Six-meson amplitude in QCD-like theories

Abstract

We calculate the relativistic six-meson scattering amplitude at low energy within the framework of QCD-like theories with $n$ degenerate quark flavors at next-to-leading order in the chiral counting. We discuss the cases of complex, real and pseudo-real representations, i.e. with global symmetry and breaking patterns $\text{SU}(n)\times \text{SU}(n)/\text{SU}(n)$ (extending the QCD case), $\text{SU}(2n)/\text{SO}(2n)$, and $\text{SU}(2n)/\text{Sp}(2n)$. In case of the one-particle-irreducible part, we obtain analytical expressions in terms of 10 six-meson subamplitudes based on the flavor and group structures. We extend on our previous results obtained within the framework of the $\text{O}(N+1)/\text{O}(N)$ non-linear sigma model, with $N$ being the number of meson flavors. This work allows for studying a number of properties of six-particle amplitudes at one-loop level.

arXiv comment19 pages, 9 figures, 1 table; v2: version accepted for publication in PRD, minor text improvements

References in corpus (41)

• Automatized One-Loop Calculations in 4 and D dimensions
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Recursion Relations for Tree Amplitudes of Gluons
• New Developments in FeynCalc 9.0
• FeynCalc 9.3: New features and improvements
• QCD-like Theories at Finite Baryon Density
• The Mesonic Chiral Lagrangian of Order $p^6$
• A relativistic, model-independent, three-particle quantization condition
• Elastic $\pi \pi$ scattering to two loops
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• Mesonic low-energy constants
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Three-body Unitarity in the Finite Volume
• Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
• Lattice QCD and Three-particle Decays of Resonances
• Finite-volume spectrum of ${\pi }^{+}{\pi }^{+}$ and ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ systems
• $I=3$ three-pion scattering amplitude from lattice QCD
• Tree-level Amplitudes in the Nonlinear Sigma Model
• Three pion spectrum in the $I=3$ channel from lattice QCD
• Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
• Three-body unitarity versus finite-volume ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ spectrum from lattice QCD
• Technicolor and other QCD-like theories at next-to-next-to-leading order
• Three-body interactions from the finite-volume QCD spectrum
• Equivalence of relativistic three-particle quantization conditions
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Meson-meson Scattering in QCD-like Theories
• Analyticity, Crossing Symmetry and the Limits of Chiral Perturbation Theory
• New Soft Theorems for Goldstone Boson Amplitudes
• Soft Bootstrap and Effective Field Theories
• Relativistic $N$-particle energy shift in finite volume
• Leading Logarithms in the Massive O(N) Nonlinear Sigma Model
• The order $p^8$ mesonic chiral Lagrangian
• The Massive O(N) Non-linear Sigma Model at High Orders
• Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Pion Mass Effects in the Large $N$ Limit of $\chiPT$
• Six-pion amplitude
• Leading logarithms in N-flavour mesonic Chiral Perturbation Theory
• Higher-order tree-level amplitudes in the nonlinear sigma model
• Trace Formulae of Characteristic Polynomial and Cayley-Hamilton's Theorem, and Applications to Chiral Perturbation Theory and General Relativity
• Two-Point Functions and S-Parameter in QCD-like Theories