Numerical Multi-Loop Calculations via Finite Integrals and One-Mass EW-QCD Drell-Yan Master Integrals

Abstract

We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the $\alpha {\alpha }_s$ corrections to Drell-Yan lepton production with up to one massive vector boson in physical kinematics. As a reference, we evaluate these planar and non-planar integrals by the method of differential equations through to weight five. Choosing a basis of finite integrals for the numerical evaluation with SecDec3 leads to tremendous performance improvements and renders the otherwise problematic seven-line topologies numerically accessible. As another example, basis integrals for massless QCD three loop form factors are evaluated with FIESTA4. Here, employing a basis of finite integrals results in an overall speedup of more than an order of magnitude.

24 pages, 1 figure, 4 tables, 2 ancillary files with analytical results; in v2: minor improvements in the text with additional references added. v2 is the version published in JHEP

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• Mixed QCD-electroweak corrections to W-boson production in hadron collisions
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• Accurate simulation of W, Z and Higgs boson decays in Sherpa
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• Master Integrals for the two-loop, non-planar QCD corrections to top-quark pair production in the quark-annihilation channel
• Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors
• Effective observables for electromagnetic duality from novel amplitude decomposition
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• Computational challenges for multi-loop collider phenomenology
• Renormalized $\epsilon$-finite master integrals and their virtues: the three-loop self energy case
• Master integrals for mixed QCD-QED corrections to charged-current Drell-Yan production of a massive charged lepton
• On the two-loop amplitude for $gg\to ZZ$ production with full top-mass dependence
• Mixed QCD-electroweak corrections to dilepton production at the LHC in the high invariant mass region
• The integrand form of infrared singularities of two-loop QCD scattering amplitudes
• Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics