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arxiv: 2606.19040 · v1 · pith:4LPNB4ROnew · submitted 2026-06-17 · ✦ hep-ph · hep-ex· hep-lat· nucl-th

Three-body unitary determination of the f₁(1285) and f₁(1420) pole positions

Tao-Ran Hu , Hai-Long Fu , Feng-Kun Guo , Ulf-G. Mei{\ss}ner , Xu Zhang This is my paper

Pith reviewed 2026-06-26 20:20 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-latnucl-th
keywords three-body unitarityresonance polesf1(1285)f1(1420)K K-bar pi systemBESIII invariant masshadronic molecule
0
0 comments X

The pith

A three-body unitary amplitude fitted to BESIII data and continued to unphysical Riemann sheets places poles for the f1(1285) at 1277 - i12 MeV and the f1(1420) at 1435 - i40 MeV.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs a unitary amplitude for the coupled pi a0 and K K-bar* channels in the 0+(1++) K K-bar pi system using the spectator-isobar representation. Short-range three-body forces are fixed by a fit to the relevant component of the BESIII invariant-mass distribution from J/psi to gamma K0S K0S pi0. Analytic continuation of the resulting amplitude locates two stable poles whose trajectories show the lower one arising from a dressed bare state and the higher one from an S-wave K K-bar* quasi-bound state. This matters because it supplies concrete complex masses and clarifies which resonance carries a molecular character. The work also isolates an extra pole generated purely by the P-wave pi a0 contact term that leaves little trace on the physical line shape.

Core claim

In the infinite-volume three-body unitary framework the fitted amplitude for the I^G(J^PC)=0^+(1^{++}) K K-bar pi system, when continued to the relevant unphysical Riemann sheets, produces two robust poles: sqrt(s_f1(1285)) = (1277±2±1) - i(12±1±0) MeV and sqrt(s_f1(1420)) = (1435±2±7) - i(40±2±1) MeV. Pole trajectories indicate the f1(1285) originates from dressing a bare state introduced in the potential, whereas the f1(1420) is predominantly dynamically generated from an S-wave K K-bar* quasi-bound state mixed with the nearby bare state, supporting its hadronic-molecule interpretation. An additional pole deeper in the complex plane appears on the same sheet as the f1(1285) and is generate

What carries the argument

The spectator-isobar representation of the coupled pi a0-K K-bar* amplitude that incorporates one-particle-exchange interactions required by three-body unitarity, plus short-range three-body contact terms constrained by data, followed by analytic continuation onto unphysical Riemann sheets.

If this is right

  • The f1(1285) is a dressed bare state while the f1(1420) is largely dynamically generated from a K K-bar* quasi-bound state.
  • The three-body framework automatically incorporates the triangle-singularity mechanism through the one-particle-exchange term.
  • An extra pole generated solely by the P-wave pi a0 contact interaction exists but produces negligible visible effect on the physical lineshape.
  • Detailed treatment of three-body cuts is required to solve the integral equation reliably.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The extracted pole positions could be inserted into predictions for branching ratios in other three-body final states not yet measured.
  • The same unitary construction might be applied to related axial-vector resonances in the strange sector to test consistency of the molecular picture.
  • Production-rate differences between the two resonances could serve as an experimental handle to distinguish bare-state versus dynamically generated components.

Load-bearing premise

The short-range three-body interaction is fixed by fitting only the 0+(1++) component of the BESIII K0S K0S pi0 invariant-mass distribution in the J/psi to gamma K0S K0S pi0 decay.

What would settle it

A high-statistics measurement of the same invariant-mass distribution in an independent production channel whose shape deviates from the fitted amplitude on the physical sheet by more than the reported uncertainties.

