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

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

2008-11-13

arxiv.org/abs/0811.2067v1

JHEP 0903:054,2009

Physics

High Energy Physics

High Energy Physics - Phenomenology

43 pages, 16 figures

Scientific paper

10.1088/1126-6708/2009/03/054

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.

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