Berends-Giele currents for higher derivative gauge theories

Abstract

We derive Berends-Giele (BG) currents for higher derivative scalar QED (HDQED) and Yang-Mills (HDYM). In HDQED, we first compute the propagators and the vertices from the higher derivative Lagrangian and discuss the pole structures of the photon and the scalar. We then compute the BG currents using the Feynman diagram setup and prove the Ward identities for these currents at two and three points. Next, we used the perturbiner formalism to re-compute these currents and show that they are consistent with the Feynman diagram approach. In a similar fashion, we derive the BG currents in higher derivative Yang-Mills and find that remarkably, these currents are equal to pure Yang-Mills currents when all external on-shell legs are massless gluons. We prove this in all generality using the BG recursion and explicitly show this at lower points. However, the genuine higher derivative structure enters when one or many on-shell states are the so called massive Merlin modes. Using the multi-particle currents, we reproduce the result that all tree level amplitudes with one Merlin particle vanishes and the three and four Merlin amplitudes match the previously computed result. The future prospects of BG recursion for higher derivative gravity and off-shell colour- kinematics duality is also discussed.