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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• 50 Years of Quantum Chromodynamics
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• Towards a theory of hadron resonances
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• 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
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• 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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• From bound states to the continuum
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• Challenges in Semileptonic B Decays
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• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• The Role of Lattice QCD in Searches for Violations of Fundamental Symmetries and Signals for New Physics
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• Scattering of two and three physical pions at maximal isospin from lattice QCD
• Light-Meson Spectroscopy with COMPASS
• The $\pi \gamma \to \pi \pi$ transition and the $\rho$ radiative decay width from lattice QCD
• Signatures of few-body resonances in finite volume
• A cross-channel study of pion scattering from lattice QCD
• Masses of positive- and negative-parity hadron ground-states, including those with heavy quarks
• Dynamically-coupled partial-waves in $\rho \pi$ isospin-2 scattering from lattice QCD
• Form factors of two-hadron states from a covariant finite-volume formalism
• Novel approaches in Hadron Spectroscopy
• High-Energy Collision of Quarks and Mesons in the Schwinger Model: From Tensor Networks to Circuit QED
• The role of boundary conditions in quantum computations of scattering observables
• Hidden-Bottom Pentaquarks
• Charged multi-hadron systems in lattice QCD+QED
• 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
• Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarisation
• Isospin-1/2 $D\pi$ scattering and the lightest $D_0^{\ast }$ resonance from lattice QCD
• Undressing Confining Flux Tubes with $T\bar{T}$
• Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions
• Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875{)}^{+}$ from finite volume energy levels
• Cross-channel constraints on resonant antikaon-nucleon scattering
• Doubly Charmed Pentaquarks
• Phenomenology of Relativistic $3\to 3$ Reaction Amplitudes within the Isobar Approximation
• Dispersive $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes from scattering data, threshold parameters and the lightest strange resonance $\kappa$ or $K_0^{\ast }(700)$
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• $I=1/2$ $S$-wave and $P$-wave $K\pi$ scattering and the $\kappa$ and $K^{\ast }$ resonances from lattice QCD
• Light- and strange-quark mass dependence of the $\rho (770)$ meson revisited
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• Modern meson spectroscopy: the fundamental role of unitarity
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• Two-particle scattering from finite-volume quantization conditions using the plane wave basis
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• Scalar and tensor charmonium resonances in coupled-channel scattering from QCD
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• Three-body resonances in pionless effective field theory
• Bound states in the B-matrix formalism for the three-body scattering
• Emergence of the $\rho$ resonance from the HAL QCD potential in lattice QCD
• Theory introduction to baryon spectroscopy
• Charmonium ${\chi }_{c0}$ and ${\chi }_{c2}$ resonances in coupled-channel scattering from lattice QCD
• New hadron configuration: The double-gluon hybrid state
• $DK/D\pi$ scattering and an exotic virtual bound state at the $SU(3)$ flavour symmetric point from lattice QCD
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• $I=2$ $\pi \pi$ potential in the HAL QCD method with all-to-all propagators
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• Scattering Amplitude from Quantum Computing with Reduction Formula
• Lattice determination of $I=0$ and 2 $\pi \pi$ scattering phase shifts with a physical pion mass
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• Splittings of low-lying charmonium masses at the physical point
• Towards the understanding of $Z_c(3900)$ from lattice QCD
• Towards a nonperturbative construction of the $S$-matrix
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• Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states
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• 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
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• Vector boson scattering from the lattice
• A fully non-perturbative charm-quark tuning using machine learning
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• 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
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• Recent progress on hadron spectroscopy from lattice QCD
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• Testing a new method for scattering in finite volume in the ${\varphi }^4$ theory
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• Scattering Theory
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• Kaon decays and other hadronic processes in lattice QCD