Boundary Contributions Using Fermion Pair Deformation

TL;DR

The paper studies boundary contributions in the boundary BCFW recursion for tree-level amplitudes, focusing on fermion-pair deformation. It develops a general strategy for isolating boundary terms and demonstrates it in standard QCD and a deformed QCD with an anomalous magnetic moment. It also extends BCFW recursion to off-shell gluon currents, necessitating summation over four helicity states due to gauge dependence, and validates the equivalence with on-shell two-gluon deformations. The results provide a practical framework for handling nonvanishing boundary contributions in gauge theories and effective operators.

Abstract

Continuing the study of boundary BCFW recursion relation of tree level amplitudes initiated in \cite{Feng:2009ei}, we consider boundary contributions coming from fermion pair deformation. We present the general strategy for these boundary contributions and demonstrate calculations using two examples, i.e, the standard QCD and deformed QCD with anomalous magnetic momentum coupling. As a by-product, we have extended BCFW recursion relation to off-shell gluon current, where because off-shell gluon current is not gauge invariant, a new feature must be cooperated.

Figures (4)

• Figure 1: A graphic description for the off-shell recursion relation of gluon current [Fig:division-m]
• Figure 2: Two parts in the recursion relation of off-shell gluon current [Fig:division-22]
• Figure 3: The $z$-flux in the gluon current encountering all 3-vertices
• Figure 4: A graphic description for the boundary term.