Abstract
We perform a canonical transformation of fields that brings the Yang-Mills action in the light-cone gauge to a new classical action, which does not involve any triple-gluon vertices. The lowest order vertex is the four-point MHV vertex. Higher point vertices include the MHV and overline{mathrm{MHV}} vertices, that reduce to the corresponding amplitudes in the on-shell limit. In general, any n-leg vertex has 2 ≤ m ≤ n − 2 negative helicity legs. The canonical transformation of fields can be compactly expressed in terms of path-ordered exponentials of fields and their functional derivative. We apply the new action to compute several tree-level amplitudes, up to 8-point NNMHV amplitude, and find agreement with the standard methods. The absence of triple-gluon vertices results in fewer diagrams required to compute amplitudes, when compared to the CSW method and, obviously, considerably fewer than in the standard Yang-Mills action.
Highlights
The subject of interest of the following work are scattering amplitudes, in particular the pure gluonic amplitudes
A interesting example of the BCFW method is when the only type of amplitudes used are the maximally helicity violating (MHV) amplitudes [8]. This type of recursion has been found earlier based on the twistor space formulation of quantum field theory by Cachazo, Svrcek and Witten (CSW) [9], who suggested that the MHV amplitudes continued off-shell are really the multileg vertices
The field transformation can be most derived as a subsequent canonical transformation of the anti-self-dual part of the MHV action, but we discuss a direct link between the new action and the Yang-Mills action
Summary
Motivated by our earlier results [26, 27], we look for a new set of classical fields describing scattering processes with gluons in the simplest possible way. We shall present more details on the implication of the transformation given by (2.6) and the exact form of the vertices in the new action. Inserting the solutions (2.10)–(2.11) to the Yang-Mills action (2.3), we find the following structure of the new action: SY(L−CM) [Z, Z ] = dx+ − d3x Tr Z Z. where the n-point interaction vertex, n ≥ 4, that couples m minus helicity fields, m ≥ 2, and n − m plus helicity fields, has the following general form: L(−LC·)· · − + · · · + =. Because the lowest vertex is the single MHV four-point vertex that corresponds to the four-gluon MHV amplitude in the on-shell limit, the new action provides an efficient way to construct tree amplitudes with high multiplicity of legs, as we will demonstrate later in section 3 by computing several examples
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