This brief review is dedicated to the memory of Maxim V. Polyakov and his pioneering contributions to pentaquark physics. We focus on his seminal 1997 work with Diakonov and Petrov that predicted the \({\mit \Theta }^+\) pentaquark, a breakthrough that initiated an intense period of research in hadron physics. The field faced a significant setback when the CLAS Collaboration at Jefferson Lab reported null results in 2006, leading to a dramatic decline in light-pentaquark research. Nevertheless, Maxim maintained his scientific conviction, supported by continued positive signals from the DIANA and LEPS collaborations. Through recent experimental findings on the \({\mit \Theta }^+\) and the nucleon-like resonance \(N^*(1685)\), we examine how Polyakov’s theoretical insights, particularly the prediction of a narrow width (\({\mit \Gamma } \approx 0.5\)–\(1.0\) MeV), remain relevant to our understanding of the \({\mit \Theta }^+\) light pentaquark. Abstract Published by the Jagiellonian University 2025 authors

South Korea

H.-Ch. Kim

Pentaquarks and Maxim V. Polyakov

Many excited states in the hadron spectrum have large branching ratios to three-hadron final states. Understanding such particles from first principles QCD requires input from lattice QCD with one-, two-, and three-meson interpolators as well as a reliable three-body formalism relating finite-volume spectra at unphysical pion mass values to the scattering amplitudes at the physical point. In this work, we provide the first-ever calculation of the resonance parameters of the <math><mi>ω</mi></math> meson from lattice QCD, including an update of the formalism through matching to effective field theories. The main result of this pioneering study, the pole position of the <math><mi>ω</mi></math> meson at <math><msqrt><msub><mi>s</mi><mi>ω</mi></msub></msqrt><mo>=</mo><mo>(</mo><mn>778.0</mn><mo>(</mo><mn>11.2</mn><mo>)</mo><mo>−</mo><mi>i</mi><mn>3.0</mn><mo>(</mo><mn>5</mn><mo>)</mo><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, agrees reasonably well with experiment. In addition we provide an estimate of the <math><mi>ω</mi><mo>−</mo><mi>ρ</mi></math> mass difference as 29(15) MeV.

China

Germany

Haobo Yan

Switzerland

United States

Maxim Mai

Marco Garofalo

Ulf-G. Meißner

Chuan Liu

Liuming Liu

Carsten Urbach

<math><mi>ω</mi></math> Meson from Lattice QCD

Starting from the SU(3) limit, we consider the nature of the dynamically generated resonances <math><mi>Λ</mi><mo>(</mo><mn>1380</mn><mo>)</mo></math>, <math><mi>Λ</mi><mo>(</mo><mn>1405</mn><mo>)</mo></math> and <math><mi>Λ</mi><mo>(</mo><mn>1680</mn><mo>)</mo></math> as the pion and kaon masses are tuned to their physical values. We show that the accidental symmetry of the two octets due to the leading order Weinberg-Tomozawa term is broken by the next-to-leading order terms. Most interestingly, we observe an interchange of the two trajectories of the <math><mi>Λ</mi><mo>(</mo><mn>1380</mn><mo>)</mo></math> and the <math><mi>Λ</mi><mo>(</mo><mn>1405</mn><mo>)</mo></math> away from the SU(3) limit at next-to-leading order. This remarkable phenomenon can be investigated using lattice QCD calculations that start from the SU(3) limit.

Feng-Kun Guo

Yuki Kamiya

Georgia

New insights into the nature of the Λ(1380) and Λ(1405) resonances away from the SU(3) limit

We propose a new finite-volume approach which implements two- and three-body dynamics in a transparent way based on an Effective Field Theory Lagrangian. The formalism utilizes a particle-dimer picture and formulates the quantization conditions based on the self-energy of the decaying particle. The formalism is studied for the case of the Roper resonance, using input from lattice QCD and phenomenology. Finally, finite-volume energy eigenvalues are predicted and compared to existing results of lattice QCD calculations. This crucially provides initial guidance on the necessary level of precision for the finite-volume spectrum.

Daniel Severt

Particle-dimer approach for the Roper resonance in a finite volume

We study the properties of three-body resonances using a lattice complex scalar φ 4 theory with two scalars, with parameters chosen such that one heavy particle can decay into three light ones. We determine the two- and three-body spectra for several lattice volumes using variational techniques, and then analyze them with two versions of the three-particle finite-volume formalism: the Relativistic Field Theory approach and the Finite-Volume Unitarity approach. We find that both methods provide an equivalent description of the energy levels, and we are able to fit the spectra using simple parametrizations of the scattering quantities. By solving the integral equations of the corresponding three-particle formalisms, we determine the pole position of the resonance in the complex energy plane and thereby its mass and width. We find very good agreement between the two methods at different values of the coupling of the theory.

