s^2) analytic QCD corrections to the dihadron angular separation distribution in e+e- annihilation, with verified cancellation of infrared poles.

  3. All planar three-loop Feynman integrals for the production of two vector bosons at hadron colliders

    hep-ph 2025-12 accept novelty 6.0 of 10

    All nine planar three-loop four-point integral families for two massive external legs are cast into canonical differential equations and evaluated numerically, completing the set needed for leading-colour N3LO diboson...

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