Flavour-ordering in the nonlinear sigma model with more derivatives and legs

Abstract: We present a generalisation of the flavour-ordering method applied to the chiral nonlinear sigma model with any number of flavours. We use an extended Lagrangian with terms containing any number of derivatives, organised in a power-counting hierarchy. The method allows diagrammatic computations at tree-level with any number of legs at any order in the power-counting. Using an automated implementation of the method, we calculate amplitudes ranging from 12 legs at leading order, $\O(p^2)$, to 6 legs at next-to-next-to-next-to-leading order, $\O(p^8)$.