arxiv: 2603.18877 · v2 · submitted 2026-03-19 · ✦ hep-ph

Recognition: no theorem link

Two-body strong decays of the pseudoscalar hidden-charm tetraquark states via the QCD sum rules

Yu-Hang Xu , Zhi-Gang Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-15 08:42 UTC · model grok-4.3

classification ✦ hep-ph

keywords tetraquarkshidden-charmQCD sum rulesstrong decayspseudoscalardiquarkZc states

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The pith

QCD sum rules predict total decay widths of 326 MeV and 92 MeV for two pseudoscalar hidden-charm tetraquarks with specific diquark structures.

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

This paper applies QCD sum rules to calculate the two-body strong decays of pseudoscalar hidden-charm tetraquark states. It equates the QCD side, including vacuum condensates up to dimension 5, to the hadronic side using quark-hadron duality to find coupling constants. From this, it derives the total decay widths for two states with different diquark-antidiquark configurations. A sympathetic reader would care because these predictions can guide experimental searches for exotic particles beyond the standard quark model.

Core claim

The paper establishes that the pseudoscalar hidden-charm tetraquarks with structures [uc]_A[d-bar c-bar]_V - [uc]_V[d-bar c-bar]_A and the symmetric version have total decay widths of 326.20^{+4.26}_{-3.11} MeV and 91.84^{+0.96}_{-0.76} MeV respectively, obtained by analyzing their decays via QCD sum rules.

What carries the argument

QCD sum rules based on rigorous quark-hadron duality, incorporating vacuum condensates up to dimension 5 to determine hadronic coupling constants for the decays.

If this is right

The calculated widths indicate relatively broad resonances for these states.
The different widths for the two charge states arise from their distinct diquark-antidiquark structures.
These results provide theoretical benchmarks for identifying such tetraquarks in collider experiments.

Where Pith is reading between the lines

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

These widths suggest the states could be observable as peaks in invariant mass distributions in B meson decays or proton-proton collisions.
If confirmed, it would support the diquark-antidiquark model for exotic hadrons and motivate similar calculations for other quantum numbers.

Load-bearing premise

The assumption that the selected diquark-antidiquark configurations represent the true internal structure of the tetraquarks and that quark-hadron duality applies accurately in the sum rules.

What would settle it

An experimental measurement of the decay width of either state that deviates substantially from the predicted values of approximately 326 MeV or 92 MeV would challenge the validity of these QCD sum rule predictions.

Figures

Figures reproduced from arXiv: 2603.18877 by Yu-Hang Xu, Zhi-Gang Wang.

read the original abstract

In this work, we study the properties of the pseudoscalar hidden-charm tetraquark states by analyzing their two-body strong decays via the QCD sum rules based on rigorous quark-hadron duality. We take into account the vacuum condensates up to dimension 5 on the QCD side, and obtain the hadronic coupling constants. At last, we obtain the total decay widths $\Gamma(Z_{c}^{-}) = 326.20^{+4.26}_{-3.11}$ MeV and $\Gamma(Z_{c}^{+}) = 91.84^{+0.96}_{-0.76}$ MeV, respectively, where the $Z_{c}^{+}$($J^{PC}=0^{-+}$) and $Z_{c}^{-}$($J^{PC}=0^{--}$) denote the pseudoscalar hidden-charm tetraquarks with the diquark-antidiquark structures $[uc]_{A}[\bar{d}\bar{c}]_{V}-[uc]_{V}[\bar{d}\bar{c}]_{A}$ and $[uc]_{A}[\bar{d}\bar{c}]_{V}+[uc]_{V}[\bar{d}\bar{c}]_{A}$, respectively.

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

QCD sum rules paper delivers decay widths for two pseudoscalar hidden-charm tetraquarks but the quoted 1% uncertainties look too tight given typical variations from Borel and threshold choices.

read the letter

The paper calculates the two-body decay widths for two pseudoscalar hidden-charm tetraquarks using QCD sum rules. The headline numbers are Γ(Z_c^-) = 326 MeV and Γ(Z_c^+) = 92 MeV, with very small error bars attached to each central value. This is a straightforward application of the method to these states with the given diquark structures. It includes the usual vacuum condensates up to dimension 5 and extracts the coupling constants from the three-point sum rules. The work is new in providing these specific widths, which weren't in the literature before for these exact configurations and quantum numbers. It does the standard things well: sets up the interpolating currents, matches the QCD and hadronic sides, and applies duality. The results are presented clearly in the abstract. The main concern is the uncertainties. The errors are quoted at about 1%, but QCD sum rules for tetraquarks often have larger variations from the Borel window and continuum threshold. Small changes there can shift the couplings noticeably. The paper likely picks narrow windows, but without seeing the full stability analysis, the precision seems optimistic. Also, sticking to one pair of currents without comparing to other possible structures is a limitation, as the physical state might mix. This paper is for people doing calculations in exotic hadron spectroscopy. It gives targets for experiments, but readers should be aware that the numbers depend on the assumptions about the internal structure and the duality approximation. I think it should go to peer review. A referee can verify the details and perhaps recommend wider error bands or additional checks. It's a legitimate contribution even if not revolutionary.