read the original abstract

We study the $I^G(J^{PC})=0^+(1^{++})$ $K\bar K\pi$ system in an infinite-volume three-body unitary framework, focusing on the pole content of the region of the $f_1(1285)$ and $f_1(1420)$ resonances. The coupled $\pi a_0$-$K\bar K^*$ amplitude is constructed in the spectator-isobar representation, where the one-particle-exchange interaction required by three-body unitarity automatically incorporates the triangle-singularity mechanism. The short-range three-body interaction is constrained by fitting the $0^+(1^{++})$ component of the BESIII $K^0_SK^0_S\pi^0$ invariant-mass distribution in the $J/\psi\to\gamma(K^0_SK^0_S\pi^0)$ decay. Analytically continuing the fitted amplitude to the relevant unphysical Riemann sheets, we find two robust poles: \begin{align} \sqrt{s_{f_1(1285)}}&= \left(1277\pm2\pm1\right) -i\left(12\pm1\pm0\right)\text{MeV}\,,\notag\\ \sqrt{s_{f_1(1420)}}&= \left(1435\pm2\pm7\right) -i\left(40\pm2\pm1\right)\text{MeV}\,.\notag \end{align} The pole trajectories indicate that the $f_1(1285)$ originates from dressing a bare state introduced in the potential. In contrast, the $f_1(1420)$ is predominantly dynamically generated, and a single-channel analysis traces it to an $S$-wave $K\bar K^*$ quasi-bound state mixed with the nearby bare state, supporting its hadronic-molecule interpretation. We also find an additional pole deeper in the complex plane in the best-fit amplitude on the same Riemann sheet as the $f_1(1285)$. This additional pole is generated by the $P$-wave $\pi a_0$ contact interaction alone. It has a sizable cutoff and two-body-input dependence, and leaves little visible imprint on the physical lineshape. Finally, we provide a detailed and pedagogical appendix on how three-body cuts affect the solution of the integral equation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript constructs a coupled-channel amplitude for the I^G(J^PC)=0^+(1++) K Kbar pi system in an infinite-volume three-body unitary spectator-isobar framework that includes one-particle exchange (automatically incorporating triangle singularities) plus a short-range three-body contact term. The single strength parameter of the contact term is fixed by a fit to the 0+(1++) projection of the BESIII K0S K0S pi0 invariant-mass distribution from J/psi -> gamma(K0S K0S pi0). Analytic continuation to the relevant unphysical Riemann sheets yields two poles whose positions are reported with statistical and systematic uncertainties; the f1(1285) is interpreted as a dressed bare state while the f1(1420) is predominantly dynamically generated from an S-wave K Kbar* quasi-bound state. An additional deeper pole generated by the P-wave pi a0 contact term is also found but has limited visible effect on the physical lineshape. A pedagogical appendix discusses three-body cuts in the integral equation.

Significance. If the extracted poles prove stable, the work supplies a unitary three-body determination of resonance parameters in the f1 sector that automatically respects three-body unitarity and triangle-singularity effects. The explicit separation of bare-state dressing versus dynamical generation, together with the detailed appendix on three-body cuts, constitutes a useful technical contribution to the study of light axial-vector mesons and hadronic molecules.

major comments (1)
  1. [Abstract and amplitude construction] Abstract (pole extraction paragraph) and amplitude-construction section: the short-range three-body interaction is fixed by a single-parameter fit to one invariant-mass distribution. The central claim that the two quoted poles are 'robust' (with the reported ±2±1 and ±2±7 uncertainties) is load-bearing, yet the manuscript provides no explicit demonstration that the pole locations remain stable under reasonable variations of the short-range functional form or under the inclusion of additional independent data sets; without such tests the quoted uncertainties may not fully capture model dependence on unphysical sheets.
minor comments (1)
  1. The notation sqrt(s_f1) for the complex pole position is conventional but would benefit from an explicit statement that it denotes the complex energy (rather than the square root of the Mandelstam variable) to avoid any ambiguity for readers.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract and amplitude construction] Abstract (pole extraction paragraph) and amplitude-construction section: the short-range three-body interaction is fixed by a single-parameter fit to one invariant-mass distribution. The central claim that the two quoted poles are 'robust' (with the reported ±2±1 and ±2±7 uncertainties) is load-bearing, yet the manuscript provides no explicit demonstration that the pole locations remain stable under reasonable variations of the short-range functional form or under the inclusion of additional independent data sets; without such tests the quoted uncertainties may not fully capture model dependence on unphysical sheets.

    Authors: We agree that explicit stability tests under variations of the short-range functional form would strengthen the robustness claim for the poles on unphysical sheets. The present work uses a minimal single-parameter contact term fitted to the single available BESIII invariant-mass distribution, with systematic uncertainties estimated from cutoff and two-body input variations. We did not perform additional fits with alternative momentum-dependent forms of the contact interaction. In the revised manuscript we will add such tests (e.g., a momentum-dependent contact term) and show the resulting pole trajectories to quantify residual model dependence. Regarding additional independent data sets, the analysis is deliberately scoped to the existing BESIII K0S K0S pi0 projection; a global fit incorporating further channels or experiments lies outside the present scope and is left for future work. The pole-trajectory analysis already provides supporting evidence for the quoted positions, but the planned tests will address the referee's concern directly. revision: partial

