Prediction of $p\bar{\Omega}$ states and femtoscopic study

Hongxia Huang; Jialun Ping; Qian Wu; Qi Huang; Ye Yan

REVIEW 3 major objections 5 minor 1 cited by

Prediction of $p\bar{\Omega}$ states and femtoscopic study

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A quark model predicts two bound states in proton-anti-Omega system.

desk verdict First QDCSM prediction of pΩ̄ bound states and of pΩ̄ femtoscopic correlation functions, but the correlation functions are built from a potential binding at 7/6 MeV while the headline says 10/9 MeV; the quantitative link needs fixing. read the letter →

arxiv 2504.21376 v1 pith:RS7QOI7N submitted 2025-04-30 hep-ph hep-exhep-lathep-th

Ye Yan , Qi Huang , Qian Wu , Hongxia Huang , Jialun Ping This is my paper · ORCID

classification hep-phhep-exhep-lathep-th PACS 14.20.Pt13.75.Ev12.39.Jh

keywords proton-anti-Omegaboundstatebaryon-antibaryoninteractionquarkdelocalizationcolorscreeningmodelfemtoscopiccorrelationfunctionMarchenkoinversescatteringphaseshiftdibaryon

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper predicts that a proton and an anti-$\Omega$ baryon form two bound states, one with spin-parity $J^P=1^-$ and one with $2^-$, with binding energies of about 10 and 9 MeV. This would make the $p\bar{\Omega}$ system a baryon-antibaryon bound state that, unlike $p\bar{p}$, cannot annihilate into the vacuum because the two clusters have no quark flavors in common. The prediction comes from a constituent quark model calculation that also yields scattering phase shifts and scattering parameters consistent with bound states. The authors go further and compute the femtoscopic correlation function for $p\bar{\Omega}$ pairs, an observable that can be measured in high-energy collisions, giving an experimental route to confirm or reject the states.

What carries the argument

The central machinery is the quark delocalization color screening model (QDCSM), a constituent quark model in which quarks can delocalize between clusters and color confinement is screened in inter-cluster interactions; it supplies the hadron–hadron dynamics that produces the scattering phase shifts. The scattering lengths and effective ranges are extracted from a low-energy effective-range expansion of $k\cot\delta$. A second key object is the Marchenko equation of the inverse scattering problem, which reconstructs a unique local potential $V(r)$ from the phase-shift data after fixing the bound-state norming constants; this reconstructed potential is what enters the Schrödinger equation for the relative wave function. The third object is the Koonin–Pratt formula, which converts that wave function, together with a Gaussian source function and the repulsive Coulomb interaction between $p$ and $\bar{\Omega}$, into the experimentally measurable correlation function $C(k)$.

What would settle it

Measure the $p\bar{\Omega}$ correlation function in high-energy $pp$ or heavy-ion collisions: if the data at relative momenta below about 50 MeV follow the Coulomb-only prediction without the strong-interaction depletion the authors calculate, the predicted 10 and 9 MeV bound states are ruled out. Alternatively, a lattice QCD calculation of the S-wave $N\bar{\Omega}$ interaction at physical quark masses that yields a negative or much smaller scattering length than 2 fm would contradict the prediction.

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Extended reading notes

Core claim

Within the quark delocalization color screening model, the authors find that the S-wave $p\bar{\Omega}$ systems with isospin $I=1/2$ and $J^P=1^-$ and $J^P=2^-$ are bound, with binding energies of 10 MeV and 9 MeV relative to the theoretical threshold. The attraction between a nucleon and an anti-$\Omega$ is slightly stronger than between a nucleon and an $\Omega$, which supports the expectation that the antibaryon channel binds more deeply. The low-energy phase shifts reach $180^\circ$ at threshold and the extracted scattering lengths are positive (2.43 fm for $1^-$, 2.79 fm for $2^-$), both standard signatures of bound states. Using the Gel'fand–Levitan–Marchenko inverse scattering method, the phase shifts are converted into an effective local potential, and the Koonin–Pratt formula then yields spin-averaged $p\bar{\Omega}$ correlation functions for several source sizes. The correlation functions show a depletion below the Coulomb-only curve in the low-momentum region, which the authors identify as the femtoscopic fingerprint of the two predicted bound states.

