{"id":"351505fc-5f68-48c5-acbc-c753abe7c587","arxiv_id":"2608.07957","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"An effective-Lagrangian calculation predicts the I=1 D*K molecule T^a_cs1(2470) has a D_s*pi0 width of 13 to 196 MeV, about 10^3 times the predicted D_s1(2460) molecular width.","lead":"The paper predicts that an unobserved isovector partner of the D_s1(2460) meson, modeled as a D*K molecule, should decay roughly a thousand times faster than D_s1(2460). It gives LHCb a concrete mass, decay channel, and width range to search for.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed 10^3 width hierarchy hinges on the isospin interference sign in Eq. (14), but as printed the same sign combination is used for both T^f and T^a in D_s*pi0 decays.","rationale":"Good-faith reading: this is a standard effective-Lagrangian molecular calculation. The couplings are fixed by the compositeness condition rather than fitted to widths, the parameter ranges are presented honestly, and the D*K/DK molecular framework has independent support from earlier work on D_s0*(2317) and T_cs0(2327). My concern is not the model choice or the unmeasured mass of T^a_cs1; it is that the written amplitudes do not manifestly encode the isospin selection rule that is the entire source of the headline hierarchy. The reader's weakest assumption, the mass of T^a_cs1, is real but secondary: varying m_Ta by tens of MeV changes phase space by a modest factor and does not overturn an isospin-allowed versus isospin-forbidden comparison; the factor of 10^3 comes from the sign of the D*0K+ diagrams. As printed, Eq. (14) assigns the same sign to both isospin combinations, which would suppress or enhance both states equally in the isospin limit. To be fair, the numerical code may have used the correct constructive sign, and the discrepancy could be a typographical error in the manuscript; that is a testable, fixable issue. Until the sign is verified, the central claim is conditional on an unstated sign convention. I therefore keep the reader's CONDITIONAL verdict rather than moving to accept or reject, because the physics could survive a corrected Eq. (14). Agreement with the reader is partial, since the reader's weakest_assumption is the mass and cutoff sensitivity, while the more load-bearing issue here is the interference sign in Eq. (14).","tokens_in":16364,"tokens_out":13029,"duration_ms":142518,"concrete_test":"Recompute Gamma(T^a_cs1 -> D_s*+ pi0) at Lambda = 1 GeV twice: once with the printed sign combination M_a + M_c + M_e - M_b - M_d - M_f and once with the isospin-constructive combination M_a + M_c + M_e + M_b + M_d + M_f, using identical masses and couplings. If only the second combination gives about 13 MeV while the first gives O(keV), then Eq. (14) is mis-signed and the manuscript must be revised before the three-orders claim is accepted. A cross-check is to set all isospin-breaking masses and couplings to zero and verify that the T^f amplitude vanishes while the T^a amplitude remains nonzero; the printed signs fail that selection rule.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the isospin interference in Eq. (14). The claimed factor ~10^3 between Gamma(T^a_cs1 -> D_s*+ pi0) = 13.35-196.1 MeV (Sec. IV.C) and Gamma(T^f_cs1 -> D_s*+ pi0) = 18.98-154.4 keV (Sec. IV.B) must come from the relative sign between the D*+K0 diagrams (M_a, M_c, M_e) and the D*0K+ diagrams (M_b, M_d, M_f). As printed, Eq. (14) writes both the T^f and T^a amplitudes for D_s*pi0 as M_a + M_c + M_e - M_b - M_d - M_f, with T^f having additional eta-pi mixing terms. With g_Tf approximately equal to g_Ta and nearly equal masses, identical sign structure cannot produce a thousand-fold difference; the hierarchy requires destructive interference for the I=0 state and constructive interference for the I=1 state. The paper never defines an implicit relative sign carried by the replacements in Eq. (10), and no isospin phase convention is stated. If Eq. (14) is taken literally, the quoted T^a width is not reproducible from the written amplitude; if the numerical code used the opposite sign, Eq. (14) must be corrected. This sign issue is more decisive than the mass and cutoff sensitivity identified by the reader, because the mass variation changes phase space by a modest factor, whereas the sign determines whether the principal decay is allowed or suppressed.