Scattering processes and resonances from lattice QCD

Abstract

The vast majority of hadrons observed in nature are not stable under the strong interaction, rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy non-perturbative region, and in addition, many probes of the limits of the electroweak sector of the Standard Model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lighter hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required non-perturbative evaluation of hadron observables. In this article, we review progress in the study of few-hadron reactions in which resonances and bound-states appear using lattice QCD techniques. We describe the leading approach which takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. We explain how from explicit lattice QCD calculations, one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. The challenges which currently limit the field are discussed along with the steps being taken to resolve them.

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• Rho resonance parameters from lattice QCD
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• Spectrum of three-body bound states in a finite volume
• Effects of finite volume on the $K_L$-$K_S$ mass difference
• Isolating the Λ(1405) in Lattice QCD
• The $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude from Lattice QCD
• Electroweak Matrix Elements in the Two-Nucleon Sector from Lattice QCD
• Study of the $Z_c^{+}$ channel using lattice QCD
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• Two Particle States in an Asymmetric Box and the Elastic Scattering Phases
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• The $\pi \pi \to \pi {\gamma }^{\star }$ amplitude and the resonant $\rho \to \pi {\gamma }^{\star }$ transition from lattice QCD
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• Lattice determination of the $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude $A_2$
• Infrared regularization for spin-1 fields
• Chiral Behaviour of the Rho Meson in Lattice QCD
• Are two nucleons bound in lattice QCD for heavy quark masses? -- Consistency check with Lüscher's finite volume formula --
• Topological phases for bound states moving in a finite volume
• Excited State Nucleon Spectrum with Two Flavors of Dynamical Fermions
• $I=2$ pion scattering amplitude with Wilson fermions
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• K pi scattering for isospin 1/2 and 3/2 in lattice QCD
• Electroexcitation of the Roper resonance for 1.7 < Q2 < 4.5 GeV2 in ep -> enpi+
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• Low energy scattering phase shifts for meson-baryon systems
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• Unquenching the Rho Meson
• Hadron Scattering in an Asymmetric Box
• Study of decuplet baryon resonances from lattice QCD
• Partial twisting for scalar mesons
• Unified chiral analysis of the vector meson spectrum from lattice QCD
• I=2 Pion scattering length with improved actions on anisotropic lattices
• The mass of the Delta resonance in a finite volume: fourth-order calculation
• Applying Twisted Boundary Conditions for Few-body Nuclear Systems
• Strategies for an accurate determination of the X(3872) energy from QCD lattice simulations
• Grand canonical ensemble, multi-particle wave functions, scattering data, and lattice field theories
• Bound states on the lattice with partially twisted boundary conditions
• Finite-volume matrix elements in multi-boson states
• Resonances in an external field: the 1+1 dimensional case
• A comparison of analysis techniques for extracting resonance parameters from lattice Monte Carlo data
• Chiral Extrapolation of the Sigma Resonance
• Comment on "Are two nucleons bound in lattice QCD for heavy quark masses? - Sanity check with Lüscher's finite volume formula -"
• Baryon spin-flavor structure from an analysis of lattice QCD results of the baryon spectrum
• Chiral extrapolation of the sigma and rho mesons from dispersion relations and Chiral Perturbation Theory

