{"id":"ce081784-a84d-449c-8fc9-e20e8149d8ce","arxiv_id":"2607.19009","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Including one-pion exchange nonperturbatively converts the lattice-QCD T_cc+ from a real-valued virtual bound state to a complex pole below the DD* threshold.","lead":"This paper reanalyzes lattice QCD data on the doubly charmed tetraquark T_cc+ and finds that including pion exchange turns the state from a virtual bound state into a subthreshold pole with a width. The result suggests pion exchange matters enough to change how the T_cc+ should be interpreted.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"K0 is constrained only above the one-pion left-hand cut, while the T_cc+ pole sits below it; the complex pole may depend on an untested polynomial extrapolation of K0 below that cut.","rationale":"The paper is a serious implementation of the Ref. [28] formalism, and the analysis shows that including one-pion exchange improves the fit to the 36 finite-volume levels while reducing the number of parameters. The multiple K0 and K0^{-1} parametrizations, AIC weighting, unitarity checks in Fig. 8, and contour-deformation diagnostics in Sec. C 1 are genuine supporting evidence. The concern raised here is not about the internal consistency of the formalism but about the domain of validity of the K0 ansatz in the continuation. The fitted K0 is constrained only for energies above the left-hand cut; the pole is found about 4 MeV below that branch point. The contour checks establish that the integral equation for M_E can be continued to the pole location without crossing OPE cuts, but they do not constrain K0 below the cut. Since K0 is only fitted above the cut, its continuation below is an assumption. The central claim - that the T_cc+ changes from a real virtual bound state to a complex subthreshold pole - is exactly the type of qualitative change that could be an artifact of this extrapolation. A concrete and decisive test is to add a quadratic term to the 3S1 K0 and re-extract the pole; if the pole moves outside the quoted uncertainty, the claim needs to be qualified. I also note the typo in Eq. (4): the imaginary part should read 25.5(14) MeV, not 255(14), to match Gamma = 54(14) MeV and Fig. 3. This is clearly a typographical error and should be corrected, but it does not change the physics. The reader's CONDITIONAL verdict is appropriate: the central claim is credible but hinges on a testable model assumption, and the paper would be strengthened by releasing code or parameter files and by running the proposed curvature check.","tokens_in":35625,"tokens_out":13575,"duration_ms":120466,"concrete_test":"Refit all 36 finite-volume levels with the K0 polynomial extended by an additional (s - s_thr)^2 term in the 3S1 partial wave, and also in the K0^{-1} variation, keeping the same AIC weighting over alpha. Recompute the second-sheet pole. If the resulting pole moves outside E_pole = 3854(15) - i25.5(14) MeV by more than the AIC-included systematic uncertainty, or if the imaginary part changes by more than about 10 MeV, the polynomial extrapolation below the single-pion left-hand cut is the load-bearing assumption and the complex-pole claim should be weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the T_cc+ becomes a complex subthreshold pole when OPE is included rests on continuing the fitted amplitude to E_pole = 3854(15) - i25.5(14) MeV (Eq. 4; the printed 255(14) appears to be a typo). The finite-volume spectrum used to constrain K0 consists of 36 levels below the D*D* threshold, with the lowest level 'just above the left-hand branch point' (Sec. B 2). The single-pion branch point E_lhc = m_D + sqrt(m_D*^2 - m_pi^2) is about 3858 MeV, roughly 4 MeV above the real part of the pole. Thus the pole lies on the far side of the OPE cut from the energy region where K0 is fitted. The contour checks in Sec. C 1 (Figs. 10-12) show that the integral equations defining M_E can be deformed without pinching the OPE cuts, and the K0 polynomial itself is trivially continuable. What is not demonstrated is that the low-order polynomial form of K0 used here (constant/linear in (s - s_thr), Eqs. B2/B3, Table III) remains valid below the lhc. Data above the lhc cannot discriminate between K0 forms that agree there but differ below it; a different K0 continuation could shift the pole or return it to the real axis. The imaginary part of the pole is generated entirely by the OPE discontinuity in the continued amplitude, so its magnitude (the 'width') is directly sensitive to this extrapolation. The spread among the variations in Table IV already spans Im E from -37 to -17 MeV; a more flexible K0 could move it outside this range. The central claim is therefore conditional on an unsupported extrapolation of K0 below the left-hand cut.