Next-to$^k$ leading log expansions by chord diagrams

Understand

Green functions in a quantum field theory can be expanded as bivariate series in the coupling and a scale parameter.

• The leading logs are given by the main diagonal of this expansion, i.e.
• the subseries where the coupling and the scale parameter appear to the same power; then the next-to leading logs are listed by the next diagonal of the expansion, where the power of the coupling is incremented by one, and so on.
• We give a general method for deriving explicit formulas and asymptotic estimates for any next-to$^k$ leading-log expansion for a large class of single scale Green functions.