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript postulates the existence of S-wave D*K and \\bar{D}*K molecular states with isospin I=0 and I=1, named T^f_c\\bar{s}1(2460), T^a_c\\bar{s}1(2470), T^f_\\bar{c}\\bar{s}1(2460), and T^a_\\bar{c}\\bar{s}1(2470). Using an effective Lagrangian approach with Gaussian form factors and couplings fixed by Weinberg's compositeness condition, the authors compute strong decay widths for channels such as T^f/a_c\\bar{s}1 -> D_s*+ pi0, D_s0*+ pi0, and T^a_c\\bar{s}0 pi. The central claim is that the isovector state T^a_c\\bar{s}1(2470) has a width roughly three orders of magnitude larger than the isoscalar T^f_c\\bar{s}1(2460), while the \\bar{c}\\bar{s} counterparts have widths of order 100 keV. The analysis is presented as a way to guide experimental searches for these states.","tokens_in":16750,"tokens_out":6875,"duration_ms":75353,"significance":"If the central prediction holds, the paper provides a concrete and falsifiable experimental discriminator: the isovector partner of D_s1(2460) would be very broad (tens to hundreds of MeV), whereas the isoscalar is narrow (tens to hundreds of keV). A strength of the calculation is that the molecular couplings are not fitted to the target decay widths but are fixed by the compositeness condition, so the predicted hierarchy is not a disguised fit. However, the numerical predictions depend on a model cutoff Lambda and on an inferred mass for the unobserved T^a_c\\bar{s}1 state, which limits the precision of the claims.","major_comments":[{"comment":"Eq. (14) gives the same non-mixing amplitude, M_a + M_c + M_e - M_b - M_d - M_f, for both T^f_c\\bar{s}1 -> D_s*+ pi0 and T^a_c\\bar{s}1 -> D_s*+ pi0. According to the molecular wave functions in Eq. (1) and the effective Lagrangians in Eq. (2), the relative sign between the D*+K0 diagrams (M_a, M_c, M_e) and the D*0K+ diagrams (M_b, M_d, M_f) must be positive for the I=0 state and negative for the I=1 state. As printed, the two amplitudes differ only by the small eta-pi mixing terms, which cannot produce the claimed factor of about 10^3 between Gamma(T^a -> D_s* pi0) = 13.35-196.1 MeV and Gamma(T^f -> D_s* pi0) = 18.98-154.4 keV. The sign structure in Eq. (14) is therefore internally inconsistent with the numerical results, and the central claim is not reproducible from the written amplitude unless an implicit sign convention is stated.","section":"Sec. III.B, Eq. (14)"},{"comment":"The mass of T^a_c\\bar{s}1 is not computed but is set to 2470 MeV using the ad hoc relation m(T^a_c\\bar{s}1) - m(T^a_c\\bar{s}0(2327)) ≈ m_D* - m_D. This mass enters the phase space of every computed width, and the paper does not investigate the sensitivity of Gamma(T^a -> D_s* pi0) to the assumed mass, in contrast to Fig. 7, which scans the mass of T^a_c\\bar{s}0 for a related decay. Given that the quoted width range already spans a factor of about 15 over the Lambda scan, the authors should either justify this relation more strongly or provide a scan over the plausible mass range around 2470 MeV to show that the three-orders-of-magnitude hierarchy is robust.","section":"Sec. IV.A and Fig. 5"},{"comment":"The widths of the \\bar{c}\\bar{s} states T^f_\\bar{c}\\bar{s}1 and T^a_\\bar{c}\\bar{s}1 are quoted as 'several hundred keV' and 'about 0.1 keV' without any explicit amplitude, diagram, or numerical result shown. These statements appear to be qualitative estimates from analogy with the c\\bar{s} transitions, but they are presented as results of the calculation. The authors should either provide the corresponding amplitudes and partial-width computations or clearly label these as estimates that are not derived within the presented framework.","section":"Sec. IV.D"}],"minor_comments":[{"comment":"The factor in Eq. (11) is written as 'md - mu over ms - m sqrt(3)/4', which is ambiguous; please insert parentheses to clarify that the intended expression is ((md - mu)/(ms - m)) * sqrt(3)/4.","section":"Eq. (11)"},{"comment":"The symbol P appears in