arxiv: 2604.14597 · v2 · submitted 2026-04-16 · ✦ hep-ph

Recognition: unknown

Search for the Λ_cSigma_c and bar{Λ}_cSigma_c dibaryon structures via the QCD sum rules

Xiu-Wu Wang , Zhi-Gang Wang , Guo-Liang Yu

Authors on Pith no claims yet

Pith reviewed 2026-05-10 11:36 UTC · model grok-4.3

classification ✦ hep-ph

keywords dibaryonmolecular stateQCD sum ruleshexaquark currentLambda_cSigma_ccharm baryons

0 comments

The pith

QCD sum rules calculations identify three possible molecular dibaryon states in the Lambda_c Sigma_c and bar-Lambda_c Sigma_c systems.

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

This work constructs eight pairs of hexaquark currents for the Lambda_c Sigma_c and anti-Lambda_c Sigma_c combinations with quantum numbers J^P of 0^-, 0^+, 1^+ and 1^-. Through QCD sum rule analysis, masses and pole residues are computed for the ground states. The results indicate that three configurations form bound molecular states while the other five do not and are instead resonances. A sympathetic reader would care because confirming such exotic states advances understanding of how quarks bind into multi-baryon systems beyond conventional hadrons.

Core claim

We construct eight pairs of hexaquark currents to search the Lambda_c Sigma_c and bar-Lambda_c Sigma_c dibaryon states via QCD sum rules. The two currents of each pair are equivalent, and one is chosen to calculate the masses and pole residues. For either system, the J^P considered are 0^-, 0^+, 1^+ and 1^-. Three possible molecular states are found: the Lambda_c Sigma_c dibaryon with J^P=1^+ and the bar-Lambda_c Sigma_c dibaryons with J^P=0^- and 1^-. The other five are unlikely to form bound dibaryon states and are assigned as resonance states.

What carries the argument

The hexaquark currents that interpolate the molecular dibaryon configurations, from which QCD sum rules extract the ground state masses and pole residues.

If this is right

If the predictions hold, experimental searches should target these specific J^P states in charm sector collisions.
The assignments distinguish bound states from resonances based on whether the calculated masses fall below or above the threshold.
Similar currents can be used to study other baryon pairs in the same framework.
The stability of the results relies on appropriate choice of Borel parameters and continuum thresholds.

Where Pith is reading between the lines

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

Observation of these states would support the molecular interpretation of some exotic hadrons in heavy flavor physics.
The approach might be applied to predict structures in bottom sector dibaryons for comparison.
Decay modes of these dibaryons could be calculated next to guide experimental detection.

Load-bearing premise

The chosen hexaquark currents correctly interpolate the molecular configurations and the Borel mass and continuum threshold windows can be chosen so the extracted masses are stable and physically meaningful.

What would settle it

An experimental search that fails to find signals at the predicted masses for the three claimed states, or finds bound states in the channels assigned as resonances, would falsify the conclusions.

Figures

Figures reproduced from arXiv: 2604.14597 by Guo-Liang Yu, Xiu-Wu Wang, Zhi-Gang Wang.

**Figure 1.** Figure 1: The dimensional contributions, where A, B, · · ·, H represent the D(n) of the states coupling to the currents J1,2,···,8, respectively. Jκ J P T 2 (GeV2 ) √ s0(GeV) µ(GeV) M(GeV) PC λ(10−3GeV8 ) ΛcΣc J1 0 − 3.6 ∼ 4.0 6.10 ± 0.1 4.2 5.60+0.08 −0.08 (53 − 42)% 3.18+0.48 −0.45 ΛcΣc J2 0 + 3.3 ∼ 3.7 5.40 ± 0.1 3.2 4.86+0.13 −0.11 (55 − 42)% 1.10+0.19 −0.17 ΛcΣc J3 1 + 3.6 ∼ 4.0 5.40 ± 0.1 3.0 4.73+0.08 −0.08 (… view at source ↗

**Figure 2.** Figure 2: The M − T 2 curves, where, the solid and dashed curves represent the central values and the error bounds, respectively. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

read the original abstract

In this paper, we construct eight pairs of hexaquark currents to search the $\Lambda_c\Sigma_c$ and $\bar{\Lambda}_c\Sigma_c$ dibaryon states via QCD sum rules. We show that the two currents of each pair are equivalent and we choose one of them to calculate the masses and pole residues of ground states. For either $\Lambda_c\Sigma_c$ or $\bar{\Lambda}_c\Sigma_c$, the $J^P$ of the considered hexaquark currents are $0^-$, $0^+$, $1^+$ and $1^-$, respectively. We found three possible molecular states, they are $\Lambda_c\Sigma_c$ dibaryon with the $J^P=1^+$ and $\bar{\Lambda}_c\Sigma_c$ dibaryons with the $J^P=0^-$ and $1^-$. The other five are unlikely to form the bound dibaryon states, and we assign them as the resonance states.

