Path integral approach to eikonal and next-to-eikonal exponentiation

Abstract

We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting with a soft gauge field is represented as a Wilson line for a semi-infinite line segment, together with calculable fluctuations. Combining such line segments, we show that exponentiation in an abelian field theory follows immediately from standard path-integral combinatorics. In the non-abelian case, we consider color singlet hard interactions with two outgoing external lines, and obtain a new viewpoint for exponentiation in terms of ``webs'', with a closed form solution for their corresponding color factors. We investigate and clarify the structure of next-to-eikonal corrections.

43 pages, 16 figures

References in corpus (4)

• Threshold Resummation in Momentum Space from Effective Field Theory
• On next-to-eikonal corrections to threshold resummation for the Drell-Yan and DIS cross sections
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Cited by in corpus (9)

• Webs in multiparton scattering using the replica trick
• Diagrammatic Exponentiation for Products of Wilson Lines
• General properties of multiparton webs: proofs from combinatorics
• Generalized double-logarithmic large-x resummation in inclusive deep-inelastic scattering
• On threshold resummation beyond leading 1-x order
• Threshold Resummation for Di-hadron Production in Hadronic Collisions
• Threshold Improved QCD Corrections for Stop-Antistop production at Hadron colliders
• On next-to-eikonal exponentiation
• On higher-order flavour-singlet splitting and coefficient functions at large x