the definition of the mass operator in Eq. (7) but is not defined; the authors should state explicitly that P is the four-momentum of the molecular state (elsewhere called p).","section":"Eq. (7)"},{"comment":"The last three lines of Eq. (14) use the same left-hand side 'M_T^a_c\\bar{s}1 -> T^a_c\\bar{s}0 pi' for three different amplitude expressions; please add the pion charge (pi0, pi+, pi-) to distinguish the channels.","section":"Eq. (14)"},{"comment":"There is a typo in the second paragraph: 'from of D_s1(2460)+ -> D_s+ pi+ pi-' should read 'from D_s1(2460)+ -> D_s+ pi+ pi-'; also, the phrase 'which further support' should be 'which further supports'.","section":"Sec. I"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal, and the topic is of current interest. The main concern is the sign issue in Eq. (14), which directly affects the central claim. I would also note that the calculation relies on couplings and masses taken from the authors' previous work [81]; this is standard practice but should be clearly identified if the present conclusions rest on those inputs. If the sign issue is corrected and the hierarchy disappears, the paper's main message would need to be substantially revised."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is the next step in the authors' DK molecular program, and the new numbers are the decay widths for the isovector T^a_{c\\bar{s}1}(2470) and the pionic transitions of the anti-D*K states. The calculation is not a disguised fit. The molecular couplings come from Weinberg's compositeness condition rather than from fitting the target widths, and the input hadronic couplings are tied to measured widths and QCD sum rules. That is a legitimate way to produce predictions, and the explicit amplitudes in Sec. III let a reader see what is being summed.\n\nThe soft spot is more serious than the reader's mass-and-cutoff worry. Eq. (14) writes both M_{T^f -> D_s* pi0} and M_{T^a -> D_s* pi0} as M_a + M_c + M_e - M_b - M_d - M_f. But the T^a wavefunction in Eq. (1) carries a relative minus between the D*+K0 and D*0K+ components, and the final pi0 vertex already contributes a sign between those two channels. With the same printed sign pattern for the I=0 and I=1 states, and with nearly equal couplings and masses, the two amplitudes have the same interference structure. That cannot produce the claimed factor of roughly 10^3 between 18.98-154.4 keV and 13.35-196.1 MeV. The hierarchy requires destructive interference for the isoscalar and constructive interference for the isovector. As printed, the T^a amplitude is the isospin-suppressed one, so the quoted T^a width is not reproducible from Eq. (14). If the code used the opposite sign, Eq. (14) has to be corrected; if Eq. (14) is literal, the abstract's main claim collapses. This is a load-bearing internal inconsistency, not a cosmetic typo.\n\nThe secondary issues are real but less decisive. The mass m(T^a)=2470 MeV is inferred from the D* - D mass splitting, and the Lambda scan alone changes the T^a -> D_s* pi0 width by a factor of about 15. The anti-D*K section in Sec. IV.D is only sketched. Those would matter after the sign issue is resolved.\n\nWho should read it: hadron spectroscopists and experimentalists at LHCb/Belle II looking for unobserved charm-strange states. I would send this to a referee rather than desk reject it, because the method is standard, the inputs are quoted, and the isovector-broad/isoscalar-narrow picture is plausible and testable. But the referee's first job is to demand a corrected and sign-consistent version of Eq. (14) and a check that the quoted widths follow from it.","headline":"New molecular decay numbers for D*K/anti-D*K states, but the printed Eq. (14) gives the same isospin interference sign for the I=0 and I=1 amplitudes, so the headline 10^3 width hierarchy is not reproducible from the paper as written.","tokens_in":17270,"tokens_out":8292,"would_cite":false,"duration_ms":94050,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper predicts that the isovector $D^*K$ molecule $T^a_{c\\bar{s}1}(2470)$, if it exists, decays dominantly to $D_s^{*+}\\pi^0$ with a width of 13--196 MeV, roughly a thousand times the width of