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

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.

47 pages, the file flavour-order.pdf contains the expressions for two more amplitudes and the diagrams for all calculated ones

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Cited by in corpus (9)

• New Soft Theorems for Goldstone Boson Amplitudes
• Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons
• Six-pion amplitude
• Operator Counting and Soft Blocks in Chiral Perturbation Theory
• Multi-spin soft bootstrap and scalar-vector Galileon
• The ChPT: top-down and bottom-up
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Hilbert series and higher-order Lagrangians for the $O(N)$ model
• Six-meson amplitude in QCD-like theories