The ChPT: top-down and bottom-up

Abstract

In this work, higher-derivative corrections of the non-linear sigma model of both even and odd intrinsic-parity sectors are systematically studied, focusing on ordered amplitudes of flavor scalars in massless limit. It should correspond to a theory known as Chiral perturbation theory (ChPT) without external sources and with only single-trace operators. We briefly overview its formal development and apply new S-matrix methods to its amplitude constructions. The bottom-up analysis of the tree-level amplitudes of different orders and multiplicities focuses on the formal structure of general ChPT. Possible theoretical simplifications based on the Kleiss-Kuijf and Bern-Carrasco-Johansson relations are presented. Finally, in the same context, the comparison with the so-called Z-function, which is connected with string theory, is also discussed.

35 pages, 9 figures, v2: new subsection added (O(p10) order), v3: minor changes, accepted for publication in JHEP

References in corpus (15)

• New Relations for Gauge-Theory Amplitudes
• Effective Field Theories from Soft Limits
• Mesonic low-energy constants
• A Periodic Table of Effective Field Theories
• Chiral Perturbation Theory Beyond One Loop
• Recursion Relations for Tree-level Amplitudes in the SU(N) Non-linear Sigma Model
• Composing Effective Prediction at Five Points
• Unification of Galileon Dualities
• Six-pion amplitude
• Higher-order tree-level amplitudes in the nonlinear sigma model
• Multi-spin soft bootstrap and scalar-vector Galileon
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• An introduction to chiral perturbation theory
• Convergence properties of $\eta \to 3\pi$ decays in chiral perturbation theory
• Extended DBI and its generalizations from graded soft theorems

Cited by in corpus (4)

• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Hilbert series and higher-order Lagrangians for the $O(N)$ model
• On the three-point order parameters of chiral symmetry breaking
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity