Towards a theory of hadron resonances

Abstract

In this review, we present the current state of the art of our understanding of the spectrum of excited strongly interacting particles and discuss methods that allow for a systematic and model-independent calculation of the hadron spectrum. These are lattice QCD and effective field theories. Synergies between both approaches can be exploited allowing for deeper understanding of the hadron spectrum. Results based on effective field theories and hadron-hadron scattering in lattice QCD or combinations thereof are presented and discussed. We also show that the often used Breit-Wigner parameterization is at odds with chiral symmetry and should not be used in case of strongly coupled channels.

arXiv comment75 pages, 21 figures, commissioned article for Physics Reports

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• Reconciling threshold and subthreshold expansions for pion-nucleon scattering
• Scattering lengths of Nambu-Goldstone bosons off $D$ mesons and dynamically generated heavy-light mesons
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• Chiral Perturbation Theory for Vector Mesons
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• Rho resonance parameters from lattice QCD
• $P$-wave $\pi \pi$ scattering and the $\rho$ resonance from lattice QCD
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• On chiral extrapolations of charmed meson masses and coupled-channel reaction dynamics
• Hadronic decay of a vector meson from the lattice
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• Infrared regularization with spin-3/2 fields
• Low-energy Scattering of $(D{\bar{D}}^{\ast }{)}^{\pm }$ System And the Resonance-like Structure $Z_c(3900)$
• The Complex-Mass Scheme and Unitarity in perturbative Quantum Field Theory
• Redundance of $\Delta$-isobar Parameters in Effective Field Theories
• Three-body interactions from the finite-volume QCD spectrum
• K^- nuclear potentials from in-medium chirally motivated models
• Determination of $s$- and $p$-wave $I=1/2$ $K\pi$ scattering amplitudes in $N_{\mathrm{f}}=2+1$ lattice QCD
• Quantum Loops in the Resonance Chiral Theory: The Vector Form Factor
• QCD and the Strange Baryon Spectrum
• The quark-mass dependence of elastic $\pi K$ scattering from QCD
• Remarks on the pion-nucleon sigma-term
• Systematics of the HAL QCD Potential at Low Energies in Lattice QCD
• Recent developments in SU(3) covariant baryon chiral perturbation theory
• Two photon couplings of the lightest isoscalars from BELLE data
• How the X(5568) challenges our understanding of QCD
• Angular Momentum on the Lattice: The Case of Non-Zero Linear Momentum
• To bind or not to bind: The H-dibaryon in light of chiral effective field theory
• The $b_1$ resonance in coupled $\pi \omega$, $\pi \varphi$ scattering from lattice QCD
• Chiral Extrapolations and the Covariant Small Scale Expansion
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Omega-phi mixing in chiral perturbation theory
• f_K/f_pi in Full QCD with Domain Wall Valence Quarks
• Equivalence of relativistic three-particle quantization conditions
• Chiral study of the $a_0(980)$ resonance and $\pi \eta$ scattering phase shifts in light of a recent lattice simulation
• Another look at $\pi \pi$ scattering in the scalar channel
• $DK$ $I=0,$ $D\bar{K}$ $I=0,1$ scattering and the $D_{s0}^{\ast }(2317)$ from lattice QCD
• On the radiative decays of light vector and axial-vector mesons
• Studying the $\rho$ resonance parameters with staggered fermions
• Lattice QCD study of the s-wave $\pi \pi$ scattering lengths in the I=0 and 2 channels
• Three-particle finite-volume formalism for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems
• Pion photoproduction off the proton in a gauge-invariant chiral unitary framework
• A novel analysis method for excited states in lattice QCD - the nucleon case
• A chiral covariant approach to $\rho \rho$ scattering
• A cross-channel study of pion scattering from lattice QCD
• Two- and three-body interactions in ${\phi }^4$ theory from lattice simulations
• Rho - omega mixing in chiral perturbation theory
