On-shell recursion relations for all Born QCD amplitudes

TL;DR

The paper generalizes on-shell recursion to all Born QCD amplitudes with gluons and both massless and massive quarks. It introduces holomorphic and anti-holomorphic two-particle spinor shifts, proves the shifted amplitude A(z) vanishes as z → ∞ under specified conditions, and derives a recursion relation that expresses n-point amplitudes as sums over lower-point on-shell subamplitudes. It provides explicit, compact results for amplitudes with a pair of massive quarks and many positive-helicity gluons, including connections to massive-scalar Ward identities, and shows how pure massive-quark amplitudes require three-particle shifts. The work offers a practical framework for efficient QCD amplitude calculations relevant to collider phenomenology, with broad applicability to Standard Model processes at high energies.

Abstract

We consider on-shell recursion relations for all Born QCD amplitudes. This includes amplitudes with several pairs of quarks and massive quarks. We give a detailed description on how to shift the external particles in spinor space and clarify the allowed helicities of the shifted legs. We proof that the corresponding meromorphic functions vanish at z --> infinity. As an application we obtain compact expressions for helicity amplitudes including a pair of massive quarks, one negative helicity gluon and an arbitrary number of positive helicity gluons.