{"id":"5422da21-9716-48f9-bc43-a075603bcdd7","arxiv_id":"2501.16188","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Using Born-Oppenheimer potentials from lattice QCD, the authors predict a bbar-bbar-ud tetraquark resonance near B*B* and virtual bound states for bbar-c-ud tetraquarks.","lead":"This paper uses quantum mechanics and supercomputer-based forces to predict four-quark particles called tetraquarks. It reports a resonance near the energy of two B* mesons and finds that bottom-charm versions appear as elusive virtual states instead of ordinary bound states.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The virtual-state claim for \\bar b\\bar c ud rests on the V5(r) potential, which the authors themselves flag in Sec. 5.2 as possibly underestimated; a modest increase in V5 attraction could turn these poles into the shallow bound states found in full lattice QCD.","rationale":"The reader's weakest_assumption correctly identifies the V5(r) potential as the load-bearing input, and the paper itself provides an explicit limitation statement in Sec. 5.2 admitting that V5 may be underestimated. My review confirms this is the most serious concern: the new physics claim is entirely about the classification of T-matrix poles, and that classification is controlled by the strength of V5 relative to the channel thresholds. Full lattice QCD results in Refs. [9-11] point to shallow bound states, which would contradict the virtual-state claim if the V5 attraction is too weak in the current fits. The quoted pole uncertainties are large enough that the distinction between 'virtual bound state' and 'shallow bound state' is not robust under plausible variations of V5. I do not see a separate, more fundamental flaw in the Born-Oppenheimer derivation itself: the transfer of static potentials from identical to unequal heavy antiquarks is standard in the static limit, and the Fierz-based construction in Sec. 3.2 is a reasonable extension. The most direct check is a sensitivity scan of the pole sheets against V5 strength; this would settle whether the virtual-state claim is a definitive prediction or an artifact of the fitted input. Since the reader already assigned CONDITIONAL and my concern does not change that verdict, I recommend UNCHANGED.","tokens_in":8583,"tokens_out":4563,"duration_ms":48111,"concrete_test":"","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central new claim is that \\bar b\\bar c ud with I(J^P)=0(0+) and 0(1+) are virtual bound states, not genuine bound states or resonances, with poles at Re(E)-(m_B+m_D) = -106 (+65/-148) MeV and Re(E)-(m_B*+m_D) = -100 (+49/-212) MeV. This classification is governed by the coupled-channel Hamiltonians in Eqs. (10) and (12), whose interaction matrices (Eqs. (4) and (13)) are built from the fitted lattice potentials V5(r) and Vj(r). The attractive potential V5(r) has parameters alpha5 = 0.34 +/- 0.03 and d5 = 0.45 (+0.12/-0.10) fm, from Nf=2 ETMC ensembles extrapolated to physical light quarks. In the final paragraph of Sec. 5.2, the authors state explicitly: 'A possible reason for that could be that the attraction of the potential V5(r) was underestimated in Refs. [1,2].' Full lattice QCD studies (Refs. [9-11]) instead find shallow bound states, with Ref. [10] strongly favoring genuine bound states over virtual states. The quoted pole-position uncertainties already reach from near-threshold energies to deeply bound-like values, and the input V5 uncertainty is large enough that a 1-sigma increase in its attraction could move a pole from the unphysical (-,+) or (-,+,+) sheet onto the physical (+,+) or (+,+,+) sheet. Thus the virtual-bound-state conclusion is not internally inconsistent, but it is a fragile prediction: it depends on the least secure input, and the paper itself concedes that input may be wrong. This is a correctness risk, not a disagreement with consensus, and it is the single most load-bearing concern because it directly determines whether the paper's main new finding is a robust statement about the physical sheets of the T-matrix poles.