Deriving CSW rules for massive scalar legs and pure Yang-Mills loops

TL;DR

This paper derives Cachazo-Svrcek-Witten (CSW) rules for massive scalars and pure Yang-Mills loops using two methods, enabling simplified calculations of scattering amplitudes and exploring their extensions to effective Higgs couplings.

Contribution

It provides two complementary derivations of CSW rules for massive scalars and Yang-Mills loops, and extends these rules to effective Higgs couplings, enhancing computational techniques in gauge theories.

Findings

Derived CSW rules for massive scalar legs.

Explicitly showed equivalence of field transformations in both derivations.

Commented on applications to one-loop pure glue amplitudes.

Abstract

This article provides two complementary detailed derivations of Cachazo-Svrcek-Witten-style Feynman rules for Yang-Mills gauge theory coupled to a massive coloured scalar as presented in earlier work. These proceed through a direct canonical transformation method on space-time and through a gauge transformation in an action constructed on twistor space. It is shown explicitly that the field transformations are identical in both cases. Some simple tree-level examples of our rules are given and we comment on the application of them to the calculation of the rational part of one-loop pure glue amplitudes. A possible direct quantum completion of pure glue CSW rules based on dimensional regularisation motivated by these results is sketched. Finally, it is shown how to derive CSW rules for effective Higgs-gluon and Higgs-matter couplings proposed in the literature directly from the action. This derivation yields additional towers of vertices which generate a subset of the contributions to effective multi-Higgs scattering amplitudes.