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

S. Abreu, F. Febres Cordero, H. Ita, M. Jaquier, B. Page, M. Zeng

TL;DR

The first numerical computation of two-loop amplitudes based on the unitarity method is presented, and the four-gluon process in the leading-color approximation is computed.

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.

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

TL;DR

The first numerical computation of two-loop amplitudes based on the unitarity method is presented, and the four-gluon process in the leading-color approximation is computed.

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.

Paper Structure

This paper contains 11 equations, 3 figures.

Figures (3)

  • Figure 1: The hierarchy of propagator structures for planar four-point two-loop gluon amplitude. Only topologically inequivalent structures are shown.
  • Figure 2: Displayed are the conventions for assigning propagators in a two-loop diagrams.
  • Figure 3: Distribution of minus the base 10 logarithm of the relative error for the numerical calculation with respect to the analytic result, over 10,000 phase-space points. The distribution corresponds to the finite ${\cal O}(\epsilon^0)$ contribution. The left plot is for the $(1_g^-,2_g^+,3_g^-,4_g^+)$ helicity configuration, and the right plot for $(1_g^-,2_g^-,3_g^+,4_g^+)$.