{"id":"5b054e0d-6585-4737-9218-f406bb520f26","arxiv_id":"2606.05791","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"The paper derives low-energy functions for pion transitions in heavy quarkonium within Born-Oppenheimer EFT in terms of three universal parameters by matching amplitudes from a proposed pion-QCD string interaction Lagrangian to the static limit of the EFT.","lead":"The paper develops a long-distance method for pion transitions in large heavy quarkonium and hybrid states by proposing a pion-QCD string interaction Lagrangian and matching it to Born-Oppenheimer EFT. This yields low-energy functions in terms of three universal parameters and enables calculations of previously inaccessible transition rates.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Long-distance domination assumption for low-energy functions lacks independent check and underpins all transition calculations","rationale":"The reader's weakest_assumption is precisely the load-bearing step for the transition results. Because the matching itself is presented as the main technical result and the domination assumption is stated explicitly, the concern is internal to the argument rather than external consensus. No other internal inconsistency is visible from the supplied material.","tokens_in":1689,"tokens_out":319,"duration_ms":16765,"concrete_test":"Compute the ratio of the long-distance contribution to the full amplitude for the process ψ(2S)\to J/ψ ππ using the three-parameter functions; if the ratio deviates from unity by more than 30% when an independent short-distance estimate (lattice or multipole) is added, the domination assumption does not hold at the claimed accuracy.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central construction matches a proposed pion-QCD-string Lagrangian to BOEFT amplitudes in the static limit, yielding the low-energy functions in terms of three universal parameters. The subsequent quarkonium and hybrid transition rates are obtained only after invoking that these functions are long-distance dominated. No cross-check (e.g., comparison against short-distance multipole results at intermediate distances, or lattice evaluation of the same matrix elements) is supplied to quantify the size of neglected short-distance pieces. If that assumption fails, the numerical estimates and phenomenological predictions do not follow from the matching.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper introduces an interaction Lagrangian coupling pions to the QCD string in order to determine the long-distance behavior of unknown low-energy functions appearing in Born-Oppenheimer EFT descriptions of pion transitions between heavy quarkonium and hybrid states. Matching the resulting amplitudes to BOEFT in the static limit expresses these functions in terms of three universal parameters; the light-quark-mass dependence of the string tension is obtained as a byproduct. Under the additional assumption that the low-energy functions are long-distance dominated, the authors compute several quarkonium-to-quarkonium and hybrid-to-quarkonium transition rates and perform a phenomenological fit of the three parameters to data.","tokens_in":1828,"tokens_out":533,"duration_ms":25190,"significance":"If the matching is correct and the long-distance-dominance assumption holds with quantifiable accuracy, the framework supplies a concrete parametrization that extends beyond the multipole expansion for states whose size exceeds the hadronic scale, while relating the string tension's quark-mass dependence to the same parameters. The explicit construction of the pion-string Lagrangian and the static-limit matching constitute a technical advance that could be tested against lattice matrix elements. The phenomenological estimates, however, are necessarily data-driven rather than first-principles predictions.","major_comments":[{"comment":"The long-distance-dominance assumption invoked after the matching (abstract and the section on transition calculations) is load-bearing for every numerical rate quoted. No cross-check against short-distance multipole results at intermediate distances or against lattice evaluations of the same matrix elements is supplied to bound the size of the neglected contributions. Without such a test the computed transition rates do not follow from the matching alone.","section":"Abstract and transition-rate section"},{"comment":"The three universal parameters are determined by fitting to existing data (phenomenological analysis section). Consequently the quoted transition rates reduce, by construction, to quantities whose numerical values are fixed by the fit rather than by independent first-principles input from the matching procedure.","section":"Phenomenological analysis section"}],"minor_comments":[{"comment":"The manuscript should state explicitly in which section the matching equations are written and which BOEFT amplitudes are used on the right-hand side.","section":"Matching section"},{"comment":"Notation for the low-energy functions should be introduced once and used consistently; currently the same symbols appear to be redefined between the Lagrangian and the transition-rate formulae.","section":"Notation throughout"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading of the manuscript and the constructive comments. We address each major comment below and indicate the revisions we will make to improve clarity.","responses":[{"response":"We agree that the long-distance-dominance assumption is essential for obtaining numerical values of the transition rates and that the matching procedure alone does not determine these rates. No cross-checks against lattice matrix elements or intermediate-distance multipole results are provided because such data are not available in the literature for the relevant transitions. We will revise the abstract and the transition-rate section to state explicitly that the quoted rates rely on this assumption and to distinguish what follows from the matching versus the assumption. This is a partial revision.","revision_made":"partial","referee_comment":"[Abstract and transition-rate section] The long-distance-dominance assumption invoked after the matching (abstract and the section on transition calculations) is load-bearing for every numerical rate quoted. No cross-check against short-distance multipole results at intermediate distances or against lattice evaluations of the same matrix elements is supplied to bound the size of the neglected contributions. Without such a test the computed transition rates do not follow from the matching alone."