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.

Desk Editor's Note private letter to a colleague

Standard QCD sum-rule calculation on eight hexaquark currents for Λ_c Σ_c channels produces three mass predictions below threshold, but they rest on Borel and s0 choices plus the molecular-current assumption.

read the letter

The paper takes the usual QCD sum-rule machinery and applies it to the Λ_c Σ_c and anti-Λ_c Σ_c systems with eight pairs of hexaquark currents. It shows the two currents in each pair are equivalent, picks one, and extracts masses and residues for the 0^-, 0^+, 1^+, and 1^- channels. Three of them come out below the two-baryon threshold and are labeled bound molecular states; the rest are called resonances. That is the concrete output: three new numerical mass values for these specific charm dibaryons. The work is competent at carrying out the standard steps—OPE up to the usual condensates, Borel transform, and continuum subtraction. It is useful to see the full set of quantum numbers treated uniformly in one place. The soft spots are exactly where this method is always soft. The masses are read off after choosing Borel windows and continuum thresholds that produce a plateau, so the numbers move if those windows shift. The abstract does not give pole-dominance fractions or explicit checks that higher condensates are suppressed, which leaves the ground-state claim less anchored than it could be. The currents are taken to interpolate molecular configurations; nothing in the calculation tests whether compact or other structures would give different results. This is incremental work that sits inside the existing literature on hexaquark sum rules. Readers who follow dibaryon mass predictions in the charm sector will want the numbers for comparison, but the paper does not introduce new techniques or resolve long-standing ambiguities in the method. It is solid enough to deserve referee time. A serious editor should send it out, with the referees asked to examine the stability windows, the size of the uncertainties, and whether the molecular interpretation is stated with appropriate caution.

Referee Report

3 major / 1 minor

Summary. The paper constructs eight pairs of hexaquark currents for the Λ_c Σ_c and bar-Λ_c Σ_c systems with J^P quantum numbers 0^-, 0^+, 1^+, and 1^-. It demonstrates the equivalence of the two currents within each pair, then applies QCD sum rules to extract the masses and pole residues of the ground states. The authors conclude that three configurations form bound molecular dibaryons (Λ_c Σ_c with J^P=1^+ and bar-Λ_c Σ_c with J^P=0^- and 1^-), while the remaining five are resonances.

Significance. If the mass extractions prove robust and lie below the relevant thresholds with controlled uncertainties, the results would indicate possible exotic dibaryon states in the charm sector, adding to the catalog of molecular candidates and motivating experimental searches. The QCD sum-rule framework is a standard tool for such spectroscopy, but the claims rest on the molecular interpretation of the currents and the existence of stable Borel windows.

major comments (3)

[Numerical results] The manuscript reports masses below the Λ_c + Σ_c threshold for the three claimed bound states, but does not provide explicit Borel-window stability plots, quantitative pole-dominance ratios (e.g., >50% ground-state contribution), or OPE convergence checks across the chosen M^2 intervals. Without these, the distinction between bound states and resonances cannot be verified (see numerical analysis and results sections).
[Current construction] The equivalence of the two currents per pair is shown algebraically, yet no additional arguments, decay-constant comparisons, or overlap calculations are given to establish that the chosen hexaquark currents preferentially interpolate the molecular Λ_c Σ_c (or bar-Λ_c Σ_c) configurations rather than compact or other structures.
[Mass extraction and parameter choice] The extracted masses depend on the fitted Borel mass M^2 and continuum threshold s0 chosen to produce plateaus; no systematic error estimates from varying these parameters within the windows or full inclusion of higher-dimensional condensates are reported, weakening the bound-state assignments.

minor comments (1)

[Introduction] The abstract and introduction would benefit from a brief comparison to prior QCD sum-rule or lattice studies of similar charmed dibaryon systems to contextualize the novelty.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments on our manuscript. We have carefully considered each point and provide our responses below. We will incorporate several improvements in the revised version to address the concerns raised.

read point-by-point responses

Referee: The manuscript reports masses below the Λ_c + Σ_c threshold for the three claimed bound states, but does not provide explicit Borel-window stability plots, quantitative pole-dominance ratios (e.g., >50% ground-state contribution), or OPE convergence checks across the chosen M^2 intervals. Without these, the distinction between bound states and resonances cannot be verified (see numerical analysis and results sections).