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This proceedings paper applies a Born-Oppenheimer framework to two heavy-antiquark–two-light-quark systems. Using the lattice-computed antistatic-antistatic potentials V5(r) and Vj(r), the authors study the bbar-bbar-ud system with I(J^P)=0(1^-), reproducing their earlier resonance prediction near the B*B* threshold, and extend the formalism to bbar-c-ud systems with I(J^P)=0(0^+) and I(J^P)=0(1^+). For the bbar-c-ud systems they find no genuine bound states or resonances, but rather virtual bound states on unphysical Riemann sheets, with pole positions Re(E)-(m_B+m_D) = -106(+65/-148) MeV and Re(E)-(m_B*+m_D) = -100(+49/-212) MeV. The paper also reports a consistency cross-check: increasing the charm quark mass to m_b and adjusting the D-D* splitting in the heavy-quark symmetry limit reproduces the bbar-bbar-ud bound state of Ref. [7]. The authors compare with full lattice QCD results from Refs. [9-11], which favor shallow bound states, and they concede that the V5 potential may have been underestimated.","tokens_in":8938,"tokens_out":3831,"duration_ms":37388,"significance":"If the virtual-state classification is robust, this is a valuable and nontrivial prediction that sharpens the contrast between the Born-Oppenheimer potential approach and full lattice QCD, and it provides a concrete target for future recomputations of the static-light potentials. The paper's strengths are that no parameter is fitted to the target tetraquark poles, the numerical implementation is cross-checked against Ref. [7] in the m_c to m_b limit, and the pole searches are carried out on all relevant Riemann sheets. The main risk, identified also by the authors, is that the central conclusion hinges on the poorly constrained attractive tail of V5(r); a modest increase of that attraction could convert the virtual poles into shallow bound states, matching recent full lattice QCD results. The paper would be significantly more convincing if it quantified this sensitivity.","major_comments":[{"comment":"The central claim that the bbar-c-ud systems are virtual bound states rather than genuine bound states rests on V5(r), whose parameters are alpha5=0.34±0.03 and d5=0.45(+0.12/-0.10) fm. In the final paragraph of §5.2 the authors state that 'a possible reason ... could be that the attraction of the potential V5(r) was underestimated in Refs. [1,2]'. Given the size of the quoted pole errors and the fact that a 1-sigma variation of V5 can move a pole from the (-,+) or (-,+,+) sheet onto the physical (+,+) or (+,+,+) sheet, the paper must provide a quantitative sensitivity study of the pole positions with respect to the V5 parameters. Without this, the virtual-versus-bound distinction is not yet established to the accuracy claimed.","section":"§5.2 (final paragraph)"},{"comment":"The T-matrix equations for the bbar-c-ud systems are omitted with the justification 'Because of the page limit, we refrain from providing the corresponding equations.' Since the virtual-state poles are extracted from these T matrices, the central numerical result cannot be reproduced or checked from the manuscript alone. The explicit 2x2 and 3x3 T-matrix definitions, or at least the determinant conditions whose roots are searched, should be included in an appendix or as supplementary material.","section":"§4.2"},{"comment":"The interaction Hamiltonian H_int = T V_diag T^{-1} is introduced with the phrase 'One can show' and the 16x16 matrix T is not displayed. The coupled-channel Hamiltonians in Eqs. (10) and (12)-(13) are load-bearing for the paper's conclusions, and their off-diagonal V5-Vj couplings follow from exactly this Fierz decomposition. Without providing the T matrix or a schematic derivation of its structure, a reader cannot verify the channel mixing used in the pole search. This is a derivational gap that should be filled.","section":"§3.2, Eq. (8)"},{"comment":"The quoted pole-position errors, e.g. Re(E)-(m_B+m_D) = -106(+65/-148) MeV, are not defined: it is not stated whether these errors come from the uncertainties of alpha5 and d5, from the quark masses, from the meson mass splittings, or from a combination. The errors are large on the scale of the binding energy, and a proper uncertainty propagation is essential for the virtual-state conclusion. The paper should explain how the quoted errors were