$I=3$ three-pion scattering amplitude from lattice QCD

Abstract

We analyze the spectrum of two- and three-pion states of maximal isospin obtained recently for isosymmetric QCD with pion mass $M\approx 200$MeV in Ref. [1]. Using the relativistic three-particle quantization condition, we find $\sim 2\sigma$ evidence for a nonzero value for the contact part of the three-${\pi }^{+}$ ($I=3$) scattering amplitude. We also compare our results to leading-order chiral perturbation theory. We find good agreement at threshold, and some tension in the energy dependent part of the three-${\pi }^{+}$scattering amplitude. We also find that the two-${\pi }^{+}$ ($I=2$) spectrum is fit well by an $s$-wave phase shift that incorporates the expected Adler zero.

arXiv commentCorrected Figs S1 and S2 in supplementary material. Main text and conclusions unchanged

References in corpus (61)

• Heavy-Quark QCD Exotica
• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• Three-pion contribution to hadronic vacuum polarization
• Finite-Volume Effects for Two-Hadron States in Moving Frames
• Scattering processes and resonances from lattice QCD
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Multiple-channel generalization of Lellouch-Luscher formula
• A relativistic, model-independent, three-particle quantization condition
• Scattering phases for meson and baryon resonances on general moving-frame lattices
• Two-particle multichannel systems in a finite volume with arbitrary spin
• Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion
• Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
• Coupled $\pi \pi ,K\overline{K}$ scattering in $P$-wave and the $\rho$ resonance from lattice QCD
• 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 particles in a finite volume
• A method to measure the antikaon-nucleon scattering length in lattice QCD
• Two Particle States and the $S$-matrix Elements in Multi-channel Scattering
• Setting the scale for the CLS $2+1$ flavor ensembles
• 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
• 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
• Lattice QCD and Three-particle Decays of Resonances
• An $a_0$ resonance in strongly coupled $\pi \eta$, $K\overline{K}$ scattering from lattice QCD
• Three-body spectrum in a finite volume: the role of cubic symmetry
• 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
• $I=1$ and $I=2$ $\pi -\pi$ scattering phase shifts from $N_{\mathrm{f}}=2+1$ lattice QCD
• Finite-volume spectrum of ${\pi }^{+}{\pi }^{+}$ and ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ systems
• Three-particle systems with resonant subprocesses in a finite volume
• Two- and three-pion finite-volume spectra at maximal isospin from lattice QCD
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• The $I=1$ pion-pion scattering amplitude and timelike pion form factor from $N_{\mathrm{f}}=2+1$ lattice QCD
• The pi+ pi+ scattering length from maximally twisted mass lattice QCD
• Implementing the three-particle quantization condition including higher partial waves
• The I=2 pipi S-wave Scattering Phase Shift from Lattice QCD
• Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
• Extracting Scattering Phase-Shifts in Higher Partial-Waves from Lattice QCD Calculations
• An solvable three-body model in finite volume
• Numerical study of the relativistic three-body quantization condition in the isotropic approximation
• The elastic $I=3/2$ $p$-wave nucleon-pion scattering amplitude and the $\Delta (1232)$ resonance from $N_{\mathrm{f}}=2+1$ lattice QCD
• Energy shift of the three-particle system in a finite volume
• Three particles in a finite volume: The breakdown of spherical symmetry
• Extraction of isoscalar $\pi \pi$ phase-shifts from lattice QCD
• Determination of $s$- and $p$-wave $I=1/2$ $K\pi$ scattering amplitudes in $N_{\mathrm{f}}=2+1$ lattice QCD
• The $b_1$ resonance in coupled $\pi \omega$, $\pi \varphi$ scattering from lattice QCD
• Two- and three-body interactions in ${\phi }^4$ theory from lattice simulations
• 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
• Signatures of few-body resonances in finite volume
• Dynamically-coupled partial-waves in $\rho \pi$ isospin-2 scattering from lattice QCD
• Isospin-0 $\pi \pi$ s-wave scattering length from twisted mass lattice QCD
• Global parameterization of $\pi \pi$ scattering up to 2 GeV
• Pion scattering in the isospin I=2 channel from elongated lattices
• Vector particle scattering on the lattice
• Threshold expansion of the three-particle quantization condition
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: $I=3/2$ $\pi K$ Scattering Length
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: isospin-1 $KK$ scattering length