Authors: We acknowledge that including the Borel stability plots, pole dominance ratios, and OPE convergence checks would enhance the transparency of our numerical analysis. In the revised manuscript, we will add these plots and report the quantitative values (such as the ground-state contribution percentages) for the selected Borel windows. This will allow readers to verify the stability and the validity of our mass extractions for the bound states versus resonances. revision: yes
Referee: The equivalence of the two currents per pair is shown algebraically, yet no additional arguments, decay-constant comparisons, or overlap calculations are given to establish that the chosen hexaquark currents preferentially interpolate the molecular Λ_c Σ_c (or bar-Λ_c Σ_c) configurations rather than compact or other structures.

Authors: The hexaquark currents are constructed by combining the interpolating currents for the Λ_c and Σ_c baryons (or their antiparticles) with appropriate Dirac and color structures to form molecular-type configurations. This is the conventional method used in QCD sum rule studies for loosely bound molecular states. The algebraic equivalence demonstrates that the two forms in each pair describe the same state. While we do not perform explicit overlap calculations with compact currents, the molecular interpretation is supported by the current structure and the resulting masses being close to the thresholds. We will add a short paragraph clarifying this construction rationale in the revised version. revision: partial
Referee: The extracted masses depend on the fitted Borel mass M^2 and continuum threshold s0 chosen to produce plateaus; no systematic error estimates from varying these parameters within the windows or full inclusion of higher-dimensional condensates are reported, weakening the bound-state assignments.

Authors: The values of M^2 and s0 were selected to ensure the existence of stable plateaus in the mass predictions while satisfying the criteria of sufficient pole contribution and OPE convergence. Although we did not explicitly tabulate the variations, the masses are robust within the windows. In the revision, we will provide estimates of the uncertainties arising from the choice of these parameters by varying them within reasonable ranges. Regarding higher-dimensional condensates, our OPE includes terms up to dimension 6, and higher terms are expected to be small in the Borel window; we will discuss the truncation effects more explicitly. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard QCD sum rules extraction remains self-contained

full rationale

The derivation constructs eight pairs of hexaquark currents, demonstrates their pairwise equivalence by direct calculation, and applies the QCD sum rules formalism to obtain masses and residues from the two-point correlation functions. The Borel parameter M^2 and continuum threshold s0 are selected according to the usual criteria (pole dominance >50%, OPE convergence, and stability of the mass plateau), but the mass itself is obtained from the ratio of moments of the spectral density derived from the OPE side, not inserted by hand or fitted to reproduce a pre-chosen value. No step reduces the reported masses to the input parameters by definition, and no load-bearing self-citation chain is invoked to justify uniqueness or forbid alternatives. The central claim therefore rests on the validity of the molecular current ansatz and the existence of acceptable windows, which are methodological assumptions rather than circular reductions.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on the standard QCD sum-rule machinery plus several channel-dependent parameters and the assumption that the currents describe molecular states.

free parameters (2)

Borel mass M^2
Chosen in a stability window for each current; value not fixed by first principles.
Continuum threshold s0
Adjusted per channel to reproduce expected resonance behavior.

axioms (2)

standard math The operator product expansion converges sufficiently in the chosen Borel window.
Core assumption of the QCD sum-rule method.
domain assumption The constructed hexaquark currents couple dominantly to the ground-state molecular configurations.
Required to interpret the extracted pole as a dibaryon.

invented entities (1)

Λ_c Σ_c molecular dibaryon no independent evidence
purpose: To label the state whose mass lies below threshold.
Postulated when the calculated mass is below the two-baryon threshold; no independent experimental evidence supplied.

pith-pipeline@v0.9.0 · 5487 in / 1521 out tokens · 60507 ms · 2026-05-10T11:36:38.894020+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

75 extracted references · 5 canonical work pages · 1 internal anchor

[1]

Yukawa, Proc

H. Yukawa, Proc. Phys. Math. Soc. Jap. 17 (1935) 48

1935
[2]

Gell-Mann, Phys

M. Gell-Mann, Phys. Lett. 8 (1964) 214

1964
[3]

Zweig, Report No

G. Zweig, Report No. CERN-TH-401
[4]

S. K. Choi et al., Phys. Rev. Lett. 91 (2003) 262001

2003
[5]

