The isospin-3 three-particle $K$-matrix at NLO in ChPT

Abstract

The three-particle $K$-matrix, ${\mathcal{K}}_{\mathrm{df},3}$, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions at maximal isospin through next-to-leading order (NLO) in Chiral Perturbation Theory (ChPT). We compare the values to existing lattice QCD results and find that the agreement between lattice QCD data and ChPT in the first two coefficients of the threshold expansion of ${\mathcal{K}}_{\mathrm{df},3}$ is significantly improved with respect to leading order once NLO effects are incorporated.

57 pages, 12 figures, 2 tables; v2: added sec. 2.3, minor changes, typos corrected, conclusions unchanged, version published in JHEP

References in corpus (15)

• A relativistic, model-independent, three-particle quantization condition
• 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
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• Implementing the three-particle quantization condition including higher partial waves
• Relativistic three-particle quantization condition for nondegenerate scalars
• Alternative derivation of the relativistic three-particle quantization condition
• Equivalence of relativistic three-particle quantization conditions
• The Energy of n Identical Bosons in a Finite Volume at O(L^{-7})
• Meson-meson Scattering in QCD-like Theories
• Lattice QCD study of mixed systems of pions and kaons
• Finite-volume energy shift of the three-pion ground state
• Six-pion amplitude
• CHIRON: a package for ChPT numerical results at two loops

Cited by in corpus (1)

• Three-pion scattering: From the chiral Lagrangian to the lattice