Polynomial Structures in One-Loop Amplitudes

Details Polynomial Structures in One-Loop Amplitudes Polynomial Structures in One-Loop Amplitudes

2008-03-21

arxiv.org/abs/0803.3147v3

JHEP 0809:089,2008

Physics

High Energy Physics

High Energy Physics - Phenomenology

44 pages, title changed to be closer to content, section 2.1 extended to section 2.1 and 2.2 to be more self-contained, refere

Scientific paper

10.1088/1126-6708/2008/09/089

A general one-loop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from tree-level input in a two-step process. First, use known formulas to write the coefficients of (4-2epsilon)-dimensional master integrals; these formulas depend on an additional variable, u, which encodes the dimensional shift. Second, convert the u-dependent coefficients of (4-2epsilon)-dimensional master integrals to explicit coefficients of dimensionally shifted master integrals. This procedure requires the initial formulas for coefficients to have polynomial dependence on u. Here, we give a proof of this property in the case of massless propagators. The proof is constructive. Thus, as a byproduct, we produce different algebraic expressions for the scalar integral coefficients, in which the polynomial property is apparent. In these formulas, the box and pentagon contributions are separated explicitly.

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