{"id":"48067f29-c354-4151-a7d2-94d25394b38e","arxiv_id":"2605.18075","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":2,"one_line_summary":"The authors compute mass spectra, rearrangement decays, and Regge trajectories for cs s-bar s-bar tetraquarks modeled as axial [cs][s-bar s-bar] systems in a Cornell potential framework with Ds threshold inputs.","lead":"This paper models compact tetraquarks with one charm quark and three strange quarks or antiquarks as diquark-antidiquark pairs and calculates their masses, possible decays into Ds mesons plus eta or phi, and Regge trajectories using a Cornell potential calibrated on known Ds states. A smart generalist might read it to see how theorists build predictions for exotic particles that could appear in collider data with hidden strangeness and open charm.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"Direct transfer of Cornell parameters from Ds mesons to [cs][s-bar s-bar] without explicit color-factor rescaling or size correction for the exotic configuration.","rationale":"The reader's weakest assumption already isolates the parameter-transfer step; the color-structure detail makes that step quantitatively testable and directly impacts the central claim of reliable candidate identification.","tokens_in":1922,"tokens_out":313,"duration_ms":24268,"concrete_test":"Recompute the lowest 0+ and 1+ tetraquark masses using the same Cornell parameters but with the color factor appropriate to the 3-bar-3 channel; if the ground-state mass shifts by more than 80 MeV relative to the published value, the direct-application assumption affects the claimed spectrum.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The mass spectra and Regge trajectories are obtained by solving the Schrödinger or semi-relativistic equation with the same V(r) = -α/r + σ r that reproduces the Ds spectrum. For the tetraquark the relevant color factors are 1/2 (3-bar-3) or -1/6 (6-6-bar) rather than the meson value of 4/3; the string tension and Coulomb strength should therefore be rescaled. The abstract and model description give no indication that such a rescaling (or an effective-radius adjustment) is performed before quoting numerical masses and decay widths. If the unadjusted parameters are used, the predicted thresholds and rearrangement amplitudes rest on an untested extrapolation.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"This paper presents a spectroscopy study of compact cs s-bar s-bar tetraquarks modeled as axial-vector diquark-antidiquark systems [cs][s-bar s-bar]. Mass spectra are computed in a Cornell-potential framework for both semi-relativistic and non-relativistic treatments, with separate analysis of 3-bar-3 and 6-6-bar color configurations. Rearrangement decays to Ds(*) eta, Ds(*) eta', and Ds(*) phi modes are formulated via spin-color Fierz recoupling and normalized with QCD sum-rule amplitudes. Orbital and radial Regge trajectories are constructed, with parameters calibrated on the conventional Ds meson spectrum to provide a phenomenological basis for identifying such states in hidden-strangeness open-charm final states.","tokens_in":2132,"tokens_out":417,"duration_ms":25458,"significance":"If the results hold after addressing parameter transfer issues, the work supplies a dedicated framework for tetraquark candidates in open-charm hidden-strangeness channels, extending potential-model techniques to exotic configurations and offering testable mass and decay predictions benchmarked against Ds thresholds.","major_comments":[{"comment":"Model section / Cornell potential application: The same V(r) = -α/r + σ r calibrated on Ds mesons is applied directly to the [cs][s-bar s-bar] tetraquark without rescaling for the different color factors (1/2 for 3-bar-3 or -1/6 for 6-6-bar versus 4/3 for mesons). This unadjusted extrapolation is load-bearing for the quoted mass spectra, threshold structures, and rearrangement decay widths, as the string tension and Coulomb strength should be modified for the exotic configuration.","section":null}],"minor_comments":[{"comment":"Abstract and introduction: Clarify whether the Pauli symmetry restrictions on the [s-bar s-bar] antidiquark are enforced at the wave-function level or only at the level of allowed J^P multiplets.