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.

arXiv comment35 pages, 9 figures, v2: new subsection added (O(p10) order), v3: minor changes, accepted for publication in JHEP

References in corpus (51)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• FLAG Review 2019
• The Amplituhedron
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• The Mesonic Chiral Lagrangian of Order $p^6$
• Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
• Effective Field Theories from Soft Limits
• Polylogarithms, Multiple Zeta Values and Superstring Amplitudes
• Mesonic low-energy constants
• The Low Energy $\pi \pi$ Amplitude to One and Two Loops
• On-Shell Recursion Relations for Effective Field Theories
• A Periodic Table of Effective Field Theories
• Color-Kinematics Duality for QCD Amplitudes
• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Chiral Perturbation Theory Beyond One Loop
• The anomalous chiral Lagrangian of order $p^6$
• Soft Bootstrap and Supersymmetry
• Amplitude Relations in Non-linear Sigma Model
• Tree-level Amplitudes in the Nonlinear Sigma Model
• Chiral expansions of the pi0 lifetime
• The anomalous chiral perturbation theory meson Lagrangian to order $p^6$ revisited
• Vector Effective Field Theories from Soft Limits
• Resumming QCD vacuum fluctuations in three-flavour Chiral Perturbation Theory
• 2, 12, 117, 1959, 45171, 1170086, ...: A Hilbert series for the QCD chiral Lagrangian
• Recursion Relations for Tree-level Amplitudes in the SU(N) Non-linear Sigma Model
• UV considerations on scattering amplitudes in a web of theories
• Composing Effective Prediction at Five Points
• New Soft Theorems for Goldstone Boson Amplitudes
• Unification of Galileon Dualities
• Soft Bootstrap and Effective Field Theories
• The order $p^8$ mesonic chiral Lagrangian
• Shift symmetries, soft limits, and the double copy beyond leading order
• Leading logarithms in the anomalous sector of two-flavour QCD
• Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons
• New Flavor-Kinematics Dualities and Extensions of Nonlinear Sigma Models
• Six-pion amplitude
• Operator Counting and Soft Blocks in Chiral Perturbation Theory
• Leading logarithms in N-flavour mesonic Chiral Perturbation Theory
• Multi-spin soft bootstrap and scalar-vector Galileon
• Higher-order tree-level amplitudes in the nonlinear sigma model
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Scattering Amplitudes and Soft Theorems in Multi-Flavor Galileon Theories
• An introduction to chiral perturbation theory
• Pi-eta scattering and the resummation of vacuum fluctuation in three-flavour ChPT
• Hidden Conformal Invariance of Scalar Effective Field Theories
• 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