• Lattice investigation of the scalar mesons a_0(980) and κ using four-quark operators
• X(3872) in lattice QCD with exact chiral symmetry
• Electromagnetic Contributions to Vector Meson Masses and Mixings
• Study of open-charm $0^{+}$ states in unitarized chiral effective theory with one-loop potentials
• Search for low-lying lattice QCD eigenstates in the Roper regime
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• Structure of the Roper Resonance from Lattice QCD Constraints
• Complex-mass renormalization in chiral effective field theory
• Amplitude analysis of $B^0\to {\bar{D}}^0{K}^{+}{\pi }^{-}$ decays
• Isospin-0 $\pi \pi$ s-wave scattering length from twisted mass lattice QCD
• Exotic bound states of two baryons in light of chiral effective field theory
• A lattice study of light scalar tetraquarks
• The role of boundary conditions in quantum computations of scattering observables
• Novel approaches in Hadron Spectroscopy
• Two-flavor Simulations of the $\rho (770)$ and the Role of the $K\bar{K}$ Channel
• Electromagnetic transitions in an effective chiral Lagrangian with the eta-prime and light vector mesons
• Wave Function of the Roper from Lattice QCD
• Relativistic-invariant formulation of the NREFT three-particle quantization condition
• Flavor-singlet meson decay constants from $N_f=2+1+1$ twisted mass lattice QCD
• Vector Meson Masses in Chiral Perturbation Theory
• Nucleon-$J/\psi$ and nucleon-${\eta }_c$ scattering in $P_c$ pentaquark channels from LQCD
• Redundancy of the off-shell parameters in chiral effective field theory with explicit spin-3/2 degrees of freedom
• Pion scattering in the isospin I=2 channel from elongated lattices
• Chiral Perturbation Theory: Introduction and Recent Results in the One-Nucleon Sector
• Isospin-1/2 $D\pi$ scattering and the lightest $D_0^{\ast }$ resonance from lattice QCD
• Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarisation
• On the quark-mass dependence of the baryon ground-state masses
• Quantum electrodynamics for vector mesons
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• Axial resonances a1(1260), b1(1235) and their decays from the lattice
• On the convergence of the chiral expansion for the baryon ground-state masses
• $F_K/F_{\pi }$ from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles
• On the structure of large N cancellations in baryon chiral perturbation theory
• Implementation of Symanzik's Improvement Program for Simulations of Dynamical Wilson Fermions in Lattice QCD
• Lattice study on ${\eta }_{c2}$ and X(3872)
• Lattice QCD approach to Nuclear Physics
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• Two-loop analysis of the pion-mass dependence of the $\rho$ meson
• Vector and scalar charmonium resonances with lattice QCD
• Finite volume corrections to the binding energy of the X(3872)
• Pole position of the $a_1(1260)$ resonance in a three-body unitary framework
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: The $\rho$-resonance
• The Optical Potential on the Lattice
• Jülich-Bonn-Washington Model for Pion Electroproduction Multipoles
• Mass and width of the Roper resonance using complex-mass renormalization
• Gauge invariance in two-particle scattering
• Where is the lightest charmed scalar meson?
• The $\rho$-resonance with physical pion mass from $N_f=2$ lattice QCD
• Consistency of the $\pi \Delta$ interaction in chiral perturbation theory
• Pole analysis on unitarized $SU(3)\times SU(3)$ one loop $\chi$PT amplitudes
• P-wave nucleon-pion scattering amplitude in the $\Delta (1232)$ channel from lattice QCD
• Three-body dynamics of the $a_1(1260)$ resonance from lattice QCD
• Chiral Extrapolations of the $\mathbf{\rho }(770)$ Meson in ${\mathbf{N}}_{\mathbf{f}}=2+1$ Lattice QCD Simulations
• Chiral corrections to the Roper mass
• Dalitz plots and lineshape of $a_1(1260)$ from a relativistic three-body unitary approach
• Multi-${\pi }^{+}$ systems in finite volume
• Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory
• Implementing the three-particle quantization condition for ${\pi }^{+}{\pi }^{+}{K}^{+}$ and related systems
• $B_s{\pi }^{+}$ scattering and search for X(5568) with lattice QCD
