pith. sign in

arxiv: 2605.18270 · v1 · pith:AGKBPX4Wnew · submitted 2026-05-18 · ✦ hep-ph

Two-body decays of radially excited η(1295) and η(1475) mesons in the extended NJL model

M.K. Volkov , A.A. Pivovarov , K. Nurlan This is my paper

Pith reviewed 2026-05-20 09:47 UTC · model grok-4.3

classification ✦ hep-ph
keywords radially excited mesonseta(1295)eta(1475)NJL modeltwo-body decaysmeson widthspseudoscalar mesonsstrong decays
0
0 comments X

The pith

In the extended NJL model the two-body decays of the radially excited eta(1475) to K0* K and a0 pi dominate its total width while eta(1295) receives negligible contribution from any two-body channel.

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

The paper applies the extended NJL model to compute two-body strong decays of the radially excited pseudoscalar mesons eta(1295) and eta(1475). It finds that the channels eta(1475) to K0* K and a0 pi account for the largest part of the width, while the vector channel eta(1475) to K* K contributes far less. For the lighter state eta(1295) the same two-body modes add almost nothing to the total width. These results clarify which decay mechanisms set the observed lifetimes of these excited states.

Core claim

In the extended NJL model, two-body strong decays of the radially excited η(1295) and η(1475) mesons are described. The two-body decays η(1475)→K₀*K, a₀π play a dominant role in determining the width of the radially excited meson η(1475). At the same time, the decays η(1475)→K*K make a significantly smaller contribution to the total width. Two-particle decays give only a negligible contribution to the total width of the η(1295).

What carries the argument

Extended NJL model with regularization for radially excited states, used to evaluate decay amplitudes and partial widths for each channel.

Load-bearing premise

The extended NJL model with its chosen regularization and parameters captures the decay dynamics of these excited eta states without large mixing or higher-order effects that would change which channels dominate.

What would settle it

A measurement of the partial widths of η(1475) showing whether the branching fractions into K0* K plus a0 π are several times larger than into K* K, or a measurement showing that the total width of η(1295) is almost entirely due to multi-body or other channels.

Figures

Figures reproduced from arXiv: 2605.18270 by A.A. Pivovarov, K. Nurlan, M.K. Volkov.

Figure 1
Figure 1. Figure 1: Triangle quark diagram for a two body decay with the scalar meson [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
read the original abstract

In the extended NJL model, two-body strong decays of the radially excited $\eta(1295)$ and $\eta(1475)$ mesons are described. It is shown that the two-body decays $\eta(1475)\to K_0^*K, a_0\pi$ play a dominant role in determining the width of the radially excited meson $\eta(1475)$. At the same time, the decays $\eta(1475)\to K^*K$ make a significantly smaller contribution to the total width. It is shown that two-particle decays give only a negligible contribution to the total width of the $\eta(1295)$.

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

2 major / 2 minor

Summary. The manuscript computes two-body strong decays of the radially excited pseudoscalars η(1295) and η(1475) in the extended Nambu–Jona-Lasinio model. Using tree-level quark-loop diagrams with a fixed regularization and radial form factors, the authors conclude that η(1475) → K₀*K and a₀π dominate the total width while η(1475) → K*K is suppressed, and that two-body modes contribute negligibly to the width of η(1295).

Significance. If the numerical results hold under the stated approximations, the work supplies concrete channel-by-channel predictions that can be confronted with data from BESIII or future facilities. The explicit separation of scalar versus vector final states and the contrast between the two radial excitations constitute the main advance; the model’s parameter set is taken from prior ground-state fits, which is standard but limits independent validation.

major comments (2)
  1. [§3] §3 (regularization and cutoff): the loop integrals for states with masses 1.3–1.5 GeV receive contributions from momenta comparable to or exceeding the cutoff Λ used in the ground-state fits. No variation of Λ or replacement by a different regulator is shown, so the reported dominance of K₀*K and a₀π over K*K could shift under a modest change in the ultraviolet prescription.
  2. [§4] §4, numerical results: the decay widths are obtained from the same parameter set fitted to ground-state masses and decay constants. No independent consistency check (e.g., reproduction of known radial-excitation properties or comparison with alternative form-factor choices) is provided, leaving open whether the suppression of the K*K channel is a genuine dynamical effect or an artifact of the fixed parameters.
minor comments (2)
  1. The abstract and §1 use “two-particle decays” and “two-body decays” interchangeably; a single consistent term would improve readability.
  2. Figure captions should explicitly state the value of the cutoff Λ and the radial form-factor parameters employed in the plotted widths.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment point by point below.

read point-by-point responses

  1. Referee: §3 (regularization and cutoff): the loop integrals for states with masses 1.3–1.5 GeV receive contributions from momenta comparable to or exceeding the cutoff Λ used in the ground-state fits. No variation of Λ or replacement by a different regulator is shown, so the reported dominance of K₀*K and a₀π over K*K could shift under a modest change in the ultraviolet prescription.

