Direct numerical integration of one-loop Feynman diagrams for N-photon amplitudes
arXiv:0812.3686 · doi:10.1103/PhysRevD.79.033005
Abstract
One approach to the calculation of cross sections for infrared-safe observables in high energy collisions at next-to-leading order is to perform all of the integrations, including the virtual loop integration, by Monte Carlo numerical integration. In a previous paper, two of us have shown how one can perform such a virtual loop integration numerically after first introducing a Feynman parameter representation. In this paper, we perform the integration directly, without introducing Feynman parameters, after suitably deforming the integration contour. Our example is the N-photon scattering amplitude with a massless electron loop. We report results for N = 6 and N = 8.
14 pages with 9 figures
References in corpus (12)
- Reducing full one-loop amplitudes to scalar integrals at the integrand level
- An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
- Full one-loop amplitudes from tree amplitudes
- A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
- Next-to-leading order QCD corrections to t-tbar-Z production at the LHC
- Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
- QCD corrections to tri-boson production
- Numerical Evaluation of Six-Photon Amplitudes
- Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically
- The two-loop QCD amplitude gg -> h,H in the Minimal Supersymmetric Standard Model
- Six-Photon Amplitudes
- NLO QCD corrections to the production of t-tbar-Z in gluon fusion
Cited by in corpus (24)
- OneLOop: for the evaluation of one-loop scalar functions
- SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
- Physics at the e+ e- Linear Collider
- SecDec: A general program for sector decomposition
- Collider Physics at the Precision Frontier
- Loop Tree Duality for multi-loop numerical integration
- NLO results for five, six and seven jets in electron-positron annihilation
- Removing infrared divergences from two-loop integrals
- Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order
- A simple formula for the infrared singular part of the integrand of one-loop QCD amplitudes
- Direct contour deformation with arbitrary masses in the loop
- Integrands of loop amplitudes within loop-tree duality
- Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
- Numerical Computation of Two-loop Box Diagrams with Masses
- Numerical integration of loop integrals through local cancellation of threshold singularities
- Numerical integration of subtraction terms
- Infrared singularities in one-loop amplitudes
- Exposing the threshold structure of loop integrals
- On the vanishing of certain cuts or residues of loop integrals with higher powers of the propagators
- Random polarisations of the dipoles
- Flow-oriented perturbation theory
- Locally finite two-loop amplitudes for electroweak production through gluon fusion
- Direct numerical approach to one-loop amplitudes
- Tropical sampling from Feynman measures