Integrands for QCD rational terms and N=4 SYM from massive CSW rules

TL;DR

This paper derives explicit integrands for rational terms in QCD and N=4 SYM using massive CSW rules, providing new recursive methods and ensuring independence from reference spinors, advancing computational techniques in gauge theories.

Contribution

It introduces compact integrand expressions for QCD rational terms and a recursive derivation of massive CSW vertex expansion for N=4 SYM, with proofs of boundary terms and supersymmetry preservation.

Findings

Explicit all-n integrands for QCD one-loop amplitudes

Systematic extraction of spurious external-bubble contributions

Recursive derivation of massive CSW vertex expansion for N=4 SYM

Abstract

We use massive CSW rules to derive explicit compact expressions for integrands of rational terms in QCD with any number of external legs. Specifically, we present all-n integrands for the one-loop all-plus and one-minus gluon amplitudes in QCD. We extract the finite part of spurious external-bubble contributions systematically; this is crucial for the application of integrand-level CSW rules in theories without supersymmetry. Our approach yields integrands that are independent of the choice of CSW reference spinor even before integration. Furthermore, we present a recursive derivation of the recently proposed massive CSW-style vertex expansion for massive tree amplitudes and loop integrands on the Coulomb-branch of N=4 SYM. The derivation requires a careful study of boundary terms in all-line shift recursion relations, and provides a rigorous (albeit indirect) proof of the recently proposed construction of massive amplitudes from soft-limits of massless on-shell amplitudes. We show that the massive vertex expansion manifestly preserves all holomorphic and half of the anti-holomorphic supercharges, diagram-by-diagram, even off-shell.