Fernando Romero-López

Akaki Rusetsky

Three-body resonances in the φ 4 theory

Chiral perturbation theory and its unitarized versions have played an important role in our understanding of the low-energy strong interaction. Yet, so far, such studies typically deal exclusively with perturbative or nonperturbative channels. In this Letter, we report on the first global study of meson-baryon scattering up to one-loop order. It is shown that covariant baryon chiral perturbation theory, including its unitarization for the negative strangeness sector, can describe meson-baryon scattering data remarkably well. This provides a highly nontrivial check on the validity of this important low-energy effective field theory of QCD. We show that the <math><mover><mi>K</mi><mo>¯</mo></mover><mi>N</mi></math> related quantities can be better described in comparison with those of lower-order studies, and with reduced uncertainties due to the stringent constraints from the <math><mi>π</mi><mi>N</mi></math> and <math><mi>K</mi><mi>N</mi></math> phase shifts. In particular, we find that the two-pole structure of <math><mi>Λ</mi><mo>(</mo><mn>1405</mn><mo>)</mo></math> persists up to one-loop order reinforcing the existence of two-pole structures in dynamically generated states.

Jun-Xu Lu

Li-Sheng Geng

Michael Doering

Cross-Channel Constraints on Resonant Antikaon-Nucleon Scattering

Masses, widths, and branching ratios of hadronic resonances are quantified by their pole positions and residues with respect to transition amplitudes on the Riemann sheets of the complex energy plane. In this study, we discuss the analytic structure in the physical energy region of three-body scattering amplitudes on such manifolds. As an application, we determine the pole position of the <math><msub><mi>a</mi><mn>1</mn></msub><mo>(</mo><mn>1260</mn><mo>)</mo></math> meson from the ALEPH experiment by allowing for <math><mi>π</mi><mi>ρ</mi></math> coupled channels in <math><mi>S</mi></math> and <math><mi>D</mi></math> waves. We find it to be <math><mrow><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msqrt><mo>=</mo><mo>(</mo><mn>123</mn><msubsup><mrow><mn>2</mn></mrow><mrow><mo>−</mo><mn>0</mn><mo>−</mo><mn>11</mn></mrow><mrow><mo>+</mo><mn>15</mn><mo>+</mo><mn>9</mn></mrow></msubsup><mo>−</mo><mi>i</mi><mn>26</mn><msubsup><mrow><mn>6</mn></mrow><mrow><mo>−</mo><mn>22</mn><mo>−</mo><mn>27</mn></mrow><mrow><mo>+</mo><mn>0</mn><mo>+</mo><mn>15</mn></mrow></msubsup><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>.

Daniel Sadasivan

Andrei Alexandru

Hakan Akdag

Felipe Amorim

Ruairí Brett

United Kingdom

Chris Culver

Michael Döring

Frank X. Lee

Pole position of the <math><msub><mi>a</mi><mn>1</mn></msub><mo>(</mo><mn>1260</mn><mo>)</mo></math> resonance in a three-body unitary framework

Resonant hadronic systems often exhibit a complicated decay pattern in which three-body dynamics play a relevant or even dominant role. In this work we focus on the <math><msub><mi>a</mi><mn>1</mn></msub><mo>(</mo><mn>1260</mn><mo>)</mo></math> resonance. For the first time, the pole position and branching ratios of a three-body resonance are calculated from lattice QCD using one-, two-, and three-meson interpolators and a three-body finite-volume formalism extended to spin and coupled channels. This marks a new milestone for ab initio studies of ordinary resonances along with hybrid and exotic hadrons involving three-body dynamics.

Three-Body Dynamics of the <math><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mn>1260</mn><mo>)</mo></mrow></math> Resonance from Lattice QCD

We perform a fit of the finite-volume QCD spectrum of three pions at maximal isospin to constrain the three-body force. We use the unitarity-based relativistic three-particle quantization condition, with the GWUQCD spectrum obtained at 315 MeV and 220 MeV pion mass in two-flavor QCD. For the heavier pion mass we find that the data is consistent with a constant contact term close to zero, whereas for the lighter mass we see a statistically significant energy dependence in tension with the prediction of leading order ChPT. Our results also suggest that with enough three-body energy levels, the two-body amplitude could be constrained.

Three-body interactions from the finite-volume QCD spectrum

We present a lattice computation of ππ–scattering in the <math><mi>I</mi><mo>=</mo><mn>1</mn></math> channel with <math><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn></math> dynamical quark flavours obtained with ensembles bracketing the physical value of the pion mass. Employing a global fit to data at three values of the pion mass, we determine the universal parameters of the ρ-resonance. We carefully investigate systematic uncertainties by determining energy eigenvalues using different methods and by comparing inverse amplitude method and Breit-Wigner type parametrizations. Overall, exploring the complex energy plane we find mass <math><msub><mrow><mi>M</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>=</mo><mn>786</mn><mo>(</mo><mn>22</mn><mo>)</mo><mspace width="0.25em"></mspace><mtext>MeV</mtext></math> and width <math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>=</mo><mn>180</mn><mo>(</mo><mn>6</mn><mo>)</mo><mspace width="0.25em"></mspace><mtext>MeV</mtext></math>, including statistical and systematic uncertainties. In contrast to previous <math><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn></math> extrapolations from higher than physical pion mass results, our mass value is in good agreement with experiment, while the width is too high.