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reanalyzes the 36 finite-volume DD* energy levels of Ref. [14] at m_pi≈391 MeV using the finite-volume formalism of Ref. [28], which incorporates one-pion exchange nonperturbatively. The authors simultaneously fit the DD*pi coupling g and a smooth short-distance matrix K0; the reference fit uses four K0 parameters plus g and gives chi2/Ndof = 0.90, compared with 1.68 for a seven-parameter fit without OPE. Continuing the reconstructed amplitude to the second Riemann sheet, they find a complex subthreshold pole at E_pole = 3854(15) - i25.5(14) MeV (printed as -i255(14) in Eq. (4)), with an inferred width Gamma = 54(14) MeV, in contrast to the real virtual bound state found in Ref. [14]. The pole is reported for all K0 parametrizations in Table IV. The authors also study the dependence on the regulator alpha and the momentum cutoff, and explore the pole trajectory as the pion mass is lowered to about 300 MeV with g and K0 held fixed.","tokens_in":35987,"tokens_out":6850,"duration_ms":64540,"significance":"This is a timely and technically substantial reanalysis. If the result is robust, it changes the lattice-QCD picture of the T_cc+ at m_pi≈391 MeV from a real virtual bound state to a subthreshold complex pole generated by the interplay of OPE and short-range dynamics. The paper's strengths are that it constrains g and K0 simultaneously from the finite-volume spectrum alone, without external inputs; it demonstrates a clear improvement in fit quality with fewer parameters; it reports unitarity checks above threshold; it verifies the absence of contour pinching in the analytic continuation; and it shows pole stability across several K0 parametrizations and regulator values. The main caveat, detailed below, is that the pole lies on the other side of the OPE cut from the energy region in which K0 is fitted, so the systematic uncertainty on the complex pole is not fully quantified. Provided this is addressed, the work is likely to be influential for both lattice and phenomenological studies of near-threshold exotics.","major_comments":[{"comment":"The central claim depends on an untested extrapolation of K0 below the one-pion left-hand cut. The quoted pole E_pole = 3854(15) - i25.5(14) MeV lies below the single-pion branch point E_lhc = m_D + sqrt(m_D*^2 - m_pi^2) ≈ 3858 MeV, while the 36 levels used to constrain K0 have their lowest energy just above that branch point (Sec. B 2, Fig. 6). The contour checks in Sec. C 1 (Figs. 10-12) show that the integral equations defining M_E can be deformed without pinching the OPE cuts, and the K0 polynomial is trivially continuable; however, those checks do not establish that the low-order polynomial form of K0 (Eqs. B2/B3, Table III) remains valid below the cut. Data above the cut cannot discriminate between K0 forms that agree there but differ below it, and the imaginary part of the pole is generated entirely by the OPE discontinuity in the continued amplitude. The spread of Im E across the variations in Table IV already spans roughly -37 to -17 MeV, and a more flexible K0 continuation could move the pole outside this range or return it to the real axis. I request an explicit robustness test that varies the K0 continuation below the lhc, for example by adding terms that vanish above the lhc or by using a parametrization that respects the analyticity domain of the amplitude, and that reports the resulting pole uncertainty.","section":"Sec. C 1, Eq. (4), Sec. B 2, Table IV"}],"minor_comments":[{"comment":"The printed imaginary part -i255(14) MeV is inconsistent with the width Gamma = 54(14) MeV