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We study the structure of soft gluon corrections to multi-leg scattering amplitudes in a non-Abelian gauge theory by analysing the corresponding product of semi-infinite Wilson lines. We prove that diagrams exponentiate such that the colour factors in the exponent are fully connected. This completes the generalisation of the non-Abelian exponentiation theorem, previously proven in the case of a Wilson loop, to the case of multiple Wilson lines in arbitrary representations of the colour group. Our proof is based on the replica trick in conjunction with a new formalism where multiple emissions from a Wilson line are described by effective vertices, each having a connected colour factor. The exponent consists of connected graphs made out of these vertices. We show that this readily provides a general colour basis for webs. We further discuss the kinematic combinations that accompany each connected colour factor, and explicitly catalogue all three-loop examples, as necessary for a direct computation of the soft anomalous dimension at this order.
|Journal||Journal of High Energy Physics|
|Publication status||Published - 24 Jun 2013|
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- 2 Finished
Particle Theory at the Tait Institute
Ball, R., Berera, A., Boyle, P., Del Debbio, L., Figueroa-O'Farrill, J., Gardi, E., Horsley, R., Kennedy, A., Kenway, R., Pendleton, B. & Simon Soler, J.
1/10/11 → 30/09/15