Circularity Check

0 steps flagged

No circularity: poles obtained via data fit plus analytic continuation in a unitary framework

full rationale

The derivation constructs a coupled-channel amplitude in the spectator-isobar representation using one-particle exchange (enforced by three-body unitarity) plus a single short-range contact term. The contact strength is fixed by a fit to the BESIII K0S K0S pi0 invariant-mass distribution; the pole positions are then located by analytic continuation of the resulting amplitude to unphysical Riemann sheets. Neither step reduces to the other by definition or by self-citation; the output poles are not inputs, and the framework does not invoke load-bearing self-citations or rename known results. The procedure is self-contained against external data and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the spectator-isobar representation of three-body unitarity and on the assumption that a fit to one experimental distribution sufficiently constrains the short-range interaction for reliable analytic continuation. Free parameters are the strengths of the short-range three-body contacts. The framework assumes the one-particle-exchange term automatically incorporates the triangle singularity without additional tuning.

free parameters (1)
  • short-range three-body interaction parameters
    Adjusted to reproduce the 0+(1++) component of the BESIII invariant-mass distribution
axioms (1)
  • domain assumption Spectator-isobar representation of the three-body amplitude with one-particle exchange
    Abstract states that this representation automatically incorporates the triangle-singularity mechanism required by three-body unitarity

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discussion (0)

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Reference graph

Works this paper leans on

106 extracted references · 89 canonical work pages · 48 internal anchors

  1. [1]

    The puzzle of anomalously large isospin violations in $\eta(1405/1475)\to 3\pi$

    J.-J. Wu, X.-H. Liu, Q. Zhao and B.-S. Zou,The Puzzle of anomalously large isospin violations inη(1405/1475)→3π,Phys. Rev. Lett.108(2012) 081803 [1108.3772]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  2. [2]

    Isospin breaking and $f_0(980)$-$a_0(980)$ mixing in the $\eta(1405) \to \pi^{0} f_0(980)$ reaction

    F. Aceti, W.H. Liang, E. Oset, J.J. Wu and B.S. Zou,Isospin breaking andf 0(980)-a0(980) mixing in theη(1405)→π 0f0(980)reaction,Phys. Rev. D86(2012) 114007 [1209.6507]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  3. [3]

    Update of the ALEPH non-strange spectral functions from hadronic $\tau$ decays

    M. Davier, A. H¨ ocker, B. Malaescu, C.-Z. Yuan and Z. Zhang,Update of the ALEPH non-strange spectral functions from hadronicτdecays,Eur. Phys. J. C74(2014) 2803 [1312.1501]. [5]COMPASScollaboration,Observation of a New Narrow Axial-Vector Mesona 1(1420), Phys. Rev. Lett.115(2015) 082001 [1501.05732]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  4. [4]

    On the nature of $a_1(1420)$

    M. Mikhasenko, B. Ketzer and A. Sarantsev,Nature of thea 1(1420),Phys. Rev. D91 (2015) 094015 [1501.07023]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  5. [5]

    The "$a_1(1420)$" peak as the $\pi f_0(980)$ decay mode of the $a_1(1260)$

    F. Aceti, L.R. Dai and E. Oset,a 1(1420)peak as theπf 0(980)decay mode of thea 1(1260), Phys. Rev. D94(2016) 096015 [1606.06893]. [8]COMPASScollaboration,Light isovector resonances inπ −p→π −π−π+pat 190 GeV/c, Phys. Rev. D98(2018) 092003 [1802.05913]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  6. [6]

    Du and Q

    M.-C. Du and Q. Zhao,Internal particle width effects on the triangle singularity mechanism in the study of theη(1405)andη(1475)puzzle,Phys. Rev. D100(2019) 036005 [1905.04207]. [10]COMPASScollaboration,Triangle Singularity as the Origin of thea 1(1420),Phys. Rev. Lett.127(2021) 082501 [2006.05342]. [11]COMPASScollaboration,Exotic mesonπ 1(1600)withJ P C =...

    work page arXiv 2019

  7. [7]

    Updated analysis of $\pi$N elastic scattering data to 2.1~GeV: The Baryon Spectrum

    R.A. Arndt, I.I. Strakovsky, R.L. Workman and M.M. Pavan,Updated analysis ofπN elastic scattering data to 2.1 GeV: The Baryon spectrum,Phys. Rev. C52(1995) 2120 [nucl-th/9505040]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  8. [8]

    Dynamical coupled-channels study of pi N --> pi pi N reactions

    H. Kamano, B. Julia-Diaz, T.S.H. Lee, A. Matsuyama and T. Sato,Dynamical coupled-channels study ofπN→ππNreactions,Phys. Rev. C79(2009) 025206 [0807.2273]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  9. [9]