quoted immediately below and with Fig. 3, which uses Im E* = -25.5 MeV; the value should presumably be -i25.5(14) MeV.","section":"Eq. (4)"},{"comment":"The abstract states that the paper predicts the pole moves closer to the real-energy axis as the pion mass approaches its physical value, but the calculation holds g and K0 fixed and varies only the pion mass in the OPE kernel. The text acknowledges this explicitly; the abstract should include the same caveat.","section":"Abstract and Conclusion"},{"comment":"There is a typo in the sentence before Eq. (B6): 'Iit is useful' should read 'It is useful'.","section":"Sec. B 4"},{"comment":"The labels 'with LHC' and 'without LHC' in the lower panel are not defined in the caption; please state explicitly that they refer to whether the one-pion left-hand cut is included in the analysis.","section":"Fig. 4"},{"comment":"The statement that the bold-faced entry in Table III is the reference parametrization would be clearer if the corresponding row were labeled 'reference' in the table itself, rather than only in the caption.","section":"Sec. B 5, Table III"}],"recommendation":"major_revision","confidential_remarks":"The K0 continuation below the left-hand cut is the key technical concern. I believe it is addressable within the scope of the manuscript, so major revision is appropriate rather than rejection. The formalism and data handling otherwise appear sound, and the paper would be a significant contribution if the requested robustness test is added."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nShort version: this is a serious paper that does something new. It includes one-pion exchange nonperturbatively in a lattice QCD analysis of T_cc+ and finds the pole becomes complex. The result is credible and worth engaging with. The main caveat is that the pole sits below the one-pion left-hand cut, so the K0 matrix is being extrapolated outside the fitted region.\n\nWhat's actually new: this is the first use of the OPE-inclusive finite-volume formalism of Ref. [28] on T_cc+. The DD*pi coupling g is determined from the lattice spectrum alone, with no external inputs. The fit quality improves substantially (chi2/Ndof from 1.68 with 7 parameters down to 0.90 with 5), and the complex pole appears in every K0 parametrization they tried. That is a real result, and it changes how we read the earlier real-virtual-state claims.\n\nThe soft spots are real but not fatal. The biggest one: the pole at 3854 - i25.5 MeV lies below the single-pion left-hand branch point (~3858 MeV), while the K0 parameters are fitted to levels above that point. The paper does careful contour checks showing the integral equations can be deformed without pinching the OPE cuts, but that doesn't certify the polynomial form of K0 below the cut. Different K0 continuations that agree in the fit region could move the pole or change its imaginary part. The spread across parametrizations (Im E from about -17 to -37 MeV) already gives a sense of the systematic uncertainty. I'd want the paper to be upfront that the width is model-dependent in that sense. This is a caveat, not a disproof: the qualitative change from real to complex pole is robust across all variations.\n\nOther issues are minor. Eq. (4) has a typo: 255(14) should be 25.5(14) to match Gamma = 54(14) MeV. The physical-pion trajectory holds K0 and g fixed, which should be stated more clearly in the abstract; it's a conditional trajectory, not a full chiral extrapolation. And the paper would benefit from releasing code or detailed parameter files for independent reproduction.\n\nThe citation pattern is fine. Ref. [28] is same-group work, but it is published and the formalism is the basis for the analysis; that's not a flaw.