MHV Vertices and Fermionic Scattering Amplitudes in Gauge Theory with Quarks and Gluinos

TL;DR

This work extends the Cachazo–Svrcek–Witten (CSW) framework to gauge theories containing quarks and gluinos by introducing fermionic MHV vertices and extending color decomposition. It computes googly amplitudes with one or two quark–antiquark pairs and with gluinos, deriving compact, explicit formulas that agree with known results and illustrating how non-MHV fermionic amplitudes can be obtained within the extended CSW rules. The paper also analyzes purely fermionic 3-pair amplitudes and discusses the implications for tree-level amplitudes in QCD-like and supersymmetric theories. Overall, the results demonstrate the robustness of the CSW approach in handling fermionic matter and SUSY partners, linking to twistor-space ideas and broadening the scope of perturbative amplitudes that can be efficiently computed.

Abstract

The Cachazo-Svrcek-Witten approach to perturbative gauge theory is extended to gauge theories with quarks and gluinos. All googly amplitudes with quark-antiquark pairs and gluinos are computed and shown to agree with the previously known results. The computations of the non-MHV or non-googly amplitudes are also briefly discussed, in particular the purely fermionic amplitude with 3 quark-antiquark pairs.

Figures (21)

• Figure 1: The graphic representation for the single pair of quark-antiquark partial amplitude. Gluons are emitted from one side of the fermion line only.
• Figure 2: The 2 MHV vertices with quark-antiquarks.
• Figure 3: The 2 different kinds of diagrams contributing to the purely fermionic amplitude with 3 quark-antiquark pairs.
• Figure 4: The decomposition for the off shell amplitude with one quark-antiquark pair when the gluons are all with positive helicities and the quark is off-shell.
• Figure 5: This diagram is characterized with $g_i$ attaching to a 3-gluon MHV vertex. $g_{i-1}$'s are disconnected from the fermion line by this vertex.