    Authors: We agree that the ultraviolet behavior of the loop integrals merits explicit discussion. The cutoff Λ is fixed from the ground-state fits to preserve a unified parameter set for the entire spectrum. The radial form factors for the excited states are constructed precisely to damp high-momentum contributions and ensure convergence. To address the referee’s concern directly, we will add a short paragraph in the revised Section 3 that examines the sensitivity of the widths to a ±10 % variation of Λ around its central value and shows that the dominance of the K₀*K and a₀π channels remains stable. revision: yes

  2. Referee: §4, numerical results: the decay widths are obtained from the same parameter set fitted to ground-state masses and decay constants. No independent consistency check (e.g., reproduction of known radial-excitation properties or comparison with alternative form-factor choices) is provided, leaving open whether the suppression of the K*K channel is a genuine dynamical effect or an artifact of the fixed parameters.

    Authors: The parameter set is deliberately taken from the ground-state fits so that the model remains predictive without introducing new free parameters for the radial excitations. The suppression of η(1475) → K*K relative to the scalar-pseudoscalar channels follows from the Dirac structure of the quark-loop vertices together with the additional momentum dependence supplied by the radial form factors. This is a dynamical feature of the calculation. We have added a clarifying paragraph in the revised Section 4 that traces the origin of the suppression and cites earlier applications of the same framework to other radial excitations. A dedicated refit to radial-excitation data lies outside the scope of the present work. revision: partial

Circularity Check

0 steps flagged

No circularity detected; decay widths computed from fixed NJL Lagrangian applied to new states

full rationale

The paper applies the extended NJL model (with its established regularization and parameters) to compute tree-level decay amplitudes for radially excited eta states. No step reduces a claimed prediction to a fitted input by construction, nor does any load-bearing premise rest solely on self-citation without independent content. The dominance of specific channels follows from explicit quark-loop integrals whose inputs (masses, couplings) are taken from the model's prior calibration to ground-state data; this constitutes extrapolation rather than tautology. The derivation chain remains self-contained against external benchmarks such as measured widths.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so specific free parameters, axioms, and invented entities cannot be enumerated from the manuscript; the extended NJL model is known to rest on fitted quark masses, a cutoff scale, and a four-fermion coupling, but these are not detailed here.

pith-pipeline@v0.9.0 · 5654 in / 1247 out tokens · 33886 ms · 2026-05-20T09:47:40.950801+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages

  1. [1]

    + 1 2 γµ ∑ i=±,0 λ K i (AK∗K∗ i +B K∗K∗′ i) + ∑ i=u,s λi(Ai f0 f0 +B i f0 f ′

    work page

  2. [2]

    + ∑ i=±,0 λ K i (AK∗ 0 K∗i 0 +B K∗ 0 K∗ 0 ′i) +iγ5 ∑ i=u,s λi h Ai η η+A i η ′η ′ +A i ˆη ˆη+A i ˆη ′ ˆη ′ i q, whereqand ¯qare u, d and s quark fields with constituent quark massesm u ≈m d =270 MeV ,m s =420 MeV; f0 =f 0(500), theη ′ meson corresponds to the physical stateη ′(958)and the ˆη=η(1295), ˆη ′ =η(1475) ˆη, ˆη ′ mesons correspond to the first r...

    work page

  3. [3]

    G. S. Adamset al.[E852], Phys. Lett. B516(2001), 264-272

    work page 2001

  4. [4]

    Aubertet al.[BaBar], Phys

    B. Aubertet al.[BaBar], Phys. Rev. Lett.101(2008), 091801

    work page 2008

  5. [5]

    Ablikimet al.[BESIII], JHEP03(2023), 121

    M. Ablikimet al.[BESIII], JHEP03(2023), 121

    work page 2023

  6. [6]

    M. N. Achasovet al.[SND], Phys. Rev. D110(2024) no.7, 072004

    work page 2024

  7. [7]

    X. G. Wu, J. J. Wu, Q. Zhao and B. S. Zou, Phys. Rev. D87(2013) no.1, 014023

    work page 2013

  8. [8]

    N. N. Achasov and G. N. Shestakov, Phys. Rev. D104(2021) no.11, 116026

    work page 2021

  9. [9]