Load-bearing premise

The whole chain depends on the effective-range expansion $k\cot\delta=-1/a_0+\tfrac{1}{2}r_{\rm eff}k^2$ being valid at every momentum used to reconstruct the strong potential, even though it is only fitted to low-energy phase shifts; if it fails at higher momenta, the reconstructed short-range potential and the predicted correlation functions are unreliable.

Editorial extensions

If this is right

If the two bound states exist, the $p\bar{\Omega}$ system should appear as narrow structures just below the $N\bar{\Omega}$ threshold in invariant-mass spectra of final states produced in high-energy collisions, at masses near 2571–2572 MeV in the model's convention.
The predicted correlation function provides a quantitative, source-size-dependent target for femtoscopy measurements in high-energy collider experiments; a measured depletion pattern would confirm the bound states, while a Coulomb-like curve would exclude them.
Because $p\bar{\Omega}$ cannot annihilate into the vacuum, a confirmed bound state would give a uniquely clean baryon-antibaryon laboratory, free of the annihilation broadening that plagues $p\bar{p}$ candidates such as X(1880).
The deeper binding of $p\bar{\Omega}$ compared with $p\Omega$ suggests the quark-model interaction is more attractive in the antibaryon channel, a pattern that can be tested by extending the same calculation to other baryon–antibaryon systems.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A direct test of the potential reconstruction would be to compute the femtoscopic correlation function by solving the Koonin–Pratt formula with the original quark-model scattering wave function, bypassing the Marchenko inverse step; agreement with the reconstructed-potential result would confirm that the effective-range expansion does not bias the short-distance physics.
The model omits coupling to open channels such as $\Delta\bar{\Omega}$ or $\Lambda\bar{\Xi}$; adding such couplings could shift the binding energies by a few MeV or give the states a small width, so the 10 and 9 MeV values should be read as single-channel estimates.
If the bound states exist, they might also be searched for in $J/\psi$ decays or in $e^+e^-$ production at electron-positron colliders, where final states containing $p\bar{\Omega}$ could reveal threshold structures.
The method of using inverse-scattering potentials to predict femtoscopic correlations could be applied to other non-annihilating baryon–antibaryon pairs, such as $\Lambda\bar{\Lambda}$ or $\Xi\bar{\Xi}$, where annihilation is absent or suppressed and the same clean-signal argument holds.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Know this about the paper: it is the first QDCSM study of pΩ̄ and the first femtoscopic correlation functions for that pair. The motivation is sound — since uud and s̄s̄s̄ share no same-flavor quark-antiquark pair, the system cannot annihilate through the usual channel, making it a clean probe of baryon-antibaryon forces. If the bound states are real, that is a genuinely useful prediction for experiments.

The good parts: the RGM bound-state calculation is standard, the model parameters come from the authors' earlier pΩ work, and Table I gives binding energies of 10 and 9 MeV for J^P = 1^- and 2^-, deeper than their pΩ 2^+ state at 6 MeV. The Coulomb repulsion and the spin-averaging weights (3/8, 5/8) are handled correctly in the correlation function. The square-well survey connecting attraction strength to the depletion feature is a helpful check.

The soft spots are real, and the stress-test note is on target. The Marchenko equation in Sec. II C is fed S(k) from the effective-range expansion with the Table II parameters, so the reconstructed potential binds at 7 and 6 MeV — not the advertised 10 and 9 MeV from Table I. The Fig. 3 correlation functions are thus the signatures of the shallower states. For J^P = 2^- the 6 MeV value does not even exceed the pΩ binding energy, undercutting the abstract's "deeper than" claim. The paper calls the difference "broadly consistent," but a 30% shift in binding energy is large enough to move the depletion feature in C(k). Since the effective-range expansion is a low-energy parametrization while the Marchenko integral samples all momenta, the short-distance potential is also uncontrolled; the authors never check the reconstructed potential's phase shifts against the QDCSM ones, and the norming constants M_i are never given.

