Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method

Abstract

We present the first numerical computation of two-loop amplitudes based on the unitarity method. As a proof of principle, we compute the four-gluon process. We discuss the new method, analyze its numerical properties and apply it to reconstruct the analytic form of the amplitudes. The numerical method is universal, and can be automated to provide multi-scale two-loop computations for phenomenologically relevant signatures at hadron colliders.

6 pages, 3 figures, Mathematica files for reconstructed analytic formulae

References in corpus (12)

• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• Algorithm FIRE -- Feynman Integral REduction
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• FIRE5: a C++ implementation of Feynman Integral REduction
• Full one-loop amplitudes from tree amplitudes
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• Precise Predictions for W + 4 Jet Production at the Large Hadron Collider
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• Subleading Poles in the Numerical Unitarity Method at Two Loops
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• Lecture Notes on Multi-loop Integral Reduction and Applied Algebraic Geometry

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