Cited by in corpus (62)

• FLAG Review 2021
• 50 Years of Quantum Chromodynamics
• Generalizing the relativistic quantization condition to include all three-pion isospin channels
• Three pion spectrum in the $I=3$ channel from lattice QCD
• Three-body unitarity versus finite-volume ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ spectrum from lattice QCD
• Preparation of the SU(3) Lattice Yang-Mills Vacuum with Variational Quantum Methods
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• The Present and Future of QCD
• The energy-dependent ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ scattering amplitude from QCD
• 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
• Equivalence of relativistic three-particle quantization conditions
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• 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
• $DDK$ system in finite volume
• New Ideas in Constraining Nuclear Forces
• Charged multi-hadron systems in lattice QCD+QED
• Relativistic-invariant formulation of the NREFT three-particle quantization condition
• Solving relativistic three-body integral equations in the presence of bound states
• Isospin-1/2 $D\pi$ scattering and the lightest $D_0^{\ast }$ resonance from lattice QCD
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Finite-volume energy shift of the three-pion ground state
• Relativistic $N$-particle energy shift in finite volume
• Elastic nucleon-pion scattering at $m_{\pi }=200\mathrm{MeV}$ from lattice QCD
• Multi-${\pi }^{+}$ systems in finite volume
• Implementing the three-particle quantization condition for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems
• Dalitz plots and lineshape of $a_1(1260)$ from a relativistic three-body unitary approach
• Interactions of $\pi K$, $\pi \pi K$ and $KK\pi$ systems at maximal isospin from lattice QCD
• Decay amplitudes to three hadrons from finite-volume matrix elements
• $\omega$ meson from lattice QCD
• Modeling few-body resonances in finite volume
• Three relativistic neutrons in a finite volume
• Three-body resonances in the ${\phi }^4$ theory
• On the three-particle analog of the Lellouch-Lüscher formula
• A lattice model of heavy-light three-body system
• Partial Wave Mixing in Hamiltonian Effective Field Theory
• Consistency checks for two-body finite-volume matrix elements: II. Perturbative systems
• Hamiltonian effective field theory in elongated or moving finite volume
• Six-pion amplitude
• Singlet channel scattering in a Composite Higgs model on the lattice
• Charged particles interaction in both a finite volume and a uniform magnetic field
• Threshold expansion formula of $N$-boson in finite volume from variational approach
• Visualizing resonances in finite volume
• The isospin-3 three-particle $K$-matrix at NLO in ChPT
• Regularisation in Nonperturbative Extensions of Effective Field Theory
• Particle-dimer approach for the Roper resonance in a finite volume
• Bound states in the B-matrix formalism for the three-body scattering
• Finite-volume energy shift of the three-nucleon ground state
• The three-pion $K$-matrix at NLO in ChPT
• Spurious poles in a finite volume
• Six-meson amplitude in QCD-like theories
• Prospects for ${\gamma }^{\star }{\gamma }^{\star }\to \pi \pi$ via lattice QCD
• Meson-Nucleon Scattering Amplitudes from Lattice QCD
• Higher order finite volume quantization conditions for two spinless particles
• Construction of general $N$-body lattice operators with arbitrary momenta
• $D_1$ and $D_2$ resonances in coupled-channel scattering amplitudes from lattice QCD
• Emergence of the $\pi (1300)$ Resonance from Lattice QCD
• Higher order quantization conditions for two spinless particles
• Three-pion scattering: From the chiral Lagrangian to the lattice
• Three-boson stability for boosted interactions towards the zero-range limit