One-Loop Helicity Amplitudes for ttbar Production at Hadron Colliders

TL;DR

This work delivers compact analytic expressions for all one-loop helicity amplitudes relevant to ttbar production at hadron colliders by combining generalized unitarity with traditional Feynman diagram techniques. It introduces a colour-ordered primitive amplitude framework for massive quarks in the gg and qqbar channels, and applies a spinor-helicity formalism tailored to massive states, enabling fast, spin-correlated computations. The authors provide detailed constructions of scalar integral coefficients, rational terms, and renormalisation in FDH with HV cross-checks, and validate their results against existing literature while demonstrating significant computational efficiency. The study также reveals simplifications in sub-leading colour contributions and establishes a robust, extensible basis for higher-multiplicity amplitudes and NNLO-like virtual corrections.

Abstract

We present compact analytic expressions for all one-loop helicity amplitudes contributing to ttbar production at hadron colliders. Using recently developed generalised unitarity methods and a traditional Feynman based approach we produce a fast and flexible implementation.

Figures (5)

• Figure 1: The 7 cut diagrams contributing to the left-moving primitive amplitude in $gg\to t{\bar{t}}$. Red dotted lines represent massive fermions, plain lines represent gluons.
• Figure 2: The 7 cut diagrams contributing to the right-moving primitive amplitude in $gg\to t{\bar{t}}$. Red dotted lines represent massive fermions, plain lines represent gluons.
• Figure 3: The 7 cut diagrams contributing to the sub-leading colour primitive amplitude in $gg\to t{\bar{t}}$. Red dotted lines represent massive fermions, plain lines represent gluons. amplitude.
• Figure 4: The 7 cut diagrams contributing to the leading colour primitive amplitude in $q{\bar{q}}\to t{\bar{t}}$. Red dotted lines represent massive fermions, plain lines represent gluons and blue dotted lines represent massless fermions.
• Figure 5: The 4 cut diagrams contributing to the sub-leading colour primitive amplitude in $q{\bar{q}}\to t{\bar{t}}$. Red dotted lines represent massive fermions, plain lines represent gluons and blue dotted lines represent massless fermions.