Higher-order tree-level amplitudes in the nonlinear sigma model

We present a generalisation of the avour-ordering method applied to the chiral nonlinear sigma model with any number of avours. 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(p2), to 6 legs at next-tonext-to-next-to-leading order, O(p8). In addition to this, we generalise several properties of amplitudes in the nonlinear sigma model to higher orders. These include the double soft limit and the uniqueness of stripped amplitudes.