Polynomial Structures in One-Loop Amplitudes

Understand

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.