obtained and, ideally, break them down by source.","section":"§5.2"}],"minor_comments":[{"comment":"There is a typo in the sentence 'One has to add thethe potentials V5(r) and Vj(r)' — 'thethe' should be 'the'.","section":"§3.2"},{"comment":"The term 'Schrödiger equation' is a typo; it should be 'Schrödinger equation'.","section":"§5.1"},{"comment":"The notation for the Riemann sheets, e.g. '(+,+,+) sheet' and '(-,+,+) sheet', is used in the figure but is not explained in the caption; the reader must infer it from the text. The caption should briefly restate the convention, or refer explicitly to the definition in Section 5.1.","section":"Figure 2 caption"},{"comment":"The reference entry for Padmanath et al. contains a duplicated '20' in the volume/page field ('132, no. 20, 20 (2024)') and should be corrected.","section":"Reference [9]"}],"recommendation":"major_revision","confidential_remarks":"This is a proceedings contribution, so some derivational details are legitimately compressed; however, the omitted T-matrix and Fierz-decomposition material could be placed in an appendix or an ancillary file without changing the main text. I see no circularity in the use of the lattice potentials — they are independent inputs — and the m_c to m_b cross-check is a genuine consistency check. The main issue is that the paper's flagship prediction is highly sensitive to the least well-determined input, V5(r), and the authors themselves acknowledge that this input may be wrong. A focused sensitivity analysis would transform the paper from a conditional prediction into a robust statement. I do not think rejection is warranted, but the central claim needs additional support."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The new piece here is the Born-Oppenheimer treatment of the bbar-c-ud systems with I(JP)=0(0+) and 0(1+). That specific application is not in the earlier literature, and the prediction is interesting: virtual states rather far below threshold, not bound states. The paper also does a useful cross-check: dialing m_c up to m_b, with the D*–D splitting scaled by HQET, reproduces the bound state from Ref [7]. That supports the numerical implementation of the coupled-channel equations.\n\nThe biggest soft spot is exactly the one the authors flag in Sec 5.2. The virtual-state classification depends on V5(r), and they write that the attraction of V5 may have been underestimated in Refs [1,2]. A stronger V5 would move their poles toward the shallow bound states found in full lattice QCD. Their own central values are Re(E)-(m_B+m_D) = -106(+65/-148) MeV and Re(E)-(m_B*+m_D) = -100(+49/-212) MeV, so at the 1-sigma level the poles range from near-threshold to deeply bound. Calling these 'virtual bound states' is a fragile conclusion. To their credit, they say this openly and have started a recomputation of the potentials.\n\nTwo smaller issues: the derivation of the 16x16 Hamiltonian is compressed to 'one can show', and the T-matrix equations are omitted for the page limit. That is fine for a proceedings if the full derivation is in Ref [8], but it does mean this paper is not self-contained.\n\nThe bbar-bbar-ud resonance is not new; it is a summary of Ref [8]. So the real new claim is the bbar-c-ud virtual-state classification. That claim is honest but not robust, and the paper says so.\n\nFor a proceedings contribution, this deserves a serious referee: the calculation is clearly described, the cross-check is real, and the load-bearing uncertainty is identified. A referee should ask for the derivation and for a quantitative statement about how much V5 would need to change to shift the poles to the physical sheet. I would send it to review, not desk reject.","headline":"New BO prediction of bbar-c-ud virtual states is honest but fragile, since the authors themselves admit the controlling V5 potential may be underestimated.","tokens_in":9603,"tokens_out":2438,"would_cite":true,"duration_ms":22216,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Bottom-charm tetraquarks predicted as virtual states, not bound","keywords":["tetraquarks","Born-Oppenheimer approximation","lattice QCD","antistatic-antistatic potentials","virtual bound states","T-matrix poles","heavy quark