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the thorough review and insightful comments on our manuscript. We address the major comment point by point below and are committed to improving the paper accordingly.","responses":[{"response":"We appreciate the referee highlighting this crucial point regarding the color structure in the potential. In our model, the Cornell potential parameters were fitted to the conventional Ds meson spectrum, which corresponds to a color factor of 4/3. For the tetraquark treated as a diquark-antidiquark system, the effective color factors are indeed different: approximately 1/2 for the 3-bar-3 configuration and -1/6 for the 6-6-bar configuration. We acknowledge that directly transferring the unrescaled potential represents an approximation that may affect the absolute mass values and derived quantities. However, since the parameters are phenomenological and the focus is on relative spectra and trajectories, this choice was made to maintain consistency with the threshold inputs. To strengthen the analysis, we will revise the manuscript to explicitly include the color-factor rescaling in the potential for each configuration. This will involve multiplying the Coulomb and linear terms by the appropriate factors, recomputing the mass spectra for both semi-relativistic and non-relativistic cases, and updating the Regge trajectories and decay width estimates. A new paragraph will be added in the model section to discuss the color factors and justify the rescaling procedure.","revision_made":"yes","referee_comment":"Model section / Cornell potential application: The same V(r) = -α/r + σ r calibrated on Ds mesons is applied directly to the [cs][s-bar s-bar] tetraquark without rescaling for the different color factors (1/2 for 3-bar-3 or -1/6 for 6-6-bar versus 4/3 for mesons). This unadjusted extrapolation is load-bearing for the quoted mass spectra, threshold structures, and rearrangement decay widths, as the string tension and Coulomb strength should be modified for the exotic configuration."}],"tokens_in":1541,"tokens_out":428,"duration_ms":48123,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"This paper gives mass spectra and decay widths for the cs s-bar s-bar tetraquark in a diquark-antidiquark model using the Cornell potential. It stands out for treating the two identical strange antiquarks with Pauli restrictions, leading to axial-vector antidiquarks for the low-lying states, and for computing rearrangement decays to Ds(*) eta, Ds(*) eta', Ds(*) phi modes through spin-color Fierz recoupling. The work also builds orbital and radial Regge trajectories for the tetraquark states and benchmarks them against the Ds spectrum. These are useful numerical results for a specific flavor sector that experimental groups might look at when searching for exotic states in hidden-strangeness open-charm final states. The calculation is done in both non-relativistic and semi-relativistic approximations and separates the 3-bar-3 and 6-6bar color channels. A clear limitation is that the potential parameters come directly from fitting Ds mesons, without any rescaling for the different color factors that apply to the tetraquark configuration. The relevant factors are 1/2 or -1/6 rather than the meson's 4/3, so the absolute mass scale could be off. The decay amplitudes are normalized with two-point and three-point QCD sum-rule amplitudes, which is a reasonable choice but adds to the model dependence. This is a paper for people already working on tetraquark phenomenology in the open-charm hidden-strangeness area. It supplies concrete numbers rather than a new method or broad reorganization of the field. I think it deserves a serious referee because the results are specific enough to be tested against future data. I would recommend sending it out for review, with a note to the authors about clarifying the color factor treatment in the potential.","headline":"Standard diquark model for cs s-bar s-bar tetraquarks with direct Ds potential transfer, but color factors likely need rescaling.","tokens_in":2645,"tokens_out":421,"would_cite":false,"duration_ms":37405,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Cost/FunctionalEquation.lean","rs_theorem":"washburn_uniqueness_aczel","paper_passage":"The interquark interaction is modeled through the Cornell potential, V(0)C+L(r) = ks αs/r + b r + V0 ... color factors ks = -4/3 and ks = -10/3 ... axial-vector diquark-antidiquark ... rearrangement topology cs s-bar s-bar → (c s-bar)(s s-bar)"},{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/DimensionForcing.lean","rs_theorem":"alexander_duality_circle_linking","paper_passage":"Regge trajectories ... L = α M² + α0 ... n = β M² + β0 ... slopes extracted from linear fits"}],"headline":"Cornell-potential diquark model for cs s-bar s-bar tetraquarks with Ds calibration and Regge trajectories","alignment":"orthogonal","rationale":"The paper's machinery is a standard phenomenological quark-model calculation: Cornell potential V(r) = -ks αs/r + b r calibrated on conventional Ds mesons, semi-relativistic/non-relativistic Schrödinger equations, Breit-Fermi spin-dependent terms, Fierz-rearranged rearrangement decays normalized by QCD sum rules, and linear Regge fits L = α M² + α0. No