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.

arXiv comment57 pages, 12 figures, 2 tables; v2: added sec. 2.3, minor changes, typos corrected, conclusions unchanged, version published in JHEP

References in corpus (51)

• Automatized One-Loop Calculations in 4 and D dimensions
• ππscattering
• FLAG Review 2021
• Scattering processes and resonances from lattice QCD
• A relativistic, model-independent, three-particle quantization condition
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• Three particles in a finite volume
• Three-particle scattering amplitudes from a finite volume formalism
• Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
• 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
• Multi-Pion Systems in Lattice QCD and the Three-Pion Interaction
• Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD
• Three-particle systems with resonant subprocesses in a finite volume
• $I=3$ three-pion scattering amplitude from lattice QCD
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• Towards a theory of hadron resonances
• Implementing the three-particle quantization condition including higher partial waves
• Generalizing the relativistic quantization condition to include all three-pion isospin channels
• Three pion spectrum in the $I=3$ channel from lattice QCD
• Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
• Three-body unitarity versus finite-volume ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ spectrum from lattice QCD
• Numerical study of the relativistic three-body quantization condition in the isotropic approximation
• On the Equivalence of Three-Particle Scattering Formalisms
• Energy shift of the three-particle system in a finite volume
• Finite-volume energy spectrum of the $K^{-}{K}^{-}{K}^{-}$ system
• Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism
• Volume Dependence of N-Body Bound States
• Three-body interactions from the finite-volume QCD spectrum
• Relativistic three-particle quantization condition for nondegenerate scalars
• Alternative derivation of the relativistic three-particle quantization condition
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• The Energy of n Identical Bosons in a Finite Volume at O(L^{-7})
• Equivalence of relativistic three-particle quantization conditions
• Scattering of two and three physical pions at maximal isospin from lattice QCD
• Three-particle finite-volume formalism for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: isospin-2 $\pi \pi$ scattering length
• A cross-channel study of pion scattering from lattice QCD
• Meson-meson Scattering in QCD-like Theories
• $DDK$ system in finite volume
• Relativistic-invariant formulation of the NREFT three-particle quantization condition
• Solving relativistic three-body integral equations in the presence of bound states
• Lattice QCD study of mixed systems of pions and kaons
• Finite-volume energy shift of the three-pion ground state
• Relativistic $N$-particle energy shift in finite volume
• Implementing the three-particle quantization condition for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems
• SU(2) Low-Energy Constants from Mixed-Action Lattice QCD
• Six-pion amplitude
• CHIRON: a package for ChPT numerical results at two loops

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