    Solution to Faddeev equations with two-body experimental amplitudes as input and application to J^P=1/2^+, S=0 baryon resonances

    A. Martinez Torres, K.P. Khemchandani and E. Oset,Solution to Faddeev equations with two-body experimental amplitudes as input and application toJ P = 1/2+, S= 0baryon resonances,Phys. Rev. C79(2009) 065207 [0812.2235]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  10. [10]

    Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model

    M. D¨ oring, C. Hanhart, F. Huang, S. Krewald and U.G. Meißner,Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model,Nucl. Phys. A 829(2009) 170 [0903.4337]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  11. [11]

    On the nature of the Roper resonance

    L. Alvarez-Ruso,On the nature of the Roper resonance, inMini-Workshop Bled 2010: Dressing Hadrons, pp. 1–8, 11, 2010 [1011.0609]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  12. [12]

    Coupled-channel dynamics in the reactions piN --> piN, etaN, KLambda, KSigma

    D. Ronchen, M. D¨ oring, F. Huang, H. Haberzettl, J. Haidenbauer, C. Hanhart et al., Coupled-channel dynamics in the reactionsπN→πN, ηN, KΛ, KΣ,Eur. Phys. J. A49 (2013) 44 [1211.6998]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  13. [13]

    Kamano and T.S.H

    H. Kamano and T.S.H. Lee,Dynamical study ofπN→ππNreactions revisited, 2601.17389. – 29 – [19]BESIIIcollaboration,Observation of a Charged Charmoniumlike Structure in e+e− →π +π−J/ψat √s=4.26 GeV,Phys. Rev. Lett.110(2013) 252001 [1303.5949]. [20]Bellecollaboration,Study ofe +e− →π +π−J/ψand Observation of a Charged Charmoniumlike State at Belle,Phys. Rev. ...

    work page arXiv 2013

  14. [14]

    Q. Wang, C. Hanhart and Q. Zhao,Decoding the riddle ofY(4260)andZ c(3900),Phys. Rev. Lett.111(2013) 132003 [1303.6355]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  15. [15]

    $Z_c(3900)$: what has been really seen?

    M. Albaladejo, F.-K. Guo, C. Hidalgo-Duque and J. Nieves,Z c(3900): What has been really seen?,Phys. Lett. B755(2016) 337 [1512.03638]. [23]JPACcollaboration,Amplitude analysis and the nature of theZ c(3900),Phys. Lett. B772 (2017) 200 [1612.06490]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  16. [16]

    The $Z_c(3900)$ peak does not come from the "triangle singularity"

    Q.-R. Gong, J.-L. Pang, Y.-F. Wang and H.-Q. Zheng,TheZ c(3900)peak does not come from the “triangle singularity”,Eur. Phys. J. C78(2018) 276 [1612.08159]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  17. [17]

    Threshold cusps and triangle singularities in hadronic reactions,

    F.-K. Guo, X.-H. Liu and S. Sakai,Threshold cusps and triangle singularities in hadronic reactions,Prog. Part. Nucl. Phys.112(2020) 103757 [1912.07030]. [26]JPACcollaboration,Novel approaches in hadron spectroscopy,Prog. Part. Nucl. Phys.127 (2022) 103981 [2112.13436]

    work page arXiv 2020

  18. [18]

    Liu, Y.-W

    M.-Z. Liu, Y.-W. Pan, Z.-W. Liu, T.-W. Wu, J.-X. Lu and L.-S. Geng,Three ways to decipher the nature of exotic hadrons: Multiplets, three-body hadronic molecules, and correlation functions,Phys. Rept.1108(2025) 1 [2404.06399]

    work page arXiv 2025

  19. [19]

    Dynamical coupled-channel models for hadron dy- namics,

    M. D¨ oring, J. Haidenbauer, M. Mai and T. Sato,Dynamical coupled-channel models for hadron dynamics,Prog. Part. Nucl. Phys.146(2026) 104213 [2505.02745]. [29]Bellecollaboration,Observation of a narrow charmonium-like state in exclusive B± →K ±π+π−J/ψdecays,Phys. Rev. Lett.91(2003) 262001 [hep-ex/0309032]

    work page arXiv 2026

  20. [20]

    Three-body $D\bar{D}\pi$ dynamics for the X(3872)

    V. Baru, A.A. Filin, C. Hanhart, Y.S. Kalashnikova, A.E. Kudryavtsev and A.V. Nefediev, Three-bodyD ¯Dπdynamics for theX(3872),Phys. Rev. D84(2011) 074029 [1108.5644]. [31]LHCbcollaboration,Determination of theX(3872)meson quantum numbers,Phys. Rev. Lett.110(2013) 222001 [1302.6269]. [32]LHCbcollaboration,Observation of an exotic narrow doubly charmed tet...