its isoscalar partner…","keywords":["D*K molecules","hadronic molecules","strong decays","effective Lagrangian","Weinberg compositeness condition","isospin violation","D_s1(2460)","T_cs0(2327)"],"falsifier":"Take the $D_s^{*+}\\pi^0$ invariant-mass distribution in high-statistics $B$-decay or $e^+e^-$ data and look near 2470 MeV: the paper predicts a broad enhancement with width between about 13 and 196 MeV, while a narrow resonance with width below 1 MeV at that mass, or the absence of any enhancement, would falsify the mass assignment and the claimed width hierarchy.","tokens_in":16137,"feed_emoji":"⚛️","tokens_out":10512,"duration_ms":106028,"temperature":0.7,"pith_summary":"The paper argues that a set of hadronic states near the $D^*K$ and $\\bar{D}^*K$ thresholds can be understood as $S$-wave molecules, and that the known $D_{s1}(2460)$ is the isoscalar member of a doublet. Its unobserved isovector partner, $T^a_{c\\bar{s}1}(2470)$, should have a dramatically different width: the paper computes $\\Gamma(T^a\\to D_s^{*+}\\pi^0)\\simeq 13$--$196$ MeV against $\\Gamma(T^f\\to D_s^{*+}\\pi^0)\\simeq 19$--$154$ keV, a gap of about three orders of magnitude. The reason is isospin: the isoscalar decays are isospin-violating or kinematically suppressed, while the isovector decay is allowed. If the calculation is right, the two partners are distinguishable by width alone, and the broad state should be searched for through its $D_s^{*}\\pi^0$ decay.","feed_headline":"Isovector D*K partner predicted 1,000 times wider than D_s1(2460)","feed_subtitle":"A broad 13-196 MeV D_s* pi0 signal should mark the missing isovector partner of D_s1(2460).","key_machinery":"The machinery is an effective Lagrangian with Gaussian vertex form factors. Each molecular state is coupled to its constituents by a Lagrangian with the correlation function $\\tilde{\\Phi}(p_E^2)=\\exp(-p_E^2/\\Lambda^2)$; the coupling is fixed by Weinberg's compositeness condition $Z=1-\\Pi'(m^2)=0$, which requires the bound state to be a pure composite of its components. Decay amplitudes are built from SU(4) heavy-meson Lagrangians, and for the isospin-violating isoscalar decays the $\\eta$--$\\pi^0$ mixing term is included. The single free parameter $\\Lambda$ is varied over 1--3 GeV, producing the quoted ranges.","core_discovery":"The central claim is that isospin, not dynamics, controls the widths of the proposed $D^*K$ molecules. With the four states $T^{f/a}_{c\\bar{s}1}$ and $T^{f/a}_{\\bar{c}\\bar{s}1}$ treated as $S$-wave molecules, the isoscalar $T^f$ decays are suppressed by isospin violation (with $\\eta$--$\\pi^0$ mixing contributing) or by small phase space, so its widths are keV-scale; the isovector $T^a$ decay to $D_s^{*+}\\pi^0$ is isospin-allowed, so its width reaches tens to hundreds of MeV. In the parameter range $\\Lambda = 1$--$3$ GeV, the partial width for $T^f_{c\\bar{s}1}\\to D_s^{*+}\\pi^0$ rises from 18.98 to 154.4 keV, while that for $T^a_{c\\bar{s}1}\\to D_s^{*+}\\pi^0$ rises from 13.35 to 196.1 MeV. The charge-conjugate $\\bar{D}^*K$ states decay, if $\\bar{D}K$ molecular states exist, only into those states plus a pion, with widths of order $10^2$ keV.","pith_inferences":["The paper leaves implicit that the same isospin switch should control the widths of analogous $B^*K$ or $\\bar{B}^*K$ molecules; testing that pattern would check whether the hierarchy is generic or specific to this mass region.","A testable extension is to repeat the calculation with a different vertex form factor, such as a monopole instead of a Gaussian: if the thousand-fold gap between isoscalar and isovector widths survives, the hierarchy is robust, and if not, it is driven by the assumed wave function.","Because the predicted width range is governed by the assumed 2470 MeV mass, the sharpest experimental check is to measure the mass and width of the state together; a mass closer to the $D^*K$ threshold would shrink the phase space and narrow the predicted width."],"forward_implications":["The unobserved isovector molecule $T^a_{c\\bar{s}1}(2470)$ should be a broad state, with $\\Gamma(T^a_{c\\bar{s}1}\\to D_s^{*+}\\pi^0)$ in the range 13.35--196.1 MeV, so $D_s^{*}\\pi^0$ is the natural