Abstract
Berends-Giele currents are fundamental building blocks for on-shell amplitudes in non-abelian gauge theory. We present a novel procedure to construct them using the Bern-Kosower formalism for one-loop gluon amplitudes. Applying the pinch procedure of that formalism to a suitable special case the currents are naturally obtained in terms of multi-particle fields and obeying colour-kinematics duality. As a feedback to the Bern-Kosower formalism we outline how the multi-particle polarisations and field-strength tensors can be used to significantly streamline the pinch procedure.
Highlights
In non-Abelian gauge theory, the nonlinearity of the Yang-Mills gauge transformations tends to make it difficult to write n-gluon amplitudes in a way that would make the gauge Ward identities transparent
We present a novel procedure to construct Yang-Mills Berends-Giele currents from the Bern-Kosower formalism for one-loop gluon amplitudes
We have presented a novel method of constructing Berends-Giele currents using the information on these contained in the pinch procedure of the Bern-Kosower formalism
Summary
In non-Abelian gauge theory, the nonlinearity of the Yang-Mills gauge transformations tends to make it difficult to write n-gluon amplitudes in a way that would make the gauge Ward identities transparent (see [1] and references therein). We will use the Bern-Kosower formalism to develop a simple and direct method to construct the currents in the BCJ gauge This formalism was originally derived using the field-theory limit of string amplitudes [15,16,17], and led to a set of rules that allows one to directly write down Feynman-Schwinger type parameter integrals for the one-loop on-shell n-gluon matrix elements. The general structure of the resulting integrands was studied by Strassler [18,19] in the framework of the worldline formalism, an alternative approach to perturbation theory that to some extent mimics string perturbation theory (for reviews see [20,21]) He found that the partial integration procedure naturally leads to the appearance of “Lorentz products cycles” Zkði of gluon field.
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