spin effects","exotic hadrons"],"falsifier":"A full lattice QCD scattering calculation for $\\bar{b}\\bar{c}ud$ with $I(J^P)=0(0^+)$ and $I(J^P)=0(1^+)$ that finds a pole on the physical Riemann sheet below the $BD$ or $B^*D$ threshold would contradict this paper's main conclusion. A cheaper check is to recompute the attractive potential $V_5(r)$ with the improved lattice setup the authors mention: if the new $V_5$ is significantly more attractive than the Gaussian fit used here, the virtual poles should move upward toward bound states.","tokens_in":8329,"feed_emoji":"⚛️","tokens_out":12936,"duration_ms":99503,"temperature":0.7,"pith_summary":"This paper uses the Born-Oppenheimer approximation with lattice QCD antistatic-antistatic potentials to ask whether two four-quark systems exist as genuine tetraquarks. For $\\bar{b}\\bar{b}ud$ with $I(J^P)=0(1^-)$ it finds a resonance just above the $B^*B^*$ threshold, with a width of about $140$ MeV and a strong preference for decaying to $B^*B^*$. For $\\bar{b}\\bar{c}ud$ with $I(J^P)=0(0^+)$ and $I(J^P)=0(1^+)$ it finds, in contrast to full lattice QCD studies that suggest shallow bound states, only virtual bound states: T-matrix poles far below the lowest meson-meson thresholds. The distinction matters because virtual states would leave almost no signal in scattering experiments, so the paper places a sharp, testable bet on what these tetraquarks are.","feed_headline":"Bottom-charm tetraquarks predicted as virtual states, not bound","feed_subtitle":"Lattice Born-Oppenheimer analysis finds the states far below threshold; raising the charm mass turns them into bound states near 2930 MeV.","key_machinery":"The central objects are the two isospin-zero antistatic-antistatic potentials $V_5(r)$ and $V_j(r)$, computed with lattice QCD for a static heavy-antiquark pair in the presence of two light quarks, and parametrized as Gaussian-damped Coulomb wells $V_X(r)=(-\\alpha_X/r)\\exp(-(r/d_X)^2)$ with $\\alpha_5=0.34$, $d_5=0.45$ fm and $\\alpha_j=-0.10$, $d_j=0.28$ fm. These potentials encode the interaction of two pseudoscalar or vector static light mesons and are fed into coupled-channel Schrödinger equations for the heavy-quark separation. The paper's method is to solve those equations, read off the T matrix at large separation, and locate its poles in the complex energy plane on all Riemann sheets; the sheet on which a pole sits is what distinguishes a bound state, a virtual bound state, and a resonance.","core_discovery":"The central discovery is that the same lattice potentials that produce a resonance in $\\bar{b}\\bar{b}ud$ produce only virtual bound states in $\\bar{b}\\bar{c}ud$. In the two- and three-channel Schrödinger equations, the T-matrix poles for the $0(0^+)$ and $0(1^+)$ systems lie on the negative real axis of unphysical Riemann sheets, at $\\mathrm{Re}(E)-(m_B+m_D)=-106^{+65}_{-148}$ MeV and $\\mathrm{Re}(E)-(m_{B^*}+m_D)=-100^{+49}_{-212}$ MeV. The paper concludes that these are neither bound states nor resonances, and that their distance from threshold makes a sizable effect on physical observables questionable. It also shows, by dialing $m_c$ from its physical value up to $m_b$, that the $0(1^+)$ pole crosses onto the physical sheet at $m_c\\approx 2930$ MeV and recovers the $\\bar{b}\\bar{b}ud$ bound state of [7] at $m_c=m_b$, a direct consistency check.","pith_inferences":["Editorial inference: The virtual-state prediction makes a clear experimental prediction: there should be no narrow near-threshold peak in $\\bar{b}\\bar{c}ud$ scattering, so searches should also look for broad, threshold-sensitive effects.","Editorial inference: If the potential $V_5$ is later found to be more attractive, the same Born-Oppenheimer machinery would move the $\\bar{b}\\bar{c}ud$ poles onto the physical sheet, reconciling this paper with the full lattice QCD bound-state results; the authors' planned recomputation is the direct test.","Editorial inference: The $m_c$ scan suggests a general crossover pattern: systems with a heavier heavy quark tend to bind, while systems with a lighter charm quark stay virtual, so analogous $\\bar{c}\\bar{c}ud$ or $\\bar{b}\\bar{s}ud$ systems could be classified by the same