Two smaller issues. There are internal parity typos: Sec. II B says the S-wave system has J^P = 1^+, 2^+, while the results use 1^-, 2^- and the Summary says 1^-, 2^+. Negative parity is correct here, so these are fixable typos. And the scattering parameters are extracted from the same QDCSM phase shifts that already contain the bound state, so calling them "support" is generous — it is a consistency check, not independent evidence. There are no error bars anywhere.

Who this is for: people in baryon-antibaryon femtoscopy (ALICE, STAR) and quark-model searches for exotic dibaryons. The qualitative prediction — attractive S-wave channels with bound states and a depletion in C(k) — is plausible, but the quantitative link between the headline binding energies and the presented correlation functions is broken as written. It deserves a serious referee; a revision that reconciles Tables I and II, validates the reconstructed potential against the full phase shifts, and fixes the typos could make it a solid contribution.

Referee Report

3 major / 5 minor

Summary. This paper investigates the p\bar{\Omega} system with J^P = 1^- and 2^- within the quark delocalization color screening model (QDCSM). The authors report resonating-group-method (RGM) bound-state calculations with binding energies of about 10 MeV and 9 MeV (Table I), which they compare with the 6 MeV binding of the p\Omega (J^P = 2^+) state from their earlier work. They also present low-energy phase shifts and extract scattering parameters (Table II, a0 \approx 2.4-2.8 fm and r_eff \approx 0.5-0.8 fm), from which effective-range binding energies of 7 and 6 MeV are derived. Finally, the paper presents, for the first time, p\bar{\Omega} femtoscopic correlation functions, using a strong potential reconstructed from the effective-range S-matrix through the Marchenko (GLM) inverse-scattering method, including the repulsive Coulomb interaction and spin averaging. The paper concludes that p\bar{\Omega} is more likely to form bound states than p\Omega and that these states should produce a characteristic depletion in the correlation function.

Significance. If correct, the prediction of two narrow, non-annihilating baryon-antibaryon bound states near the p\bar{\Omega} threshold would be a concrete, falsifiable target for femtoscopic measurements at ALICE and STAR, extending the successful p\Omega correlation program. The strengths of the paper are its use of a model with parameters fixed in earlier work on p\Omega (so the bound-state prediction is not fitted to p\bar{\Omega} data), the standard RGM formalism, a self-contained presentation of the GLM/Marchenko reconstruction, and the first explicit p\bar{\Omega} correlation-function prediction. The main caveat is that the quantitative link between the headline RGM binding energies and the potential actually used for the femtoscopic prediction is currently broken: the correlation functions are computed with a potential that binds at the effective-range energies (7/6 MeV), not at the RGM energies (10/9 MeV).

major comments (3)

[Section III (Tables I-II) and Section II C (Eqs. 22-24)] The strong potential used to generate the correlation functions is reconstructed from the Marchenko equation with S(k) built entirely from the effective-range expansion (Section II C: k cot(delta) = -1/a0 + (r_eff/2) k^2) using the Table II parameters. By construction, the reconstructed potential reproduces the input S-matrix and its bound-state pole, so the bound state in V_Strong sits at the effective-range energy E'_B = 7 MeV (1^-) and 6 MeV (2^-), not at the RGM energies E_B = 10 and 9 MeV of Table I. The correlation functions of Fig. 3 therefore encode a 7/6 MeV bound state, not the advertised 10/9 MeV state; the statement that the two determinations are 'broadly consistent' in Section III understates a 30% discrepancy that visibly affects the depletion feature. Moreover, for J^P = 2^- the effective-range binding energy (6 MeV) is not deeper than the p\Omega binding energy (6 MeV), contrary to the Section III claim that the scattering-parameter binding energies are 'slightly deeper'. Please reconstruct the potential from the full QDCSM phase shifts across the momentum range sampled by Eq. (23) with the bound-state pole imposed at the RGM energy, or provide a quantitative sensitivity study showing that C(k) is unchanged within the E_B versus E'_B difference.
[Section II C, last paragraph] The assertion that fixing the norming constants M_i from the Jost solution makes the reconstructed potential unique is a statement of mathematical uniqueness within the class of potentials with the same S-matrix and bound-state data; it does not fix the physically relevant potential, because M_i (equivalently the asymptotic normalization of the bound-state wave function) is not determined by the QDCSM dynamics. Since the correlation function depends on the off-shell wave function, the paper should either determine M_i from the RGM bound-state wave function or demonstrate numerically that the predicted C(k) is insensitive to the M_i choice.
[Section II C, Eq. (23)] The effective-range expansion is a low-energy parameterization, but it is used here to define S(k) for all momenta entering the Marchenko kernel. The paper does not show that the ERE phase shifts reproduce the QDCSM phase shifts of Fig. 1 over the momentum range that contributes significantly to the integral in Eq. (23). Without such a comparison, the short-distance behavior of the reconstructed V_Strong, which controls the correlation function, is uncontrolled. At minimum, the domain of validity of the ERE input should be quantified, and the reconstructed potential should be tested by checking that it reproduces the QDCSM phase shifts over a wide energy range.