Aaij et al., Nat

R. Aaij et al., Nat. Phys. 18 (2022) 751

2022
[6]

Z. G. Wang, Front. Phys. 21 (2026) 016300

2026
[7]

H. X. Chen, W. Chen, X. Liu and S. L. Zhu, Phys. Rept. 639 (2016 ) 1

2016
[8]

F. K. Guo, C. Hanhart, U. G. Meißner, Q. Wang, Q. Zhao and B. S. Zou, Rev. Mod. Phys. 90 (2018) 015004

2018
[9]

Altmannshofer et al., PTEP 2019 (2019) 123C01, [Erratum: PT EP 2020 (2020) 029201]

W. Altmannshofer et al., PTEP 2019 (2019) 123C01, [Erratum: PT EP 2020 (2020) 029201]

2019
[10]

Oset et al., EPJ Web Conf

E. Oset et al., EPJ Web Conf. 199 (2019) 01003

2019
[11]

J. M. Richard, Few Body Syst. 57 (2016) 1185

2016
[12]

F. K. Guo et al., Rev. Mod. Phys. 90 (2018) 015004

2018
[13]

Martinez Torres, K

A. Martinez Torres, K. P. Khemchandani, L. Roca and E. Oset, Few Body Syst. 61 (2020) 35

2020
[14]

X. K. Dong, F. K. Guo and B. S. Zou, Commun. Theor. Phys. 73 ( 2021) 125201

2021
[15]

Clement and T

H. Clement and T. Skorodko Chinese Phys. C45 (2021) 022001

2021
[16]

Strakovsky, AIP Conf

I. Strakovsky, AIP Conf. Proceeds. 221 (1991) 218; Echay a (Fiz. El. Chast. At. Yadra) 22 (1991) 615

1991
[17]

M. P. Locher, M. E. Sainio and A. Svarc, Advances in Nucl. Phys. 17 (1986) 47

1986
[18]

H. C. Urey, F. G. Brickwedde and G. M. Murphy, Phys. Rev. 39 ( 1932) 164

1932
[19]

Bashkanov et al., Phys

M. Bashkanov et al., Phys. Rev. Lett. 102 (2009) 052301. 11

2009
[20]

Adlarson et al., Phys

P. Adlarson et al., Phys. Rev. Lett. 106 (2011) 242302

2011
[21]

Adlarson et al., Phys

P. Adlarson et al., Phys. Lett. B721 (2013) 229

2013
[22]

Ikeno, R

N. Ikeno, R. Molina and E. Oset, Phys. Rev. C104 (2021) 014614

2021
[23]

Molina, N

R. Molina, N. Ikeno and E. Oset, Chin. Phys. C47 (2023) 041001

2023
[24]

Z. C. Xia, S. J. Fan, X. M. Zhu, H. X. Huang and J. L. Ping, Phys. Rev. C105 (2022) 025201

2022
[25]

H. X. Huang, X. M. Zhu, J. L. Ping, F. Wang and T. Goldman, arXiv :2004.12876

work page arXiv 2004
[26]

Z. T. Lu, H. Y. Jiang and J. He, Phys. Rev. C102 (2020) 045202

2020
[27]

J. T. Zhu, L. Q. Song and J. He, Phys. Rev. D103 (2021) 074007

2021
[28]

X. K. Dong, F. K. Guo and B. S. Zou, Progr. Phys. 41 (2021) 65

2021
[29]

H. X. Huang, J. L. Ping, X. M. Zhu and F. Wang, arXiv:2011.00513

work page arXiv 2011
[30]

T. F. Carames and A. Valcarce, Phys. Rev. D92 (2015) 034015

2015
[31]

Morita, A

K. Morita, A. Ohnishi, F. Etminan and T. Hatsuda, Phys. Rev. C94 (2016) 031901(R)

2016
[32]

Morita, S

K. Morita, S. Gongyo, T. Hatsuda, T. Hyodo, Y. Kamiya and A. O hnishi, Phys. Rev. C101 (2020) 015201

2020
[33]

Kodama, M

N. Kodama, M. Oka and T. Hatsuda, Nucl. Phys. A580 (1994) 445

1994
[34]

H. X. Chen, E. L. Cui, W. Chen, T. G. Steele and S. L. Zhu, Phys. Rev. C91 (2015) 025204

2015
[35]

Z. G. Wang, Eur. Phys. J. C77 (2017) 642

2017
[36]

B. D. Wan, L. Tang and C. F. Qiao, Eur. Phys. J. C80 (2020) 121

2020
[37]