criterion."],"forward_implications":["For $\\bar{b}\\bar{b}ud$ with $I(J^P)=0(1^-)$, the paper predicts a tetraquark resonance at $2m_{B^*}+4.0^{+1.3}_{-5.4}$ MeV with width $140^{+86}_{-66}$ MeV, slightly above the $B^*B^*$ threshold.","The resonance decays about three times more often to $B^*B^*$ than to $BB$, with branching ratios $\\mathrm{BR}(BB)=26^{+9}_{-4}\\%$ and $\\mathrm{BR}(B^*B^*)=74^{+4}_{-9}\\%$.","For $\\bar{b}\\bar{c}ud$ with $I(J^P)=0(0^+)$ and $0(1^+)$, the T-matrix has virtual-state poles at $\\mathrm{Re}(E)-(m_B+m_D)=-106^{+65}_{-148}$ MeV and $\\mathrm{Re}(E)-(m_{B^*}+m_D)=-100^{+49}_{-212}$ MeV, so neither system is a genuine bound state or resonance.","Dialing $m_c$ from its physical value to $m_b$ moves the $0(1^+)$ pole from the virtual sheet to the physical sheet at $m_c\\approx 2930$ MeV, recovering at $m_c=m_b$ the known $\\bar{b}\\bar{b}ud$ bound-state binding energy.","The paper concludes that the $\\bar{b}\\bar{c}ud$ virtual states may have little effect on physical scattering rates or cross sections, a question it plans to investigate further."],"supporting_citations":[{"why":"Supplies the lattice QCD parametrization of the attractive potential V5(r) used in the coupled-channel equations.","marker":"[2]"},{"why":"Supplies the Vj(r) parametrization and the earlier µb̄b̄ud bound-state calculation that the m_c scan must reproduce at m_c=m_b.","marker":"[7]"},{"why":"The companion paper deriving the coupled-channel Schrödinger equation and T-matrix pole search for the bb̄ud 0(1-) system.","marker":"[8]"},{"why":"Full lattice QCD result for a shallow bound state in the 0(0+) bottom-charm channel, the main comparison target.","marker":"[9]"},{"why":"Full lattice QCD scattering analysis for the 0(1+) bottom-charm channel shown in the m_c scan, which cannot rule out virtual states.","marker":"[10]"},{"why":"Full lattice QCD result for the bottom-charm system, used alongside [9,10] as evidence for shallow bound states.","marker":"[11]"},{"why":"Provides the quark masses m_b and m_c used to solve the Schrödinger equations.","marker":"[12]"},{"why":"Provides the experimental B-B* and D-D* mass splittings used as input.","marker":"[13]"}],"fun_headline_variants":["Lattice QCD: bottom-charm tetraquarks are virtual, not bound","Bottom-charm tetraquarks: lattice predicts virtual states","Virtual states, not bound: bottom-charm tetraquarks from lattice","Lattice finds bottom-charm tetraquarks virtual, not bound","Virtual bound states: bottom-charm tetraquarks from lattice QCD"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Everything rests on the strength of the attractive potential between the two heavy antiquarks; the authors themselves note that it may have been underestimated, and a stronger attraction would shift their virtual states toward the shallow bound states seen in full lattice QCD.","fun_headline_variants_meta":{"raw":{"variants":["Lattice QCD: bottom-charm tetraquarks are virtual, not bound","Bottom-charm tetraquarks: lattice predicts virtual states","Virtual states, not bound: bottom-charm tetraquarks from lattice","Lattice finds bottom-charm tetraquarks virtual, not bound","Virtual bound states: bottom-charm tetraquarks from lattice QCD"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000461,"raw_usage":{"total_tokens":2333,"prompt_tokens":994,"completion_tokens":1339,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":610,"completion_tokens_details":{"reasoning_tokens":1245}},"tokens_in":610,"tokens_out":1339,"duration_ms":9352,"temperature":1.0,"reasoning_tokens":1245,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T13:37:00.960627+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A full lattice QCD scattering calculation for $\\bar{b}\\bar{c}ud$ with $I(J^P)=0(0^+)$ and $I(J^P)=0(1^+)$ that finds a pole on the physical Riemann sheet below the $BD$ or $B^*D$ threshold would contradict this paper's main conclusion. A cheaper check is to recompute the attractive potential $V_5(r)$ with the improved lattice setup the authors mention: if the new $V_5$ is significantly more attractive than the Gaussian fit used here, the virtual poles should move upward toward bound states.","supporting_citations":[],"review_version":1}