Getting a number out of a QCD amplitude

Ryan Moodie

16 Dec 2020

Outline

Aim

Aim

Tree level

Helicity sum

Diagram sum

Colour sum

Recursion

Spinor helicity

Amplitude squared

Higher order corrections

Next-to-Leading-Order

Cross-section

Infrared divergences

Subtraction scheme

Loops

Algebraic

  • Integrand reduction
  • Coefficients
    • Generalised unitarity
    • OPP
  • Master integrals
    • Integration-by-parts identities
    • Laporta

Analytic

  • Polylogarithms
  • Laurent expansion

Computation

Techniques

  • Large intermediate numbers
    • Finite fields
      • Momentum twistor variables
  • High performance
    • FORM
    • C++

Overview

Overview

  • Calculation organisation
  • Infrared regulation
  • Loop reduction
  • Computation

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