},{"response":"We acknowledge that the three parameters are obtained from a fit to data and that the numerical transition rates are therefore fixed by this fit. The matching determines the functional form in terms of the parameters and yields the light-quark-mass dependence of the string tension as a byproduct, but the specific values remain phenomenological. We will revise the phenomenological analysis section to clarify this distinction and to note that the rates are not independent first-principles predictions from the matching.","revision_made":"yes","referee_comment":"[Phenomenological analysis section] The three universal parameters are determined by fitting to existing data (phenomenological analysis section). Consequently the quoted transition rates reduce, by construction, to quantities whose numerical values are fixed by the fit rather than by independent first-principles input from the matching procedure."}],"tokens_in":1398,"tokens_out":433,"duration_ms":34230,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"This paper constructs an interaction Lagrangian between pions and the QCD string, then matches its amplitudes to the Born-Oppenheimer effective field theory in the static limit. That fixes the long-distance behavior of the unknown low-energy functions in terms of three universal parameters.\n\nWhat stands out is the explicit Lagrangian and the matching step. It gives a way to handle pion transitions for heavy quark states whose size is comparable to or larger than the hadronic scale, where the standard multipole expansion does not apply.\n\nThe work is clear on the motivation and on how the matching works. It also derives the light quark mass dependence of the string tension as a byproduct.\n\nThe main limitation is the reliance on the long-distance dominance assumption to compute the actual transition rates. The paper invokes this to get the quarkonium and hybrid transitions, but does not provide a cross-check, such as a comparison with multipole results at intermediate distances or a lattice calculation of the matrix elements. If short-distance contributions are not negligible, the estimates will not hold.\n\nThe three parameters are determined from data, which means the predictions incorporate that fitting rather than coming purely from the matching.\n\nThis paper is aimed at researchers in heavy-quark spectroscopy and exotic hadron phenomenology. It supplies a practical tool for a niche but relevant set of calculations.\n\nThe central construction is sound enough on its own terms to warrant peer review, even though the assumption about long-distance dominance will need careful examination by referees.","headline":"The paper matches a pion-QCD string Lagrangian to static BOEFT amplitudes to express long-distance low-energy functions via three parameters, but all transition rates rest on an unchecked long-distance dominance assumption.","tokens_in":2355,"tokens_out":382,"would_cite":false,"duration_ms":20802,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Pion transitions in heavy quarkonium and hybrid states are determined by matching a pion-QCD string interaction Lagrangian to the Born-Oppenheimer effective field theory, expressing the low-energy functions in three universal parameters.","keywords":["pion transitions","heavy quarkonium","Born-Oppenheimer effective field theory","QCD string","hybrid states","low energy functions","string tension"],"falsifier":"A measured transition rate between a specific hybrid state and a quarkonium state that cannot be reproduced by any choice of the three universal parameters within their phenomenologically estimated ranges.","tokens_in":2883,"feed_emoji":"","tokens_out":486,"duration_ms":71632,"temperature":0.7,"pith_summary":"The paper addresses pion transitions for heavy quarkonium and exotic states whose sizes exceed the range where the QCD multipole expansion applies. An interaction Lagrangian between pions and the QCD string is introduced to capture the long-distance regime of the required low-energy functions. Matching the resulting amplitudes to those of the Born-Oppenheimer effective field theory in the static limit determines these functions using three universal parameters and also yields the light-quark mass dependence of the string tension. Under the assumption that the functions are long-distance dominated, the approach is applied to compute quarkonium-to-quarkonium and hybrid-to-quarkonium transitions after estimating the constants from phenomenology.","feed_headline":"Three parameters fix pion transitions in heavy quarkonium","feed_subtitle":"Matching a pion-QCD string Lagrangian to effective field theory determines the long-distance form for states larger than the hadronic scale.","key_machinery":"The interaction Lagrangian for pions and the QCD string, matched to Born-Oppenheimer effective field theory amplitudes in the static limit, which fixes the long-distance behavior of the unknown low-energy functions.","core_discovery":"By proposing an interaction Lagrangian for pions and the QCD string and matching its amplitudes to the Born-Oppenheimer effective field theory in the static limit, the low energy functions for pion transitions are obtained in terms of three universal parameters, along with the light quark mass dependence of the string tension. Assuming long-distance dominance, the method is used to calculate several quarkonium-to-quarkonium and hybrid-to-quarkonium transitions.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Three parameters fix quarkonium pion transitions via QCD string","QCD string Lagrangian matched to three pion transition parameters","Three parameters set long-distance form for heavy quarkonium pions","Born-Oppenheimer EFT determines three universal transition parameters"],"cache_read_input_tokens":2560,"weakest_assumption_plain":"The low energy functions are long-distance dominated.","fun_headline_variants_meta":{"raw":{"variants":["Three parameters fix quarkonium pion transitions via QCD string","QCD string Lagrangian matched to three pion transition parameters","Three parameters set long-distance form for heavy quarkonium pions","Born-Oppenheimer EFT determines three universal transition parameters"]},"model":"grok-4.3","cost_usd":0.008032,"raw_usage":{"total_tokens":3557,"prompt_tokens":635,"num_sources_used":0,"completion_tokens":63,"cost_in_usd_ticks":80315500,"prompt_tokens_details":{"text_tokens":635,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2859,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":635,"tokens_out":63,"duration_ms":31902,"temperature":1.0,"reasoning_tokens":2859,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T00:49:47.579832+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A measured transition rate between a specific hybrid state and a quarkonium state that cannot be reproduced by any choice of the three universal parameters within their phenomenologically estimated ranges.","supporting_citations":[],"review_version":1}