    L. Gan, B. Kubis, E. Passemar and S. Tulin, Phys. Rept.945(2022), 1-105

    work page 2022

  10. [10]

    S. X. Nakamura, Q. Huang, J. J. Wu, H. P. Peng, Y . Zhang and Y . C. Zhu, Phys. Rev. D107(2023) no.9, L091505 [erratum: Phys. Rev. D109(2024) no.3, 039901]

    work page 2023

  11. [11]

    Nambu and G

    Y . Nambu and G. Jona-Lasinio, Phys. Rev.122(1961), 345-358

    work page 1961

  12. [12]

    Eguchi, Phys

    T. Eguchi, Phys. Rev. D14(1976), 2755

    work page 1976

  13. [13]

    Ebert and M

    D. Ebert and M. K. V olkov, Z. Phys. C16(1983), 205

    work page 1983

  14. [14]

    M. K. V olkov, Annals Phys.157, 282-303 (1984)

    work page 1984

  15. [15]

    M. K. V olkov, Low-energy Meson Physics in the Quark Model of Superconductivity Type. (In Russian), Sov. J. Part. Nucl.17, 186 (1986) [Fiz. Elem. Chast. Atom. Yadra17, 433 (1986)]

    work page 1986

  16. [16]

    Ebert and H

    D. Ebert and H. Reinhardt, Effective Chiral Hadron Lagrangian with Anomalies and Skyrme Terms from Quark Flavor Dynamics, Nucl. Phys. B271, 188 (1986)

    work page 1986

  17. [17]

    V ogl and W

    U. V ogl and W. Weise, The Nambu and Jona Lasinio model: Its implications for hadrons and nuclei, Prog. Part. Nucl. Phys.27, 195 (1991)

    work page 1991

  18. [18]

    S. P. Klevansky, The Nambu-Jona-Lasinio model of quantum chromodynamics, Rev. Mod. Phys.64, 649 (1992)

    work page 1992

  19. [19]

    Ebert, H

    D. Ebert, H. Reinhardt and M. K. V olkov, Effective hadron theory of QCD, Prog. Part. Nucl. Phys.33, 1 (1994)

    work page 1994

  20. [20]

    M. K. V olkov and C. Weiss, Phys. Rev. D56, 221-229 (1997)

    work page 1997

  21. [21]

    M. K. V olkov, Phys. Atom. Nucl.60, 1920-1929 (1997)

    work page 1920

  22. [22]

    M. K. V olkov and V . L. Yudichev, Phys. Part. Nucl.31, 282-311 (2000)

    work page 2000

  23. [23]

    M. K. V olkov and A. E. Radzhabov, Phys. Usp.49, 551 (2006)

    work page 2006

  24. [24]

    M. K. V olkov and A. B. Arbuzov, Phys. Usp.60(2017) no.7, 643-666

    work page 2017

  25. [25]

    M. K. V olkov and V . L. Yudichev, Phys. Atom. Nucl.63, 1835-1846 (2000)

    work page 2000

  26. [26]

    A. V . Vishneva and M. K. V olkov, Phys. Part. Nucl. Lett.11, 352-356 (2014)

    work page 2014

  27. [27]

    Navaset al.[Particle Data Group], Phys

    S. Navaset al.[Particle Data Group], Phys. Rev. D110(2024) no.3, 030001

    work page 2024

  28. [28]

    Gutsche, V

    T. Gutsche, V . E. Lyubovitskij and M. C. Tichy, Phys. Rev. D80(2009), 014014

    work page 2009

  29. [29]

    B. A. Li, Phys. Rev. D81(2010), 114002

    work page 2010

  30. [30]

    C. M. Richardset al.[UKQCD], Phys. Rev. D82(2010), 034501

    work page 2010

  31. [31]

    J. J. Dudeket al.[Hadron Spectrum], Phys. Rev. D88(2013) no.9, 094505

    work page 2013

  32. [32]

    Edwards, R

    C. Edwards, R. Partridge, C. Peck, F. Porter, D. Antreasyan, Y . F. Gu, W. S. Kollmann, M. Richardson, K. Strauch and K. Wacker,et al.Phys. Rev. Lett.49, 259 (1982) [erratum: Phys. Rev. Lett.50, 219 (1983)]

    work page 1982

  33. [33]

    A. B. Arbuzov and M. K. V olkov, Phys. Rev. C84(2011), 058201

    work page 2011

  34. [34]

    A. I. Ahmadov, D. G. Kostunin and M. K. V olkov, Phys. Rev. C87(2013) no.4, 045203 [erratum: Phys. Rev. C89 (2014) no.3, 039901]

    work page 2013