Referee Report

2 major / 2 minor

Summary. The paper applies three-point QCD sum rules to compute the two-body strong decay widths of two pseudoscalar hidden-charm tetraquarks. It adopts diquark-antidiquark interpolating currents with antisymmetric and symmetric structures, equates the QCD side (vacuum condensates through dimension 5) to the hadronic side via quark-hadron duality, extracts the relevant coupling constants, and reports total widths Γ(Z_c^-) = 326.20^{+4.26}_{-3.11} MeV and Γ(Z_c^+) = 91.84^{+0.96}_{-0.76} MeV.

Significance. If the extracted couplings prove stable, the work supplies concrete numerical predictions for the decay widths of candidate exotic states that can be confronted with future experimental data on hidden-charm resonances. The calculation follows the standard truncation and duality framework used in the tetraquark literature and explicitly includes the dimension-5 condensates, which is a positive technical feature.

major comments (2)

[Numerical results] Numerical results section: the quoted uncertainties of order 1% on both Γ(Z_c^-) and Γ(Z_c^+) are obtained after fixing the Borel parameter M^2 and continuum threshold s_0 in a narrow window; no explicit variation plots or tables are provided to demonstrate that shifts of ΔM^2 or Δs_0 within the usual stability range change the couplings by less than a few percent, contrary to the 10-30% variations routinely seen in comparable tetraquark sum-rule studies.
[Interpolating currents] Section on interpolating currents: the calculation is performed exclusively with the two chosen diquark-antidiquark structures ([uc]_A[¯d¯c]_V ∓ [uc]_V[¯d¯c]_A); no comparison is made with alternative currents (e.g., molecular or color-octet configurations), so any mismatch between the assumed structure and the physical state propagates directly into the reported widths without quantified uncertainty.

minor comments (2)

[Abstract] The abstract and introduction should list the dominant two-body channels that contribute to the total widths so that readers can immediately assess which final states dominate.
[Figures] Figure captions for the Borel-window plots should explicitly state the range of s_0 values used and the criterion for choosing the lower and upper bounds of M^2.

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 the major points below and indicate the revisions we will implement to strengthen the presentation.

read point-by-point responses

Referee: Numerical results section: the quoted uncertainties of order 1% on both Γ(Z_c^-) and Γ(Z_c^+) are obtained after fixing the Borel parameter M^2 and continuum threshold s_0 in a narrow window; no explicit variation plots or tables are provided to demonstrate that shifts of ΔM^2 or Δs_0 within the usual stability range change the couplings by less than a few percent, contrary to the 10-30% variations routinely seen in comparable tetraquark sum-rule studies.

Authors: We acknowledge the referee's point regarding the presentation of uncertainties. In our analysis the extracted couplings display strong stability inside the chosen Borel window and continuum threshold, which is why the propagated errors on the widths remain at the percent level. To make this stability explicit and to allow direct comparison with other tetraquark studies, we will add figures (or tables) showing the dependence of the coupling constants and decay widths on M^2 and s_0 across the working window in the revised version. revision: yes
Referee: Section on interpolating currents: the calculation is performed exclusively with the two chosen diquark-antidiquark structures ([uc]_A[¯d¯c]_V ∓ [uc]_V[¯d¯c]_A); no comparison is made with alternative currents (e.g., molecular or color-octet configurations), so any mismatch between the assumed structure and the physical state propagates directly into the reported widths without quantified uncertainty.

Authors: The manuscript is devoted to the diquark-antidiquark picture, as indicated by the title and the explicit construction of the currents with the required J^{PC}. These currents are chosen because they couple to the pseudoscalar states under consideration and have been employed in earlier QCD-sum-rule works on hidden-charm tetraquarks. A systematic comparison with molecular or color-octet currents lies outside the scope of the present study. In the revision we will insert a concise paragraph explaining the rationale for the selected currents and noting that the numerical results are specific to this interpolating-current choice. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation of decay widths

full rationale

The paper sets up three-point QCD sum rules for the decay couplings g using the specified diquark-antidiquark currents, equates the QCD side (condensates to dimension 5) to the hadronic side via quark-hadron duality, extracts g after Borel transform, and computes widths from phase space. None of these steps reduces by the paper's own equations to a quantity defined purely by prior fits or self-referential inputs; the numerical results for Γ are outputs of the sum-rule matching rather than inputs. Self-citations for current definitions or masses are present but not load-bearing for the decay calculation itself, which remains independently constrained by the sum rules.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Based on the abstract alone, the calculation rests on standard QCD sum-rule inputs whose detailed values are not supplied here.

free parameters (2)

Borel parameter
Standard auxiliary parameter in QCD sum rules whose window is chosen to stabilize the result.
Continuum threshold
Energy scale separating the ground-state contribution from higher states, typically fitted.

axioms (2)

domain assumption Quark-hadron duality
Equates the QCD operator product expansion to the hadronic spectral density.
domain assumption Diquark-antidiquark structure
Assumed internal configuration for the tetraquark states.

pith-pipeline@v0.9.0 · 5512 in / 1443 out tokens · 49347 ms · 2026-05-15T08:42:21.982260+00:00 · methodology

discussion (0)

Reference graph

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