minor comments (5)

[Section II B] The text states that the S-wave p\bar{\Omega} system has J^P = 1^+ and 2^+, but the paper studies S-wave channels with J^P = 1^- and 2^- (Section III). Since a baryon-antibaryon S-wave state has negative parity in the standard convention, please correct the parity assignment or state the convention used so that the partial wave used in the correlation function is unambiguous.
[Section IV (Summary)] The summary states that 'the p\bar{\Omega} systems with both J^P = 1^- and 2^+ form bound states'; the second entry should evidently read 2^-.
[Tables I and II] No error bars or systematic uncertainties are given for the binding energies or the scattering parameters. Given the 3-4 MeV spread between the RGM and effective-range determinations, a statement of the expected model uncertainty would help the reader assess whether the 10/9 MeV and 7/6 MeV results are consistent.
[Section III, around Eq. (25)] The energy range and number of phase-shift points used for the effective-range fit in Eq. (25) are not specified; stating them would make the extraction of a0 and r_eff in Table II reproducible.
[Fig. 2 caption and Section III] The text reads 'squire well potentials' in two places; this should be 'square well potentials'.

Circularity Check

1 steps flagged · score 4.0 of 10

The femtoscopic 'verification' of p-bar-Omega bound states is built from the same effective-range S-matrix that already contains the bound state, so the correlation depletion is an input, not an independent prediction.

self definitional [Section II C (Eqs. 22-24) and Section III (Fig. 3 discussion, Table II)]
"The partial-wave scattering matrix S(k) is given by S(k) = exp(2i δ(k)), where δ(k) is the scattering phase shift satisfying k cotδ = −1/a0 + 1/2reﬀk2. ... Since two bound states are obtained in our calculation, it is very important to verify this conclusion in the correlation functions."

The correlation function is computed from V(r) reconstructed by the Marchenko equation from S(k)=exp(2iδ(k)), with δ(k) fixed by the effective-range expansion whose parameters (a0, r_eff) are taken from the same phase shifts that already display the bound-state signature (δ→180° at threshold). The reconstructed potential therefore contains a bound state at the effective-range value E'_B (7 and 6 MeV, Table II), not at the dynamical EB (10 and 9 MeV, Table I). The depletion below the Coulomb-only correlation in Fig. 3 is thus an inevitable reflection of the input S(k), not an independent verification of the RGM bound state. Using it to 'verify this conclusion' is circular: the bound state is an input to the potential generating the observable.

full rationale

The central bound-state prediction (Table I) is a genuine RGM eigenvalue output from the QDCSM Hamiltonian, with parameters fixed in prior work on other channels; that part is not circular. The scattering phase shifts and the extracted a0/r_eff are outputs of the same Hamiltonian, so their agreement with the bound state is a consistency check rather than independent evidence. The identifiable circularity is confined to the femtoscopic application: the GLM/Marchenko potential used for C(k) is reconstructed from S(k)=exp(2iδ(k)) with δ(k) mandated by the fitted effective-range parameters (Section II C). Hence the bound-state depletion in Fig. 3 is guaranteed by construction at E'_B=7/6 MeV (Table II), not at the advertised 10/9 MeV, and cannot independently verify the Table I states. The paper itself acknowledges the two binding-energy determinations are only 'broadly consistent.' This is a partial circularity in a supporting prediction, while the central model calculation retains independent content. No load-bearing self-citation chain or uniqueness theorem imported from the authors' prior work was found.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper contributes a model calculation, so the ledger tracks the parameters and assumptions inherited from prior fits plus the methodological assumptions introduced here. No new entities are postulated.

