Efficient Evaluation of Massive Mellin--Barnes Integrals

Abstract

We show how to evaluate one-dimensional Minkowski-region Mellin-Barnes representations arising from massive loop integrals, by modifying the contours of integration. We implement an exact solution to the differential equation determining the contours of stationary phase. We also present several simple approximations to these contours. Our approach points the way to more efficient computations of massless and massive Mellin-Barnes integrals in both Euclidean and Minkowski regions.

53 pages, 32 figures

References in corpus (19)

• Collier: a fortran-based Complex One-Loop LIbrary in Extended Regularizations
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• OneLOop: for the evaluation of one-loop scalar functions
• Quark and gluon form factors to three loops
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Numerical NLO QCD calculations
• The two-loop electroweak bosonic corrections to ${\sin }^2{\theta }_{\mathrm{eff}}^{\mathrm{b}}$
• Numerical Evaluation of Tensor Feynman Integrals in Euclidean Kinematics
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• The QCD form factor of heavy quarks at NNLO
• Virtual Hadronic and Leptonic Contributions to Bhabha Scattering
• Master integrals for the two-loop penguin contribution in non-leptonic B-decays
• A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the doubly unresolved subtraction terms
• Numerical multi-loop integrals and applications
• Virtual Hadronic and Heavy-Fermion O(alpha^2) Corrections to Bhabha Scattering
• An Analytic Approach to Sunset Diagrams in Chiral Perturbation Theory: Theory and Practice
• Numerical evaluation of multi-loop integrals using subtraction terms

Cited by in corpus (13)

• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Collider Physics at the Precision Frontier
• A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec
• The two-loop electroweak bosonic corrections to ${\sin }^2{\theta }_{\mathrm{eff}}^{\mathrm{b}}$
• Determine Arbitrary Feynman Integrals by Vacuum Integrals
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Mellin-Barnes meets Method of Brackets: A novel approach to Mellin-Barnes representations of Feynman integrals
• A novel approach to the computation of one-loop three- and four-point functions. I -- The real mass case
• Asymptotics of the contour of the stationary phase and efficient evaluation of the Mellin-Barnes integral for the F_3 structure function
• 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
• Multi-loop calculations: numerical methods and applications
• Two-loop scalar functions with $I$ internal lines, $I\le 5$