Although developed for pure gluon scattering, extensions exist for massive particles, scalars (the Higgs) and for fermions (quarks and their interactions in QCD).
Such amplitudes are known as "maximally helicity violating" and have an extremely simple form in terms of momentum bilinears, independent of the number of gluons present: The compactness of these amplitudes makes them extremely attractive, particularly for data taking at the LHC, for which it is necessary to remove the dominant background of standard model events.
[2] The MHV were given a geometrical interpretation using Witten's twistor string theory[3] which in turn inspired a technique of "sewing" MHV amplitudes together (with some off-shell continuation) to build arbitrarily complex tree diagrams.
[4] The CSW rules can be generalised to the quantum level by forming loop diagrams out of MHV vertices.
[6] The LCYM Lagrangrian has the following helicity structure: The transformation involves absorbing the non-MHV three-point vertex into the kinetic term in a new field variable: When this transformation is solved as a series expansion in the new field variable, it gives rise to an effective Lagrangian with an infinite series of MHV terms:[7] The perturbation theory of this Lagrangian has been shown (up to the five-point vertex) to recover the CSW rules.
Moreover, the missing amplitudes which plague the CSW approach turn out to be recovered within the MHV Lagrangian framework via evasions of the S-matrix equivalence theorem.
[8] An alternative approach to the MHV Lagrangian recovers the missing pieces mentioned above by using Lorentz-violating counterterms.