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• Three-particle systems with resonant subprocesses in a finite volume
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• $I=3$ three-pion scattering amplitude from lattice QCD
• Towards a theory of hadron resonances
• The $I=1$ pion-pion scattering amplitude and timelike pion form factor from $N_{\mathrm{f}}=2+1$ lattice QCD
• Implementing the three-particle quantization condition including higher partial waves
• Three pion spectrum in the $I=3$ channel from lattice QCD
• Generalizing the relativistic quantization condition to include all three-pion isospin channels
• Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states
• Masses of ground-state mesons and baryons, including those with heavy quarks
• 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
• Tetraquark operators in lattice QCD and exotic flavour states in the charm sector
• Charmonium-like resonances with $J^{PC}=0^{++},2^{++}$ in coupled $D\bar{D}$, $D_s{\bar{D}}_s$ scattering on the lattice
• On the Equivalence of Three-Particle Scattering Formalisms
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• Oracles for Gauss's law on digital quantum computers
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• Review of the $\mathbf{\Lambda }$(1405): A curious case of a strange-ness resonance
• From bound states to the continuum
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• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism
• Lattice QCD and baryon-baryon interactions: HAL QCD method
• Challenges in Semileptonic B Decays
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• Dynamically-coupled partial-waves in $\rho \pi$ isospin-2 scattering from lattice QCD
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• Novel approaches in Hadron Spectroscopy
• High-Energy Collision of Quarks and Mesons in the Schwinger Model: From Tensor Networks to Circuit QED
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• Solving relativistic three-body integral equations in the presence of bound states
• Global parameterization of $\pi \pi$ scattering up to 2 GeV
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
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• Undressing Confining Flux Tubes with $T\bar{T}$
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• Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875{)}^{+}$ from finite volume energy levels
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• The nature of ${\chi }_{c1}\left(3872\right)$ and $T_{cc}^{+}\left(3875\right)$
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• Phenomenological view on baryon-baryon potentials from lattice QCD simulations
• Density of States of a Coupled-Channel System
• Two-current transition amplitudes with two-body final states
• Is two-poles' $\Lambda (1405)$ one state or two?
• Scattering phase shifts and mixing angles for an arbitrary number of coupled channels on the lattice
• Radiative Transitions in Charmonium from Lattice QCD
• Fully-strange tetraquark states with the exotic quantum numbers $J^{PC}=0^{+-}$ and $2^{+-}$
• Lattice study of $cc\bar{u}\bar{s}$ tetraquark channel in $D^{(\ast )}{D}_s^{(\ast )}$ scattering
• Vector boson scattering from the lattice
• A fully non-perturbative charm-quark tuning using machine learning
• Scattering length in holographic confining theories
• P-Wave Two-Particle Bound and Scattering States in a Finite Volume including QED
• Physical-mass calculation of $\rho (770)$ and $K^{\ast }(892)$ resonance parameters via $\pi \pi$ and $K\pi$ scattering amplitudes from lattice QCD
• Light double-gluon hybrid states with the exotic quantum numbers $J^{PC}=1^{-+}$ and $3^{-+}$
• The HAL QCD potential in $I=1$ $\pi \pi$ system with the $\rho$ meson bound state
• Prospects for ${\gamma }^{\star }{\gamma }^{\star }\to \pi \pi$ via lattice QCD
• Analytical dispersive parameterization for elastic scattering of spinless particles
• Towards high partial waves in lattice QCD with a dumbbell-like operator
• Lattice QCD and Baryon-Baryon Interactions
• Charmoniumlike Channels $1^{+}$ with Isospin $1$ from Lattice and Effective Field Theory
• A lattice QCD study of pion-nucleon scattering in the Roper channel
• Meson-Nucleon Scattering Amplitudes from Lattice QCD
• Multibody decay analyses -- a new phenomenological model for meson-meson subamplitudes
• S-wave kaon-nucleon potentials with all-to-all propagators in the HAL QCD method
• Charmonium and exotics from lattice QCD
• The $\pi \pi$ scattering amplitude at large $N_{\text{c}}$
• Construction of general $N$-body lattice operators with arbitrary momenta
• Decay properties of light $1^{-+}$ hybrids
• Quark mass dependence of on-shell and half off-shell scattering amplitudes from Bethe-Salpeter wave function inside the interaction range
• Thermal evolution of dark matter and gravitational-wave production in the early universe from a symplectic glueball model
• Recent progress on hadron spectroscopy from lattice QCD
• $D_1$ and $D_2$ resonances in coupled-channel scattering amplitudes from lattice QCD
• Exotic properties of N^*(1895) and its impact on photoproduction of light hyperons
• Low-energy constants from charmed baryons on QCD lattices
• Theoretical results for hadronic masses and their widths in the framework of the SO(4) model
• A model-independent framework for determining finite-volume effects of spatially nonlocal operators
• Chiral symmetry: An analytic $SU(3)$ unitary matrix
• Emergence of the $\pi (1300)$ Resonance from Lattice QCD
• Pion scattering in finite volume within the Inverse Amplitude Method
• Nuclear correlation functions using first-principle calculations of lattice quantum chromodynamics
• Unitary model analysis of $f_0(500)$ pole positions by continuously varying $m_{\pi }$: comparison with discrete lattice predictions
• Investigating vector boson scattering: A fully gauge-invariant study
• Three particles on the lattice
• Fermion quartets on the square lattice
• Testing a new method for scattering in finite volume in the ${\varphi }^4$ theory
• Hadronic decay of vector charmonium from the lattice
• Scattering Theory
• Low-energy $DD$ scattering in lattice QCD
• Kaon decays and other hadronic processes in lattice QCD