\n\nWho is this for? Lattice QCD practitioners and anyone working on near-threshold states and left-hand cut effects. It deserves a serious referee. I'd send it to review with a request to address the K0 extrapolation caveat explicitly and fix the typo.","headline":"A serious lattice QCD paper that credibly changes T_cc+ from a real virtual state to a complex subthreshold pole once one-pion exchange is included; the main uncertainty is the K0 extrapolation below the left-hand cut.","tokens_in":36589,"tokens_out":3191,"would_cite":true,"duration_ms":30614,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.38.Gc"],"model":"deepseek-v4-flash","headline":"Pion exchange turns the T_cc+ from a virtual state into a complex pole.","keywords":["doubly charmed tetraquark","T_cc+","one-pion exchange","left-hand cut","finite-volume scattering","lattice QCD","complex pole","DD* scattering"],"falsifier":"Compute the $DD^*\\pi$ coupling independently from lattice three-point correlation functions and compare with $g=11.8(7)$; alternatively, generate finite-volume energies at physical pion mass or at additional volumes with levels lying closer to the subthreshold region and check whether the complex pole appears and moves toward the real axis as predicted.","tokens_in":35398,"feed_emoji":"⚛️","tokens_out":6322,"duration_ms":59562,"temperature":0.7,"pith_summary":"The paper reanalyzes the finite-volume $DD^*$ spectrum from lattice QCD at $m_\\pi\\approx391\\,\\mathrm{MeV}$ using a scattering formalism that keeps one-pion exchange explicit. It claims that once pion exchange is included nonperturbatively, the $T_{cc}^+$ is no longer a real-valued virtual bound state but a complex pole on the second sheet at $E_{\\mathrm{pole}}=3854(15)-i\\,25.5(14)\\,\\mathrm{MeV}$, corresponding to a width $\\Gamma=54(14)\\,\\mathrm{MeV}$. The same analysis determines the $DD^*\\pi$ coupling directly from the spectrum as $g=11.8(7)$, without using effective-field-theory input, and predicts that the pole moves toward the real axis as the pion mass approaches its physical value. The result matters because earlier analyses that neglected the one-pion-exchange left-hand cut could misidentify the state, and it sharpens the broader question of whether the $T_{cc}^+$ is better described as a compact tetraquark or a $DD^*$ molecule.","feed_headline":"Pion exchange turns the T_cc+ into a complex pole","feed_subtitle":"Lattice QCD reanalysis turns a virtual bound state into a subthreshold pole with a width of 54 MeV.","key_machinery":"The load-bearing object is the finite-volume quantization condition $\\det\\big[(K_0)^{-1}+F_{\\mathrm{pv}}+C_L\\big]=0$, where $F_{\\mathrm{pv}}$ is the standard two-body finite-volume function and $C_L$ is a new term that encodes one-pion exchange through the $DD^*\\pi$ coupling $g$. This fixes $K_0$, the smooth short-distance kernel, and the physical amplitude is then reconstructed as $\\mathcal{M}=\\mathcal{M}_E+\\mathcal{M}_{K_0}$, where $\\mathcal{M}_E$ is the full one-pion-exchange ladder amplitude obtained from coupled integral equations. The pole is extracted by continuing to the second sheet through $\\mathcal{M}^{\\mathrm{II}}=\\big[(\\mathcal{M}^{\\mathrm{I}})^{-1}+2i\\rho\\big]^{-1}$, with careful checks that the integration contour avoids the one-pion-exchange branch cuts for the energies in question. This separation of long-range pion physics from short-distance dynamics is what lets the paper determine both $g$ and the pole position from the lattice spectrum alone.","core_discovery":"With the nearest left-hand cut from one-pion exchange made explicit, the isoscalar $J^P=1^+$ $DD^*$ amplitude below threshold no longer has a pole on the real-energy axis; instead, analytic continuation to the second sheet yields a complex pole at $E_{\\mathrm{pole}}=3854(15)-i\\,25.5(14)\\,\\mathrm{MeV}$, i.e. $\\Gamma=54(14)\\,\\mathrm{MeV}$. This pole is present across every explored parametrization of the short-distance $K_0$ matrix, and replacing the $K_0$ polynomial with its inverse leaves the result unchanged. The paper also shows that the $DD^*\\pi$ coupling and $K_0$ can be constrained simultaneously from the same 36 finite-volume energy levels, and that varying only the exchanged pion mass in the one-pion-exchange kernel pushes the pole toward the real axis as the pion mass is lowered.","pith_inferences":["If the predicted pole trajectory is correct, a physical-mass lattice calculation should find the $T_{cc}^+$ with a considerably smaller width, a test that could be performed with existing methodology in the next few years.","The $K_0$ parameters are scheme dependent, so direct comparisons with earlier K-matrix analyses should