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  21. [21]

    M.-L. Du, V. Baru, X.-K. Dong, A. Filin, F.-K. Guo, C. Hanhart et al.,Coupled-channel approach toT + cc including three-body effects,Phys. Rev. D105(2022) 014024 [2110.13765]

    work page arXiv 2022

  22. [22]

    Lin, J.-B

    Z.-Y. Lin, J.-B. Cheng and S.-L. Zhu,T + cc andχ c1(3872)with the complex scaling method andDD( ¯D)πthree-body effect,Phys. Rev. D110(2024) 054008 [2205.14628]

    work page arXiv 2024

  23. [23]

    Zhang,Relativistic three-body scattering and theD 0D∗+-D+D∗0 system,Phys

    X. Zhang,Relativistic three-body scattering and theD 0D∗+-D+D∗0 system,Phys. Rev. D 109(2024) 094010 [2402.02151]

    work page arXiv 2024

  24. [24]

    Hansen, F

    M.T. Hansen, F. Romero-L´ opez and S.R. Sharpe,IncorporatingDDπeffects and left-hand cuts in lattice QCD studies of theT cc(3875)+,JHEP06(2024) 051 [2401.06609]

    work page arXiv 2024

  25. [25]

    Dawid, F

    S.M. Dawid, F. Romero-L´ opez and S.R. Sharpe,Finite- and infinite-volume study ofDDπ scattering,JHEP01(2025) 060 [2409.17059]. – 30 –

    work page arXiv 2025

  26. [26]

    Dawid, F

    S.M. Dawid, F. Romero-L´ opez and S.R. Sharpe,Comparison of integral equations used to studyT + cc for a stableD ∗,JHEP09(2025) 058 [2505.05466]

    work page arXiv 2025

  27. [27]

    Khuri and S.B

    N.N. Khuri and S.B. Treiman,Pion-Pion Scattering andK ± →3πDecay,Phys. Rev.119 (1960) 1115

    1960

  28. [28]

    Final State Interactions and Khuri-Treiman Equations in $\eta\to 3\pi$ decays

    J. Kambor, C. Wiesendanger and D. Wyler,Final state interactions and Khuri-Treiman equations inη→3πdecays,Nucl. Phys. B465(1996) 215 [hep-ph/9509374]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  29. [29]

    Rescattering effects in eta {\to} 3pi decays

    S.P. Schneider, B. Kubis and C. Ditsche,Rescattering effects inη→3πdecays,JHEP02 (2011) 028 [1010.3946]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  30. [30]

    Analytical dispersive construction of $\eta\to3\pi$ amplitude: First order in isospin breaking

    K. Kampf, M. Knecht, J. Novotny and M. Zdrahal,Analytical dispersive construction of η→3πamplitude: first order in isospin breaking,Phys. Rev. D84(2011) 114015 [1103.0982]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  31. [31]

    Dispersive analysis of omega --> 3pi and phi --> 3pi decays

    F. Niecknig, B. Kubis and S.P. Schneider,Dispersive analysis ofω→3πandϕ→3π decays,Eur. Phys. J. C72(2012) 2014 [1203.2501]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  32. [32]

    Dispersive Analysis of $\omega/\phi \rightarrow 3\pi,\,\pi \gamma^*$

    I.V. Danilkin, C. Fern´ andez-Ram´ ırez, P. Guo, V. Mathieu, D. Schott, M. Shi et al., Dispersive analysis ofω/ϕ→3π/πγ ∗,Phys. Rev. D91(2015) 094029 [1409.7708]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  33. [33]

    Three-body Final State Interaction in $\eta \to 3 \pi$

    P. Guo, I.V. Danilkin, D. Schott, C. Fern´ andez-Ram´ ırez, V. Mathieu and A.P. Szczepaniak, Three-body final state interaction inη→3π,Phys. Rev. D92(2015) 054016 [1505.01715]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  34. [34]

    Zhang and F.-K

    Z.-H. Zhang and F.-K. Guo,D ±D∗∓ Hadronic Atom as a Key to Revealing theX(3872) Mystery,Phys. Rev. Lett.127(2021) 012002 [2012.08281]

    work page arXiv 2021

  35. [35]

