Unitarity via Quantum Off-Shell Recursions

Abstract

The challenge of accurately calculating differential cross-sections in QCD and the Standard Model has many applications, especially in analysing data from particle accelerators such as the LHC. The efficiency of traditional methods of cross-section calculation can be improved by bypassing some tedious intermediate steps and in order to do so we propose a new application of the quantum off-shell recursion framework in conjunction with the Largest Time Equation. We intend to use unitarity of the S-matrix to obtain higher point tree order cross-sections from lower point loop order amplitudes. We first review the quantum off-shell recursion framework with a pedagogical calculation in 𝜙4 theory. We then introduce a field-doubling prescription for 𝜙4 theory which when used in conjunction with the recursion framework allows us to exhibit unitarity explicitly. We finally obtain a proof-of-concept by deriving the tree order 6-point cross-section in the regular 𝜙4 theory from the 3-loop order 4-point amplitude in the field-doubled 𝜙4 theory.