Helicity amplitudes for QCD with massive quarks
Alexander Ochirov
TL;DR
This work applies the massive spinor-helicity formalism to QCD with a single massive quark pair and $n-2$ gluons, deriving two all-multiplicity, gauge-invariant color-ordered amplitudes for distinct helicity configurations: all-plus and one-minus adjacent to a quark. The amplitudes are obtained via on-shell BCFW recursion, yielding compact closed-form expressions that smoothly interpolate to the massless limit and reproduce known Parke–Taylor/MHV results as $m\to 0$. Extensive checks include massless-limit analyses, numerical comparisons with six-point Feynman diagrams, and compatibility with BCJ and color-kinematics relations, demonstrating the consistency and utility of the massive spinor-helicity approach. The results pave the way for analytic and efficient tree- and loop-level QCD calculations involving massive quarks within a unifying spinor-helicity framework.
Abstract
The novel massive spinor-helicity formalism of Arkani-Hamed, Huang and Huang provides an elegant way to calculate scattering amplitudes in quantum chromodynamics for arbitrary quark spin projections. In this note we compute two families of tree-level QCD amplitudes with one massive quark pair and n-2 gluons. The two cases include all gluons with identical helicity and one opposite-helicity gluon being color-adjacent to one of the quarks. Our results naturally incorporate the previously known amplitudes for both quark spins quantized along one of the gluonic momenta. In the all-multiplicity formulae presented here the spin quantization axes can be tuned at will, which includes the case of the definite-helicity quark states.