Z. G. Wang, Eur. Phys. J. C74 (2014) 2963

2014
[38]

Z. G. Wang, Eur. Phys. J. C74 (2014) 2874

2014
[39]

M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B147 (1979) 385

1979
[40]

M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B147 (1979) 448

1979
[41]

Agaev, K

S.S. Agaev, K. Azizi and H. Sundu, Phys. Rev. D96 (2017) 034026

2017
[42]

Chen and S.L

W. Chen and S.L. Zhu, Phys. Rev. D81 (2010) 105018

2010
[43]

Chen and S.L

W. Chen and S.L. Zhu, Phys. Rev. D83 (2011) 034010

2011
[44]

Ozdem and K

U. Ozdem and K. Azizi, Phys. Rev. D97 (2018) 014010

2018
[45]

S. H. Lee, M. Nielsen and U. Wiedner, J. Korean Phys. Soc. 55 (2 009) 424
[46]

J. R. Zhang and M. Q. Huang, Commun. Theor. Phys. 54 (2010) 1075

2010
[47]

J. R. Zhang, M. Zhong and M. Q. Huang, Phys. Lett. B704 (2011) 312

2011
[48]

R. D. Matheus, F. S. Navarra, M. Nielsen and C. M. Zanetti, Phy s. Rev. D80 (2009) 056002

2009
[49]

S. H. Lee, A. Mihara, F. S. Navarra and M. Nielsen, Phys. Lett. B28 (2008) 661

2008
[50]

R. M. Albuquerque and M. Nielsen, Nucl.Phys. A53 (2009) 815. 12

2009
[51]

R. M. Albuquerque and M. Nielsen, Erratum, Nucl. Phys. A48 (2011) 857

2011
[52]

Z. Y. Di, Z. G. Wang and G. L. Yu, Commun. Theor. Phys. 71 (201 9) 685
[53]

Z. G. Wang and T. Huang, Phys. Rev. D89 (2014) 054019

2014
[54]

Z. G. Wang and T. Huang, Eur. Phys. J. C74 (2014) 2891

2014
[55]

Z. G. Wang, Eur. Phys. J. C76 (2016) 387

2016
[56]

Z. G. Wang, Eur. Phys. J. C76 (2016) 70

2016
[57]

Z. G. Wang and T. huang, Eur. Phys. J. C76 (2016) 43

2016
[58]

Z. G. Wang, Phys. Rev. D102 (2020) 034008

2020
[59]

X. H. Zhang, S. Q. Zhang, C. F. Qiao, Eur. Phys. J. C85 (2025) 693

2025
[60]

H. X. Chen, D. Zhou, W. Chen, X. Liu and S. L. Zhu, Eur. Phys. J . C76 (2016) 602

2016
[61]

X. H. Zhang, C. F. Qiao, arXiv:2512.22019

work page internal anchor Pith review Pith/arXiv arXiv
[62]

Ablikim et al., Phys

M. Ablikim et al., Phys. Rev. Lett. 131 (2023) 151901

2023
[63]

X. W. Wang, Z. G. Wang and G. L. Yu, Eur. Phys. J. A57 (2021) 275

2021
[64]

X. W. Wang and Z. G. Wang, Adv. High Energy Phys. 2022 (2022) 6224597

2022
[65]

Ablikim et al., arXiv:2508.16871

M. Ablikim et al., arXiv:2508.16871

work page arXiv
[66]

Ablikim et al

M. Ablikim et al., arXiv:2508.18594

work page arXiv
[67]

L. J. Reinders, H. Rubinstein and S. Yazaki, Phys. Rept. 127 (1 985) 1
[68]

QCD: Renormalization for the pra ctitioner

P. Pascual and R. Tarrach, “QCD: Renormalization for the pra ctitioner”, Springer Berlin Heidelberg (1984)

1984
[69]

Z. G. Wang, Phys. Lett. B819 (2021) 136464

2021
[70]

Z. G. Wang, Int. J. Mod. Phys. A35 (2020) 2050073

2020
[71]

Z. G. Wang, Int. J. Mod. Phys. A34 (2019) 1950097

2019
[72]

Z. G. Wang, Chin. Phys. C41 (2017) 083103

2017
[73]

Patrignani et al., Chin

C. Patrignani et al., Chin. Phys. C40 (2016) 100001

2016
[74]

P. A. Zyla et al., Prog. Theor. Exp. Phys. (2020) 083C01

2020
[75]

Narison and R

S. Narison and R. Tarrach, Phys. Lett. B125 (1983) 217. 13

1983