On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations

Abstract

An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the extraction of ultraviolet and infrared divergencies. The coefficients of these singularities and the non-singular part can be integrated numerically. However, the numerical integration often does not converge for diagrams with massive propagators and physical branch cuts. In this work, several steps are proposed which substantially improve the behavior of the numerical integrals. The efficacy of the method is demonstrated by calculating several two-loop examples, some of which have not been known before.

13 pp. LaTeX

References in corpus (26)

• An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• Electroweak gauge boson production at hadron colliders through O(alpha_s^2)
• NLO Electroweak Corrections to Higgs Boson Production at Hadron Colliders
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Direct extraction of one-loop integral coefficients
• Full one-loop amplitudes from tree amplitudes
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• Next-to-Leading Order QCD Predictions for W+3-Jet Distributions at Hadron Colliders
• Precise Predictions for W + 3 Jet Production at Hadron Colliders
• Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD
• Golem95: a numerical program to calculate one-loop tensor integrals with up to six external legs
• Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
• Electroweak two-loop corrections to the effective weak mixing angle
• Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
• Heavy-quark production in gluon fusion at two loops in QCD
• Two-Loop Fermionic Corrections to Heavy-Quark Pair Production: the Quark-Antiquark Channel
• Generalized unitarity at work: first NLO QCD results for hadronic W+3jet production
• Heavy-quark production in massless quark scattering at two loops in QCD
• Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel
• Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically
• One-loop amplitudes for W+3 jet production in hadron collisions
• Bosonic Corrections to The Effective Weak Mixing Angle at O(alpha^2)
• Two-loop electroweak fermionic corrections to sin^2 theta_{eff}^{b anti-b}
• The effective electroweak mixing angle ${\sin }^2{\theta }_{eff}$ with two-loop bosonic contributions
• Combining Monte Carlo generators with next-to-next-to-leading order calculations: event reweighting for Higgs boson production at the LHC

Cited by in corpus (13)

• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0
• The two-loop electroweak bosonic corrections to ${\sin }^2{\theta }_{\mathrm{eff}}^{\mathrm{b}}$
• Geometrical approach to causality in multi-loop amplitudes
• Quantum algorithm for Feynman loop integrals
• Numerical multi-loop integrals and applications
• Efficient Evaluation of Massive Mellin--Barnes Integrals
• New prospects for the numerical calculation of Mellin-Barnes integrals in Minkowskian kinematics
• Numerical evaluation of multi-loop integrals using subtraction terms
• A novel approach to the computation of one-loop three- and four-point functions. I -- The real mass case
• A novel approach to the computation of one-loop three- and four-point functions. II - The complex mass case
• Framework for a novel mixed analytical/numerical approach for the computation of two-loop $N$-point Feynman diagrams
• Two-loop scalar functions with $I$ internal lines, $I\le 5$