The Sudakov form factor at four loops in maximal super Yang-Mills theory

Understand

The four-loop Sudakov form factor in maximal super Yang-Mills theory is analysed in detail.

• It is shown explicitly how to construct a basis of integrals that have a uniformly transcendental expansion in the dimensional regularisation parameter, further elucidating the number-theoretic properties of Feynman integrals.
• The physical form factor is expressed in this basis for arbitrary colour factor.
• In the nonplanar sector the required integrals are integrated numerically using a mix of sector-decomposition and Mellin-Barnes representation methods.