discovery channel.","The known $T^f_{c\\bar{s}1}(2460)$, identified with $D_{s1}(2460)$, stays narrow with keV-scale widths, consistent with the small experimental width of that state.","The isospin-allowed but kinematically suppressed transitions from $T^a_{c\\bar{s}1}$ to $D_{s0}^{*}(2317)\\pi^0$ and $T^a_{c\\bar{s}0}(2327)\\pi$ come out near 0.1--0.2 MeV, not broad.","The charge-conjugate $\\bar{D}^*K$ molecules $T^{f/a}_{\\bar{c}\\bar{s}1}$, if they exist, should have widths of order $10^2$ keV through their transitions to $\\bar{D}K$ molecular states plus a pion.","A measurement of the $D_s^{*+}\\pi^0$ spectrum near 2470 MeV can therefore distinguish the isovector molecular picture from other interpretations of the $D_{s1}$ family."],"supporting_citations":[{"why":"supplies the measured masses of $D_{s0}^{*}(2317)$ and $D_{s1}(2460)$, the decay constants, and the strong couplings used as input.","marker":"[23]"},{"why":"observes the isovector DK state near the DK threshold and the double-bump structure that motivates the $D^*K$ molecular picture and the existence of an isovector $D^*K$ partner.","marker":"[7]"},{"why":"establishes the effective-Lagrangian treatment and couplings for the related DK molecular states that appear as intermediate states in the transitions.","marker":"[81]"},{"why":"supplies the Gaussian correlation function and the molecular vertex form-factor method used in the decay amplitudes.","marker":"[38]"},{"why":"provides Weinberg's compositeness condition used to fix the $D^*K$ molecular couplings from the mass operator.","marker":"[86]"},{"why":"together with [99], gives the QCD sum-rule values of the $D_s DK$ and $D_s^* DK$ couplings used in the amplitudes.","marker":"[98]"}],"fun_headline_variants":["Isospin sets D*K molecule widths: isovector partner MeV, isoscalar keV","D*K molecule: isospin flips width by 1000-fold","Isovector D*K partner decays to D_s* pi0 with MeV width","Isospin controls D*K decay widths: isovector 1000x isoscalar"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes the unseen $T^a_{c\\bar{s}1}$ has mass 2470 MeV, fixed by the analogy $m(T^a_{c\\bar{s}1})-m(T^a_{c\\bar{s}0}(2327))\\approx m_{D^*}-m_D$, and that one Gaussian size parameter $\\Lambda$ between 1 and 3 GeV describes both $D^*K$ and $DK$ molecules; a different mass for the state would change every computed width and could shrink or erase the three-orders-of-magnitude gap.","fun_headline_variants_meta":{"raw":{"variants":["Isospin sets D*K molecule widths: isovector partner MeV, isoscalar keV","D*K molecule: isospin flips width by 1000-fold","Isovector D*K partner decays to D_s* pi0 with MeV width","Isospin controls D*K decay widths: isovector 1000x isoscalar"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000766,"raw_usage":{"total_tokens":3473,"prompt_tokens":1095,"completion_tokens":2378,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":711,"completion_tokens_details":{"reasoning_tokens":2280}},"tokens_in":711,"tokens_out":2378,"duration_ms":20718,"temperature":1.0,"reasoning_tokens":2280,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T00:37:01.639283+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the $D_s^{*+}\\pi^0$ invariant-mass distribution in high-statistics $B$-decay or $e^+e^-$ data and look near 2470 MeV: the paper predicts a broad enhancement with width between about 13 and 196 MeV, while a narrow resonance with width below 1 MeV at that mass, or the absence of any enhancement, would falsify the mass assignment and the claimed width hierarchy.","supporting_citations":[{"cited_title":"Determining the width of $D_{s0}^{*}(2317)$ by using $T_{c\\bar{s}0}^{a}(2327)$ in a molecular frame","cited_arxiv_id":"2507.19641","evidence_quote":"establishes the effective-Lagrangian treatment and couplings for the related DK molecular states that appear as intermediate states in the transitions."},{"cited_title":"Analysis of the vertices $D^*D_sK$, $D^*_sDK$,$D_0D_sK$ and $D_{s0}DK$ with the light-cone QCD sum rules","cited_arxiv_id":"hep-ph/0606002","evidence_quote":"together with [99], gives the QCD sum-rule values of the $D_s DK$ and $D_s^* DK$ couplings used in the amplitudes."}],"review_version":1}