J-cost function, cosh(ρ ln φ) structure, golden-ratio ladder, 8-tick periodicity, or parameter-free derivation from a single distinction appears. This is a conventional spectroscopy computation in the domain of hadronic exotics; RS has no opinion on it.","tokens_in":76528,"confidence":"high","tokens_out":394,"duration_ms":14275,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Compact cs s-bar s-bar tetraquarks form axial diquark-antidiquark states whose masses and decays are predicted by a Cornell potential tuned to the Ds spectrum.","keywords":["tetraquarks","diquark-antidiquark","Cornell potential","rearrangement decays","Regge trajectories","open charm","hidden strangeness","Ds mesons"],"falsifier":"A measured mass or decay branching ratio for a narrow resonance in the Ds eta or Ds phi invariant-mass spectrum that lies well outside the range predicted for the ground-state multiplet would directly test whether the potential calibrated on two-quark mesons applies to this configuration.","tokens_in":2820,"feed_emoji":"⚛️","tokens_out":611,"duration_ms":42974,"temperature":0.7,"pith_summary":"This paper models the cs bar s bar s tetraquark as a compact bound state of a charm-strange diquark and a strange-antistrange antidiquark. It computes the mass spectrum in both semi-relativistic and non-relativistic versions of a Cornell potential whose parameters are fixed by reproducing the known Ds meson spectrum. Pauli symmetry forces the antidiquark to be axial-vector for the lowest states, and the calculation yields concrete predictions for rearrangement decays into Ds star eta, Ds star eta prime and Ds star phi pairs via spin-color recoupling. Orbital and radial Regge trajectories are built to organize the excited states. A sympathetic reader would care because the results supply specific mass and decay targets for experiments looking for exotic open-charm states that also carry hidden strangeness.","feed_headline":"Axial diquark model predicts masses for cs s-bar s-bar tetraquarks","feed_subtitle":"Cornell potential fitted to Ds mesons yields spectra, rearrangement decays to Ds eta and phi modes, and Regge lines for the compact multi-qu","key_machinery":"Axial-vector diquark-antidiquark configuration [cs][bar s bar s] treated in the Cornell potential framework, with color and spin symmetries used to generate the spectrum and to obtain decay amplitudes through Fierz recoupling.","core_discovery":"The authors claim that the cs bar s bar s system forms compact tetraquarks in the bar 3-3 and 6-bar 6 color configurations, with the bar s bar s antidiquark restricted to an axial-vector state by Pauli symmetry, and that the same Cornell potential calibrated on conventional Ds mesons yields reliable masses, threshold structures, rearrangement decay widths to Ds star eta, eta prime and phi modes, and Regge trajectories for the J^P = 0^+, 1^+, 2^+ multiplet.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Axial antidiquarks form compact cs s-bar s-bar tetraquarks","Cornell potential yields masses for charm-strange tetraquarks","Rearrangement decays target Ds eta and phi in tetraquark study","Regge trajectories for J^P 0+ 1+ 2+ tetraquarks in charm sector","Ds calibrated Cornell model maps tetraquark Regge lines and decays"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The model assumes that the exotic four-quark cs bar s bar s state can be described by the identical Cornell potential parameters fitted to ordinary Ds mesons without extra corrections arising from its multi-quark nature.","fun_headline_variants_meta":{"raw":{"variants":["Axial antidiquarks form compact cs s-bar s-bar tetraquarks","Cornell potential yields masses for charm-strange tetraquarks","Rearrangement decays target Ds eta and phi in tetraquark study","Regge trajectories for J^P 0+ 1+ 2+ tetraquarks in charm sector","Ds calibrated Cornell model maps tetraquark Regge lines and decays"]},"model":"grok-4.3","cost_usd":0.010667,"raw_usage":{"total_tokens":4810,"prompt_tokens":871,"num_sources_used":0,"completion_tokens":90,"cost_in_usd_ticks":106674500,"prompt_tokens_details":{"text_tokens":871,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3849,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":871,"tokens_out":90,"duration_ms":49202,"temperature":1.0,"reasoning_tokens":3849,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-20T10:01:06.975685+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A measured mass or decay branching ratio for a narrow resonance in the Ds eta or Ds phi invariant-mass spectrum that lies well outside the range predicted for the ground-state multiplet would directly test whether the potential calibrated on two-quark mesons applies to this configuration.","supporting_citations":[],"review_version":1}