Scattering of two and three physical pions at maximal isospin from lattice QCD

Abstract

We present the first direct $N_f=2$ lattice QCD computation of two- and three-${\pi }^{+}$ scattering quantities that includes an ensemble at the physical point. We study the quark mass dependence of the two-pion phase shift, and the three-particle interaction parameters. We also compare to phenomenology and chiral perturbation theory (ChPT). In the two-particle sector, we observe good agreement to the phenomenological fits in $s$- and $d$-wave, and obtain $M_{\pi }{a}_0=-0.0481(86)$ at the physical point from a direct computation. In the three-particle sector, we observe reasonable agreement at threshold to the leading order chiral expansion, i.e.\@ a mildly attractive three-particle contact term. In contrast, we observe that the energy-dependent part of the three-particle quasilocal scattering quantity is not well described by leading order ChPT.

Published version

References in corpus (21)

• On the generalized eigenvalue method for energies and matrix elements in lattice field theory
• A novel quark-field creation operator construction for hadronic physics in lattice QCD
• A relativistic, model-independent, three-particle quantization condition
• S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Resonances in coupled πK,ηK scattering from quantum chromodynamics
• Three-body Unitarity in the Finite Volume
• Scalar mesons in a finite volume
• Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
• Multi-Pion States in Lattice QCD and the Charged-Pion Condensate
• Scalar mesons moving in a finite volume and the role of partial wave mixing
• Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD
• The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• Implementing the three-particle quantization condition including higher partial waves
• Alternative derivation of the relativistic three-particle quantization condition
• Equivalence of relativistic three-particle quantization conditions
• Lattice QCD study of the s-wave $\pi \pi$ scattering lengths in the I=0 and 2 channels
• Modeling few-body resonances in finite volume
• pi-pi Scattering in Twisted Mass Chiral Perturbation Theory

Cited by in corpus (33)

• FLAG Review 2021
• 50 Years of Quantum Chromodynamics
• Three-body interactions from the finite-volume QCD spectrum
• Three-particle finite-volume formalism for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems
• Novel approaches in Hadron Spectroscopy
• Solving relativistic three-body integral equations in the presence of bound states
• Relativistic-invariant formulation of the NREFT three-particle quantization condition
• Isospin-1/2 $D\pi$ scattering and the lightest $D_0^{\ast }$ resonance from lattice QCD
• Elastic nucleon-pion scattering at $m_{\pi }=200\mathrm{MeV}$ from lattice QCD
• Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
• Implementing the three-particle quantization condition for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems
• Interactions of $\pi K$, $\pi \pi K$ and $KK\pi$ systems at maximal isospin from lattice QCD
• $\omega$ meson from lattice QCD
• Three relativistic neutrons in a finite volume
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• Three-body resonances in the ${\phi }^4$ theory
• Quark mass dependence of $\pi \pi$ scattering in isospin 0, 1, and 2 from lattice QCD
• Six-pion amplitude
• The isospin-3 three-particle $K$-matrix at NLO in ChPT
• Particle-dimer approach for the Roper resonance in a finite volume
• Finite-volume energy shift of the three-nucleon ground state
• Lattice determination of $I=0$ and 2 $\pi \pi$ scattering phase shifts with a physical pion mass
• Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD
• $\Delta I=3/2$ and $\Delta I=1/2$ channels of $K\to \pi \pi$ decay at the physical point with periodic boundary conditions
• The three-pion $K$-matrix at NLO in ChPT
• Spurious poles in a finite volume
• $\pi \pi$ scattering in partially-quenched twisted-mass chiral perturbation theory
• Construction of general $N$-body lattice operators with arbitrary momenta
• Higher order finite volume quantization conditions for two spinless particles
• $D_1$ and $D_2$ resonances in coupled-channel scattering amplitudes from lattice QCD
• Position-space sampling for local multiquark operators in lattice QCD using distillation and the importance of tetraquark operators for $T_{cc}(3875{)}^{+}$
• Pion scattering in finite volume within the Inverse Amplitude Method
• Emergence of the $\pi (1300)$ Resonance from Lattice QCD