Six-Quark Amplitudes from Fermionic MHV Vertices

TL;DR

Problem addressed: validate the fermionic extension of the CSW (MHV) approach by computing six-quark QCD amplitudes with three quark–antiquark pairs. The method: use an extended CSW framework with fermionic MHV vertices, off-shell continuation, and fermion propagators to assemble all relevant diagrams. The main result: the purely fermionic amplitudes obtained from CSW precisely match those from standard Feynman rules (up to an overall phase) for the considered helicity configurations. The work reinforces the consistency of CSW rules in non-MHV fermionic sectors and clarifies the role of diagrammatic structures.

Abstract

The fermionic extension of the CSW approach to perturbative gauge theory coupled with fermions is used to compute the six-quark QCD amplitudes. We find complete agreement with the results obtained by using the usual Feynman rules.

Figures (4)

• 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 CSW diagrams contributing to the purely fermionic amplitude with 3 quark-antiquark pairs. In these diagrams $i$ can take $1,2,3$ and the indices are understood as mod $3$. So totally there are $6$ diagrams.
• Figure 4: The 2 different kinds of Feynman diagrams contributing to the purely fermionic amplitude with 3 quark-antiquark pairs. In the left diagram $j$ can take $1,2,3$ and the indices are understood as mod $3$. So totally there are $4$ diagrams.