String-inspired representations of photon/gluon amplitudes

TL;DR

This paper introduces a systematic integration-by-parts algorithm for string-inspired photon and gluon amplitude calculations, enhancing gauge invariance and efficiency in off-shell QCD and string theory contexts.

Contribution

The authors develop a gauge-invariant IBP algorithm applicable to arbitrary N, optimizing the integrand for one-loop photon and gluon amplitudes in QCD and string theory.

Findings

Achieves manifest transversality in photon amplitudes.

Naturally decomposes gluon amplitudes into transversal and longitudinal parts.

Provides an efficient off-shell Green's function calculation method.

Abstract

The string-based Bern-Kosower rules provide an efficient way for obtaining parameter integral representations of the one-loop N - photon/gluon amplitudes involving a scalar, spinor or gluon loop, starting from a master formula and using a certain integration-by-parts (`IBP') procedure. Strassler observed that this algorithm also relates to gauge invariance, since it leads to the absorption of polarization vectors into field strength tensors. Here we present a systematic IBP algorithm that works for arbitrary N and leads to an integrand that is not only suitable for the application of the Bern-Kosower rules but also optimized with respect to gauge invariance. In the photon case this means manifest transversality at the integrand level, in the gluon case that a form factor decomposition of the amplitude into transversal and longitudinal parts is generated naturally by the IBP, without the necessity to consider the nonabelian Ward identities. Our algorithm is valid off-shell, and provides an extremely efficient way of calculating the one-loop one-particle-irreducible off-shell Green's functions (`vertices') in QCD. It can also be applied essentially unchanged to the one-loop gauge boson amplitudes in open string theory. In the abelian case, we study the systematics of the IBP also for the practically important case of the one-loop N - photon amplitudes in a constant field.