• Finite volume effects and quark mass dependence of the N(1535) and N(1650)
• Bottomonium resonances with $I=0$ from lattice QCD correlation functions with static and light quarks
• Tetraquark interpolating fields in a lattice QCD investigation of the $D_{s0}^{\ast }(2317)$ meson
• Decay amplitudes to three hadrons from finite-volume matrix elements
• On the generalised eigenvalue method and its relation to Prony and generalised pencil of function methods
• Charmonium resonances with $J^{PC}=1^{--}$ and $3^{--}$ from $\bar{D}D$ scattering on the lattice
• Lattice QCD study on $K^{\ast }(892)$ meson decay width
• Modeling few-body resonances in finite volume
• $Z_c(3900)$: Confronting theory and lattice simulations
• Finite volume treatment of pi pi scattering and limits to phase shifts extraction from lattice QCD
• Nucleon Excited States in N${}_f$=2 lattice QCD
• Aspects of the low-energy constants in the chiral Lagrangian for charmed mesons
• Determination of Delta resonance parameters from lattice QCD
• Eta-photoproduction in a gauge-invariant chiral unitary framework
• Light- and strange-quark mass dependence of the $\rho (770)$ meson revisited
• On the three-particle analog of the Lellouch-Lüscher formula
• $I=1/2$ $S$-wave and $P$-wave $K\pi$ scattering and the $\kappa$ and $K^{\ast }$ resonances from lattice QCD
• The width of the Roper resonance in baryon chiral perturbation theory
• Exploring twisted mass Lattice QCD with the Clover term
• Excited and exotic bottomonium spectroscopy from lattice QCD
• A gauge invariant unitary theory for pion photoproduction
• Study of decuplet baryon resonances from lattice QCD
• Towards the Minimal Spectrum of Excited Baryons
• $\Lambda (1405)$ Contribution to Kaon-Nucleon Scattering Lengths In Chiral Perturbation Theory
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: $I=3/2$ $\pi K$ Scattering Length
• $K\to \pi \pi$ Decays in SU(2) Chiral Perturbation Theory
• Threshold expansion formula of $N$-boson in finite volume from variational approach
• Topological susceptibility and ${\eta }^{\prime }$ meson mass from $N_f=2$ lattice QCD at the physical point
• $I=0$ $\pi \pi$ $s$-wave scattering length from lattice QCD
• The Role of the Roper in QCD
• Visualizing resonances in finite volume
• Implications of chiral symmetry on $S$-wave pionic resonances and the scalar charmed mesons
• The Role of the Roper in Chiral Perturbation Theory
• $d^{\ast }(2380)$ dibaryon from lattice QCD
• The N/D method with non-perturbative left-hand-cut discontinuity and the ${}^1{S}_0$ $NN$ partial wave
• The Role of Lambda(1405) in Kaon-Proton Interactions
• The width of the $\Delta$-resonance at two loop order in baryon chiral perturbation theory
• Low-energy Scattering of $(D^{\ast }{\bar{D}}^{\ast }{)}^{\pm }$ System and the Resonance-like Structure $Z_c(4025)$
• Infrared regularization with vector mesons and baryons
• Renormalization of the baryon axial vector current in large-N_c chiral perturbation theory: Effects of the decuplet-octet mass difference and flavor symmetry breaking
• A coupled-channel lattice study on the resonance-like structure $Z_c(3900)$
• On the definition of the Δmass and width
• Emergence of the $\rho$ resonance from the HAL QCD potential in lattice QCD
• Nucleon-Nucleon scattering from the dispersive N/D method: next-to-leading order study
• Preliminary lattice study of $\sigma$ meson decay width
• Strategies for an accurate determination of the X(3872) energy from QCD lattice simulations
• Baryon magnetic moments in large-N_c chiral perturbation theory: Effects of the decuplet-octet mass difference and flavor symmetry breaking
• Vector form factor of the pion in chiral effective field theory
• Anatomy of the $\rho$ resonance from lattice QCD at the physical point
• Search for H dibaryon on the lattice
• A Lattice Study of $({\bar{D}}_1{D}^{\ast }{)}^{\pm }$ Near-threshold Scattering
• One-loop renormalization of the chiral Lagrangian for spinless matter fields in the SU(N) fundamental representation
• Towards the understanding of $Z_c(3900)$ from lattice QCD
• Subtraction of power counting breaking terms in chiral perturbation theory: spinless matter fields