be made through the pole position and the coupling $g$, not through the individual $K_0$ coefficients.","A direct lattice QCD computation of the $DD^*\\pi$ three-point vertex would provide an independent check of $g=11.8(7)$, which is currently inferred solely from the two-body energy spectrum.","The same framework could be extended to reactions with coupled channels and higher partial waves, where the one-pion-exchange left-hand cut may lie even closer to the energy region of interest."],"forward_implications":["At $m_\\pi\\approx391\\,\\mathrm{MeV}$ the $T_{cc}^+$ must be regarded as a subthreshold complex pole rather than a real virtual bound state, so analyses that ignore the left-hand cut can misclassify it.","The $DD^*\\pi$ coupling is determined directly from finite-volume spectra, giving $g=11.8(7)$, so this channel no longer needs external effective-field-theory input at this pion mass.","As the exchanged pion mass is lowered, the pole trajectory moves toward the real-energy axis, predicting a progressively narrower $T_{cc}^+$ as physical quark masses are approached.","Including one-pion exchange improves the spectrum fit quality, from $\\chi^2/N_{\\mathrm{dof}}\\approx1.7$ with seven parameters down to $\\chi^2/N_{\\mathrm{dof}}\\approx0.9$ with three to five parameters, meaning much of the short-distance freedom is absorbed by the pion-exchange ladder.","The same formalism is transferable to other channels with nearby left-hand cuts, such as the two-nucleon sector."],"supporting_citations":[{"why":"Supplies the 36 finite-volume $DD^*$ energy levels and the previous no-left-hand-cut analysis whose virtual bound state is reinterpreted.","marker":"[14]"},{"why":"Provides the finite-volume scattering formalism that incorporates one-pion exchange nonperturbatively through $C_L$ and the $K_0$ separation.","marker":"[28]"},{"why":"Gives the analytic-continuation and integral-equation methods used to reach the second-sheet pole and to check the domain of analyticity.","marker":"[22]"},{"why":"Defines the standard finite-volume function $F$ entering the quantization condition.","marker":"[31]"},{"why":"First pointed out that neglecting pion exchange in this channel can invalidate conclusions drawn from lattice QCD studies.","marker":"[5]"},{"why":"A hybrid analysis using external inputs that predicted a subthreshold second-sheet pole with a width near 30 MeV at $m_\\pi\\approx280$ MeV, consistent with the trend reported here.","marker":"[10]"}],"fun_headline_variants":["Pion exchange turns T_cc+ into a complex pole","Lattice QCD: T_cc+ pole goes complex with 54 MeV width","Including pion exchange gives T_cc+ a width of 54 MeV","Complex T_cc+ pole emerges from pion-exchange lattice QCD"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The extraction assumes that the fitted smooth $K_0$ polynomial remains valid when extrapolated from the energy region of the lattice levels down to the subthreshold pole, and that the integral equations can be analytically continued below the single-pion left-hand cut without encountering an undetected singularity.","fun_headline_variants_meta":{"raw":{"variants":["Pion exchange turns T_cc+ into a complex pole","Lattice QCD: T_cc+ pole goes complex with 54 MeV width","Including pion exchange gives T_cc+ a width of 54 MeV","Complex T_cc+ pole emerges from pion-exchange lattice QCD"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000235,"raw_usage":{"total_tokens":1491,"prompt_tokens":926,"completion_tokens":565,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":542,"completion_tokens_details":{"reasoning_tokens":485}},"tokens_in":542,"tokens_out":565,"duration_ms":5256,"temperature":1.0,"reasoning_tokens":485,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:32:40.610632+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the $DD^*\\pi$ coupling independently from lattice three-point correlation functions and compare with $g=11.8(7)$; alternatively, generate finite-volume energies at physical pion mass or at additional volumes with levels lying closer to the subthreshold region and check whether the complex pole appears and moves toward the real axis as predicted.","supporting_citations":[],"review_version":1}