The non-Abelian exponentiation theorem for multiple Wilson lines

Abstract

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.

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Correspondence to Jennifer M. Smillie.

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ArXiv ePrint: 1304.7040

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Gardi, E., Smillie, J.M. & White, C.D. The non-Abelian exponentiation theorem for multiple Wilson lines. J. High Energ. Phys. 2013, 88 (2013). https://doi.org/10.1007/JHEP06(2013)088

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Keywords

  • Wilson
  • ’t Hooft and Polyakov loops
  • Scattering Amplitudes
  • Resummation
  • QCD