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

TL;DR

This paper extends the computational methods for tree-level amplitudes in the nonlinear sigma model, enabling calculations with many legs and higher-order derivatives, and generalizes key amplitude properties to higher orders.

Contribution

It introduces a generalized flavor-ordering method for the nonlinear sigma model that allows automated, high-order, multi-leg amplitude calculations and extends amplitude properties to higher orders.

Findings

Calculated amplitudes up to 12 legs at leading order.

Extended properties like double soft limit to higher orders.

Automated method facilitates complex amplitude computations.

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, $\mathcal{O}(p^2)$, to 6 legs at next-to-next-to-next-to-leading order, $\mathcal{O}(p^8)$. 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.