    Ji, X.-K

    T. Ji, X.-K. Dong, F.-K. Guo and B.-S. Zou,Prediction of a Narrow Exotic Hadronic State with Quantum NumbersJ P C = 0−−,Phys. Rev. Lett.129(2022) 102002 [2205.10994]

    work page arXiv 2022

  36. [36]

    Zhang, H.-L

    X. Zhang, H.-L. Fu, F.-K. Guo and H.-W. Hammer,Neutron scattering off one-neutron halo nuclei in halo effective field theory,Phys. Rev. C108(2023) 044304 [2308.12815]

    work page arXiv 2023

  37. [37]

    Zhang, T

    Z.-H. Zhang, T. Ji, X.-K. Dong, F.-K. Guo, C. Hanhart, U.-G. Meißner et al.,Predicting isovector charmonium-like states fromX(3872)properties,JHEP08(2024) 130 [2404.11215]

    work page arXiv 2024

  38. [38]

    Ji, X.-K

    T. Ji, X.-K. Dong, F.-K. Guo, C. Hanhart and U.-G. Meißner,Precise determination of the properties ofX(3872)and of its isovector partnerW c1,2502.04458

    work page arXiv

  39. [39]

    Fu, Y.-H

    H.-L. Fu, Y.-H. Lin, F.-K. Guo, H.-W. Hammer, U.-G. Meißner, A. Rusetsky et al., Exploring Efimov states in D ∗D∗D∗ and DD ∗D∗ three-body systems,JHEP07(2025) 081 [2503.19709]

    work page arXiv 2025

  40. [40]

    A relativistic, model-independent, three-particle quantization condition

    M.T. Hansen and S.R. Sharpe,Relativistic, model-independent, three-particle quantization condition,Phys. Rev. D90(2014) 116003 [1408.5933]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  41. [41]

    Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude

    M.T. Hansen and S.R. Sharpe,Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude,Phys. Rev. D92(2015) 114509 [1504.04248]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  42. [42]

    Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles

    R.A. Brice˜ no, M.T. Hansen and S.R. Sharpe,Relating the finite-volume spectrum and the two-and-three-particleSmatrix for relativistic systems of identical scalar particles,Phys. Rev. D95(2017) 074510 [1701.07465]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  43. [43]

    Jackura, R.A

    A.W. Jackura, R.A. Brice˜ no, S.M. Dawid, M.H.E. Islam and C. McCarty,Solving relativistic three-body integral equations in the presence of bound states,Phys. Rev. D104 (2021) 014507 [2010.09820]. – 31 –

    work page arXiv 2021

  44. [44]

    Dawid, M.H.E

    S.M. Dawid, M.H.E. Islam and R.A. Brice˜ no,Analytic continuation of the relativistic three-particle scattering amplitudes,Phys. Rev. D108(2023) 034016 [2303.04394]

    work page arXiv 2023

  45. [45]

    M. Mai, B. Hu, M. D¨ oring, A. Pilloni and A. Szczepaniak,Three-body Unitarity with Isobars Revisited,Eur. Phys. J. A53(2017) 177 [1706.06118]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  46. [46]

    Dalitz plots and lineshape ofa 1(1260) from a relativistic three- body unitary approach,

    D. Sadasivan, M. Mai, H. Akdag and M. D¨ oring,Dalitz plots and lineshape ofa 1(1260)from a relativistic three-body unitary approach,Phys. Rev. D101(2020) 094018 [2002.12431]

    work page arXiv 2020

  47. [47]

    Pole position of the a1(1260) resonance in a three-body unitary framework,

    D. Sadasivan, A. Alexandru, H. Akdag, F. Amorim, R. Brett, C. Culver et al.,Pole position of thea 1(1260)resonance in a three-body unitary framework,Phys. Rev. D105(2022) 054020 [2112.03355]

    work page arXiv 2022

  48. [48]

    Y. Feng, F. Gil, M. D¨ oring, R. Molina, M. Mai, V. Shastry et al.,Unitary coupled-channel three-body amplitude with pions and kaons,Phys. Rev. D110(2024) 094002 [2407.08721]

    work page arXiv 2024

  49. [49]

    Effects of Final State Interactions on Landau Singularities

    A.S. Sakthivasan, M. Mai, A. Rusetsky and M. D¨ oring,Effects of final state interactions on Landau singularities,JHEP10(2024) 246 [2407.17969]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  50. [50]

    Three-body Unitarity in the Finite Volume

    M. Mai and M. D¨ oring,Three-body Unitarity in the Finite Volume,Eur. Phys. J. A53 (2017) 240 [1709.08222]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  51. [51]