• Chiral symmetry constraints on resonant amplitudes
• Phenomenological view on baryon-baryon potentials from lattice QCD simulations
• Hadronic decays from the lattice
• Complex-mass renormalization in hadronic EFT: applicability at two-loop order
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• Remark on the effective range approach to the f_0-a_0 mesons
• A study of $\rho -\omega$ mixing in resonance chiral theory
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• Electromagnetic transition form factors of the Roper resonance in baryon chiral perturbation theory
• $\pi \pi$ scattering in partially-quenched twisted-mass chiral perturbation theory
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• An updated review of the new hadron states
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• Cross-channel constraints on resonant antikaon-nucleon scattering
• Light baryon resonances from a coupled-channel study including $\mathbf{K\Sigma }$ photoproduction
• Femtoscopic signatures of the lightest S-wave scalar open-charm mesons
• Benchmark calculations of fully heavy compact and molecular tetraquark states
• Interactions of $\pi K$, $\pi \pi K$ and $KK\pi$ systems at maximal isospin from lattice QCD
• $\omega$ meson from lattice QCD
• Production of exotic hadrons in $pp$ and nuclear collisions
• Revealing the nature of hidden charm pentaquarks with machine learning
• Three-body resonances in the ${\phi }^4$ theory
• Decay behaviors of the fully-bottom and fully-charm tetraquark states
• Determination of crossing-symmetric $\pi \pi$ scattering amplitudes and the quark mass evolution of the $\sigma$ constrained by lattice QCD
• Doubly heavy tetraquark bound and resonant states
• The isospin-3 three-particle $K$-matrix at NLO in ChPT
• Particle-dimer approach for the Roper resonance in a finite volume
• New Hadrons Discovered at BESIII
• Fully strange tetraquark resonant states as the cousins of $X(6900)$
• Fully heavy tetraquark resonant states with different flavors
• $\sigma$ exchange in the one-boson exchange model involving the ground state octet baryons
• Hadronic molecular states with the quark contents $bc\bar{s}\bar{q}$, $b\bar{c}s\bar{q}$, and $b\bar{c}\bar{s}q$
• Effects of Final State Interactions on Landau Singularities
• Double-strangeness exchange reactions in a hybrid Regge-plus-resonance approach
• Physical-mass calculation of $\rho (770)$ and $K^{\ast }(892)$ resonance parameters via $\pi \pi$ and $K\pi$ scattering amplitudes from lattice QCD
• Global Data-Driven Determination of Baryon Transition Form Factors
• ${\bar{B}}^0\to {\bar{K}}^{(\ast )0}X$, $B^{-}\to K^{(\ast )-}X$, ${\bar{B}}_s^0\to \eta ({\eta }^{\prime },\varphi )X$ from the $X(3872)$ molecular perspective
• Interpretation of near-threshold peaks using the method of independent S-matrix poles
• Fully charmed P-wave tetraquark resonant states in the quark model
• Polarization observables in double neutral pion photoproduction
• Decay properties of light $1^{-+}$ hybrids
• Correlations of $C$ and $CP$ violation in $\eta \to {\pi }^0{\ell }^{+}{\ell }^{-}$ and ${\eta }^{\prime }\to \eta {\ell }^{+}{\ell }^{-}$
• Is the $3S$-$2D$ mixing strong for the charmonia $\psi (4040)$ and $\psi (4160)$?
• Construction of general $N$-body lattice operators with arbitrary momenta
• A coupled-channel perspective analysis on bottom-strange molecular pentaquarks
• Interactions of the Pseudoscalar Meson Octet and the Baryon Decuplet in the Continuum and a Finite Volume
• A note on the tensor and vector exchange contributions to $K\bar{K}\to K\bar{K},D\bar{D}\to D\bar{D}$ and ${\pi }^{+}{\pi }^{-}\to {\pi }^{+}{\pi }^{-}$ reactions
• Investigating the two-pion exchange of the double charm $D{D}^{\ast }$ chiral interactions and $T_{cc}$
• Emergence of the $\pi (1300)$ Resonance from Lattice QCD
• Form factors of the $\rho$ meson from effective field theory and the lattice
• Learning Pole Structures of Hadronic States using Predictive Uncertainty Estimation
• Scattering Theory
• An analysis on doubly bottom molecular tetraquarks composed of $H_{(s)}$ and $T_{(s)}$ doublets
• Low-energy $DD$ scattering in lattice QCD