Massive two-loop four-point Feynman integrals at high energies with AsyInt

Abstract

We present analytic techniques for parametric integrations of massive two-loop four-point Feynman integrals at high energies, and their implementation in the toolbox AsyInt. In the high-energy region, the Feynman integrals involving external and internal massive particles, such as the top quark, Higgs and vector bosons, can be asymptotically expanded and directly calculated in the small-mass limit. With this approach, analytic results for higher-order terms in the expansion parameter and the dimensional regulator can be obtained with AsyInt. These results are important ingredients for the two-loop electroweak and QCD corrections for $2\to 2$ scattering processes in the large transverse momenta region, which is relevant to both precision collider phenomenology and new physics searches at current and future high-energy colliders. In this paper, analytic results of representative planar and non-planar Feynman integrals are presented.

arXiv commentAsyInt v.1.0 is publicly available at: https://gitlab.com/asyint/asyint-public

References in corpus (57)

• Harmonic Polylogarithms
• Multiloop integrals in dimensional regularization made simple
• Asymptotic expansion of Feynman integrals near threshold
• Differential Equations for Two-Loop Four-Point Functions
• An automatized algorithm to compute infrared divergent multi-loop integrals
• Harmonic sums, Mellin transforms and Integrals
• Automatized analytic continuation of Mellin-Barnes integrals
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• Higgs production and decay: Analytic results at next-to-leading order QCD
• AMFlow: a Mathematica package for Feynman integrals computation via Auxiliary Mass Flow
• Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
• SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
• A Systematic and Efficient Method to Compute Multi-loop Master Integrals
• Full top quark mass dependence in Higgs boson pair production at NLO
• Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD
• Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• Gluon fusion into Higgs pairs at NLO QCD and the top mass scheme
• Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism
• The singular behavior of massive QCD amplitudes
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
• Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5
• Two-loop QED corrections to Bhabha scattering
• Geometric approach to asymptotic expansion of Feynman integrals
• Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
• Two-Loop Photonic Corrections to Massive Bhabha Scattering
• Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box
• An Analytical Method for the NLO QCD Corrections to Double-Higgs Production
• Iterated Binomial Sums and their Associated Iterated Integrals
• Double Higgs boson production at NLO in the high-energy limit: complete analytic results
• Solving differential equations for Feynman integrals by expansions near singular points
• Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction
• Simplifying differential equations for multi-scale Feynman integrals beyond multiple polylogarithms
• Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams
• FeynGame
• Massive vector form factors to three loops
• On Genera of Curves from High-loop Generalized Unitarity Cuts
• Two-loop $gg\to Hg$ amplitude mediated by a nearly massless quark
• Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers
• Multiple Series Representations of $N$-fold Mellin-Barnes Integrals
• Higgs boson contribution to the leading two-loop Yukawa corrections to $gg\to HH$
• Next-to-leading order electroweak corrections to $gg\to HH$ and $gg\to gH$ in the large-$m_t$ limit
• A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $\overline{\mathrm{MS}}$-pole quark mass relation
• Virtual corrections to $gg\to ZH$ in the high-energy and large-$m_t$ limits
• High-Energy Expansion of Two-Loop Massive Four-Point Diagrams
• Analytic approximations of $2\to 2$ processes with massive internal particles
• MB Tools reloaded
• Electroweak corrections to double Higgs production at the LHC
• Two-Loop Electroweak Corrections with Fermion Loops to $e^{+}{e}^{-}\to ZH$
• Massive two-loop four-point Feynman integrals at high energies with AsyInt
• Master Integrals for Electroweak corrections to $gg\to \gamma \gamma$ -- Light quark contributions

Cited by in corpus (1)

• Massive two-loop four-point Feynman integrals at high energies with AsyInt