    Three-body spectrum in a finite volume: the role of cubic symmetry

    M. D¨ oring, H.-W. Hammer, M. Mai, J.-Y. Pang, A. Rusetsky and J. Wu,Three-body spectrum in a finite volume: the role of cubic symmetry,Phys. Rev. D97(2018) 114508 [1802.03362]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  52. [52]

    Finite-volume spectrum of $\pi^+\pi^+$ and $\pi^+\pi^+\pi^+$ systems

    M. Mai and M. Doring,Finite-Volume Spectrum ofπ +π+ andπ +π+π+ Systems,Phys. Rev. Lett.122(2019) 062503 [1807.04746]. [66]GWQCDcollaboration,Three-Body Dynamics of thea 1(1260)Resonance from Lattice QCD,Phys. Rev. Lett.127(2021) 222001 [2107.03973]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  53. [53]

    H. Yan, M. Mai, M. Garofalo, U.-G. Meißner, C. Liu, L. Liu et al.,ωMeson from Lattice QCD,Phys. Rev. Lett.133(2024) 211906 [2407.16659]

    work page arXiv 2024

  54. [54]

    H. Yan, M. Mai, M. Garofalo, Y. Feng, M. D¨ oring, C. Liu et al.,Emergence of theπ(1300) Resonance from Lattice QCD,Phys. Rev. Lett.136(2026) 141901 [2510.09476]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  55. [55]

    Y. Feng, C. Culver, M. D¨ oring, M. Mai, A. Alexandru and F.X. Lee,Coupled-channel approach to isotensorπππscattering from lattice QCD,2601.16916

    work page arXiv

  56. [56]

    Meißner and A

    U.-G. Meißner and A. Rusetsky,Effective Field Theories, Cambridge University Press (8, 2022), 10.1017/9781108689038

    work page doi:10.1017/9781108689038 2022

  57. [57]

    Aitchison and R

    I.J.R. Aitchison and R. Pasquier,Three-Body Unitarity and Khuri-Treiman Amplitudes, Phys. Rev.152(1966) 1274

    1966

  58. [58]

    Unitarity, Analyticity and Crossing Symmetry in Two- and Three-hadron Final State Interactions

    I.J.R. Aitchison,Unitarity, Analyticity and Crossing Symmetry in Two- and Three-hadron Final State Interactions,1507.02697. [73]JPACcollaboration,Phenomenology of relativistic3→3reaction amplitudes within the isobar approximation,Eur. Phys. J. C79(2019) 56 [1809.10523]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  59. [59]

    Lattice QCD and Three-particle Decays of Resonances,

    M.T. Hansen and S.R. Sharpe,Lattice QCD and Three-particle Decays of Resonances,Ann. Rev. Nucl. Part. Sci.69(2019) 65 [1901.00483]

    work page arXiv 2019

  60. [60]

    Jackura, S.M

    A.W. Jackura, S.M. Dawid, C. Fern´ andez-Ram´ ırez, V. Mathieu, M. Mikhasenko, A. Pilloni et al.,Equivalence of three-particle scattering formalisms,Phys. Rev. D100(2019) 034508 [1905.12007]. – 32 –

    work page arXiv 2019

  61. [61]

    Blanton and S.R

    T.D. Blanton and S.R. Sharpe,Equivalence of relativistic three-particle quantization conditions,Phys. Rev. D102(2020) 054515 [2007.16190]. [77]Particle Data Groupcollaboration,Review of Particle Physics,Int. J. Mod. Phys. A41 (2026) 2630011. [78]Athens-Bari-Birmingham-CERNcollaboration,Spin Parity Analysis of the E Meson Centrally Produced in the Reaction...

    work page arXiv 2020

  62. [62]

    Godfrey and N

    S. Godfrey and N. Isgur,Mesons in a Relativized Quark Model with Chromodynamics, Phys. Rev. D32(1985) 189

    1985

  63. [63]

    Implications of the Glueball-qqbar filter on the 1++ nonet

    F.E. Close and A. Kirk,Implications of the Glueball-q¯qfilter on the1 ++ nonet,Z. Phys. C 76(1997) 469 [hep-ph/9706543]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  64. [64]

    Light axial vector mesons

    K. Chen, C.-Q. Pang, X. Liu and T. Matsuki,Light axial vector mesons,Phys. Rev. D91 (2015) 074025 [1501.07766]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  65. [65]

    Longacre,TheE(1420)Meson as aK ¯KπMolecule,Phys

    R.S. Longacre,TheE(1420)Meson as aK ¯KπMolecule,Phys. Rev. D42(1990) 874

    1990

  66. [66]