free parameters (4)

color screening parameters mu_qq, mu_qs, mu_ss = 0.45, 0.19, 0.08 fm^-2
Fitted to deuteron properties, NN and YN phase shifts (Ref. [85]); used in the confinement potential Eq. (3) for the p\bar{\Omega} calculation.
quark-gluon coupling parameters alpha0, mu0, Lambda0 = not stated in paper
Scale-dependent coupling in Eq. (5), taken from previous work; values not listed.
confinement parameters a_c, V0 = not stated
Appear in V_CON Eq. (3); fixed in prior QDCSM fits, not given in this paper.
source size R = scanned from 1.0 to 2.5 fm
Source size in Eq. (14); the correlation function prediction depends strongly on it, though it is not fitted to data.

assumptions (5)

domain assumption The QDCSM Hamiltonian, with parameters taken from previous fits to deuteron and NN/YN scattering, describes the N-\bar{\Omega} interaction.
Section II A states all parameters are from the previous p\Omega work [77]; no p\bar{\Omega} data constrains them.
domain assumption There is no quark-antiquark annihilation in the p\bar{\Omega} system because the flavor contents of N (u/d) and \bar{\Omega} (\bar{s}) differ.
Used in Section II A to omit annihilation terms in V_{q\bar{q}}; if annihilation occurred, the bound states could be broad resonances instead of narrow states.
ad hoc to paper The effective-range expansion k*cot(delta) = -1/a0 + 0.5*r_eff*k^2 is valid at all momenta needed to build the Marchenko kernel F(r,r').
Section II C and III use this expansion to define S(k) for the inverse scattering problem; no high-momentum phase shifts or validation are shown.
ad hoc to paper Fixing the norming constants M_i from the Jost solution selects the unique phase-equivalent potential relevant for femtoscopy.
Section II C states this without presenting the Jost solution or checking that correlation functions are insensitive to the remaining ambiguity.
standard math The Koonin-Pratt formula with a Gaussian source and only the S-wave modified applies to p\bar{\Omega} pairs.
Eqs. (13)-(16) assume S-wave dominance and a Gaussian source; this is standard in femtoscopy but is an assumption about the emission source.

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Pith. "Pith review of Prediction of $p\bar{\Omega}$ states and femtoscopic study." pith.science (2026). https://pith.science/paper/RS7QOI7N

@misc{pith2026250421376,
  author       = {Pith},
  title        = {Pith review of: Prediction of $p\bar\Omega$ states and femtoscopic study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RS7QOI7N}},
  note         = {Machine review of arXiv:2504.21376}
}

abstract

Inspired by recent researches on the $p \Omega$ and $p \bar{\Lambda}$ systems, we investigate the $p \bar{\Omega}$ systems within the framework of a quark model. Our results show that the attraction between a nucleon and $\bar{\Omega}$ is slightly stronger than that between a nucleon and $\Omega$, suggesting that the $p \bar{\Omega}$ system is more likely to form bound states. The dynamic calculations indicate that the $p \bar{\Omega}$ systems with both $J^{P}=1^{-}$ and $2^{-}$ can form bound states, with binding energies deeper than those of the $p \Omega$ systems with $J^{P}=2^{+}$. The scattering phase shift and scattering parameter calculations also support the existence of $p \bar{\Omega}$ states. Additionally, we discuss the behavior of the femtoscopic correlation function for the $p \bar{\Omega}$ pairs for the first time. Considering the significant progress in experimental measurements of the correlation function of the $p \Omega$ system, the further study of the $p \bar{\Omega}$ systems using femtoscopic techniques will be a very valuable work.

Figures

Figures reproduced from arXiv: 2504.21376 by the authors.

**Figure 2.** FIG. 2: The correlation functions for different square well p [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** FIG. 3: The [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

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