    From the Deuteron to Deusons, an Analysis of Deuteronlike Meson-Meson Bound States

    N.A. Tornqvist,From the deuteron to deusons, an analysis of deuteronlike meson-meson bound states,Z. Phys. C61(1994) 525 [hep-ph/9310247]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  67. [67]

    On meson resonances and chiral symmetry

    M.F.M. Lutz and E.E. Kolomeitsev,On meson resonances and chiral symmetry,Nucl. Phys. A730(2004) 392 [nucl-th/0307039]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  68. [68]

    L. Roca, E. Oset and J. Singh,Low lying axial-vector mesons as dynamically generated resonances,Phys. Rev. D72(2005) 014002 [hep-ph/0503273]. – 33 –

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  69. [69]

    Pseudocalar meson and vector meson interactions and dynamically generated axial-vector mesons

    Y. Zhou, X.-L. Ren, H.-X. Chen and L.-S. Geng,Pseudoscalar meson and vector meson interactions and dynamically generated axial-vector mesons,Phys. Rev. D90(2014) 014020 [1404.6847]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  70. [70]

    Reevaluating thea 1(1420) enhancement and its molecular partners in the low-lying axial-vector meson spectrum,

    M.-J. Yan, C.-S. An and C.-R. Deng,Reevaluating thea 1(1420)enhancement and its molecular partners in the low-lying axial-vector meson spectrum,2512.02655

    work page arXiv

  71. [71]

    Revising the $f_1(1420)$ resonance

    V.R. Debastiani, F. Aceti, W.-H. Liang and E. Oset,Revising thef 1(1420)resonance, Phys. Rev. D95(2017) 034015 [1611.05383]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  72. [72]

    Landau,On the Analytic Properties of Vertex Parts in Quantum Field Theory,Zh

    L.D. Landau,On the Analytic Properties of Vertex Parts in Quantum Field Theory,Zh. Eksp. Teor. Fiz.37(1960) 62

    1960

  73. [73]

    Coleman and R.E

    S. Coleman and R.E. Norton,Singularities in the physical region,Nuovo Cim.38(1965) 438

    1965

  74. [74]

    A Discussion on Triangle Singularities in the $\Lambda_b \to J/\psi K^{-} p$ Reaction

    M. Bayar, F. Aceti, F.-K. Guo and E. Oset,A Discussion on Triangle Singularities in the Λb →J/ψK −pReaction,Phys. Rev. D94(2016) 074039 [1609.04133]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  75. [75]

    Understanding the property of $\eta(1405/1475)$ in the $J/\psi$ radiative decay

    X.-G. Wu, J.-J. Wu, Q. Zhao and B.-S. Zou,Understanding the property ofη(1405/1475)in theJ/ψradiative decay,Phys. Rev. D87(2013) 014023 [1211.2148]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  76. [76]

    $f_1(1285)$ decays into $a_0(980)\pi^0$, $f_0(980)\pi^0$ and isospin breaking

    F. Aceti, J.M. Dias and E. Oset,f 1(1285)decays intoa 0(980)π0,f 0(980)π0 and isospin breaking,Eur. Phys. J. A51(2015) 48 [1501.06505]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  77. [77]

    The $K \bar K \pi$ decay of the $f_1(1285)$ and its nature as a $K^* \bar K -cc$ molecule

    F. Aceti, J.-J. Xie and E. Oset,TheK ¯Kπdecay of thef 1(1285)and its nature as a K ∗ ¯K−ccmolecule,Phys. Lett. B750(2015) 609 [1505.06134]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  78. [78]

    Mechanisms of the isospin-breaking decay $f_1(1285)\to f_0(980)\pi^0\to\pi^+\pi^-\pi^0$

    N.N. Achasov, A.A. Kozhevnikov and G.N. Shestakov,Mechanisms of the isospin-breaking decayf 1(1285)→f 0(980)π0 →π +π−π0,Phys. Rev. D93(2016) 114027 [1604.00177]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  79. [79]

    J.-J. Xie, G. Li and X.-H. Liu,Radiative decays off 1(1285)as theK ∗ ¯Kmolecular state, Chin. Phys. C44(2020) 114104 [1907.12202]

    work page arXiv 2020

  80. [80]

    Du and Q

    M.-C. Du and Q. Zhao,Comprehensive study of light axial vector mesons with the presence of triangle singularity,Phys. Rev. D104(2021) 036008 [2103.16861]

    work page arXiv 2021

Showing first 80 references.