{"id":"9d5d35a7-4b4f-4fee-87a4-a15f5efe17f8","arxiv_id":"2411.11413","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"The paper presents new RIQ-model predictions for B_c decay ratios (R_D/D*, R_eta_c/J/psi, and tau/mu leptonic ratios) with no derivation or error bars.","lead":"This paper reviews B_c meson physics and lists new predictions for ratios of semileptonic and leptonic branching fractions, such as R_D/D* = 0.146 and (R_tau/mu)^Bc = 246.77. A generalist reader might look here for benchmark observables that future LHCb and e+e- collider data could use to test lepton flavor universality.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Claimed Bc leptonic ratio 246.77 conflicts with the paper's own Eq (5); recomputing from PDG masses gives ~239, so the central numerical claim is internally inconsistent.","rationale":"The reader's overall REJECT verdict is supported, but the specific weakest assumption is partly misidentified. The most decisive problem is not the reliability of RIQ model form factors: the leptonic ratio (Rτ/μ)^Bc is, from Eq (5), independent of all hadronic parameters (f_Bc and Vcb cancel), so the discrepancy between 246.77 and the kinematic value ~239.4 is an internal inconsistency of the paper's own equations. This is a model-independent, checkable error that undermines the credibility of the central new predictions. The reader's secondary concern about (Rτ/μ)^Bc* = 0.883 conflicting with Eq (5) is incorrect, because Eq (5) applies to the pseudoscalar Bc, not the vector Bc*; the vector-meson formula gives about 0.88. However, the paper still fails to provide any formula for the Bc* decay, so that number remains unverifiable from the text. The semileptonic ratios also lack derivations, but the concrete internal inconsistency of Eq (7) is the strongest load-bearing concern.","tokens_in":14537,"tokens_out":23458,"duration_ms":203045,"concrete_test":"Recompute R = (m_τ^2/m_μ^2) × [(1 - m_τ^2/M^2)/(1 - m_μ^2/M^2)]^2 with PDG masses M=6.2749 GeV, m_τ=1.77686 GeV, m_μ=0.10566 GeV. If the result is ≈239.4, then Eq (7) is inconsistent with Eq (5); the authors should either correct the number or supply the additional mechanism that justifies the 3% shift.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central new results include (Rτ/μ)^Bc = B(Bc→τν)/B(Bc→μν) = 246.77 (Eq 7). According to the paper's own Eq (5), Γ(Bc→lν) = (1/8π)|Vcb|^2 G_F^2 M f_Bc^2 m_l^2 (1 - m_l^2/M^2)^2. In the ratio, f_Bc and |Vcb| cancel completely, leaving a purely kinematic expression that depends only on m_τ, m_μ, and M. Using PDG values M=6.2749 GeV, m_τ=1.77686 GeV, m_μ=0.10566 GeV, one obtains R ≈ 239.4, not 246.77. No source of a 3% correction (e.g., QED corrections) is mentioned in the paper. Thus the quoted value does not follow from the stated formula; it is an unexplained numerical discrepancy in the central claim. For completeness, the companion Bc* ratio 0.883 is not covered by Eq (5), which applies to the pseudoscalar Bc; the standard vector-meson formula yields about 0.88, so the reader's specific objection that Eq (5) would give 239 for Bc* is not valid—but the paper still does not state any formula for the vector-meson decay.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reviews the production and decay properties of the B_c meson, including semileptonic, leptonic, and non-leptonic modes, and presents several new predictions for ratios of branching fractions using the relativistic independent quark (RIQ) model. The claimed new results are R_{D/D*} = 0.146 and R_{η_c/J/ψ} = 0.140 for semileptonic decays, and (R_τ/μ)^{B_c} = 246.77 and (R_τ/μ)^{B_c*} = 0.883 for leptonic decays. The paper gives no derivations for these numbers, relying instead on self-cited earlier RIQ model papers, and it contains no uncertainty estimates for the new predictions.","tokens_in":14864,"tokens_out":10111,"duration_ms":100201,"significance":"If the predictions were established, they would be of interest as potential lepton-flavor-universality observables for future LHCb and FCC-ee studies, and the ratio construction is a reasonable way to cancel some hadronic uncertainties. However, the manuscript does not provide enough information to verify any of the central predictions: the semileptonic ratios are asserted without the underlying form-factor calculation, and the leptonic ratio (R_τ/μ)^{B_c} is inconsistent with the formula quoted in the same paper. The paper also conflates a parameter-free kinematic prediction with a model-dependent result. For these reasons, the significance of the contribution is not currently established.","major_comments":[{"comment":"The quoted value (R_τ/μ)^{B_c} = 246.77 does not follow from Eq. (5). In the ratio, the decay constant f_{B_c} and the CKM factor cancel, so the result is purely kinematic. Using the PDG masses M_{B_c}=6.2749 GeV, m_τ=1.77686 GeV, and m_μ=0.10566 GeV, Eq. (5) gives R ≈ 239.4, not 246.77. No source of a 3% correction (such as QED effects) is mentioned. Since this is one of the two central leptonic predictions, the discrepancy is a load-bearing error that must be corrected or explained.","section":"§2.2, Eq. (7)"},{"comment":"The value (R_τ/μ)^{B_c*} = 0.883 is presented without any formula for the leptonic decay of a vector meson. While this value is compatible with the standard vector-meson formula Γ(V → lν) ∝ M^3 f_V^2 (1 - m_l^2/M^2)^2 (1 + m_l^2/2M^2) if the decay constant cancels, the manuscript neither states nor derives that formula. As a result, the reader cannot determine whether this number is a genuine RIQ model prediction or simply a kinematic consequence, and the paper needs to specify the vector-meson decay formalism explicitly.","section":"§2.2, Eq. (8)"},{"comment":"The semileptonic ratios R_{D/D*} = 0.146 and R_{η_c/J/ψ} = 0.140 are quoted as RIQ model predictions with no derivation. No form factors, no q^2 integration, no input masses, and no uncertainty estimates are given, nor is a specific equation or table in the cited references [38–41,52] identified. Since these ratios are the paper's central new semileptonic results, the absence of any calculational detail makes them impossible to verify or reproduce. The authors must present the calculation or at least spell out exactly how the numbers are obtained from the RIQ model.","section":"§2.1, after Eq. (2)"},{"comment":"The paper claims the RIQ model uses no adjustable free parameters because the potential parameters and quark masses were fixed in earlier spectroscopy papers. However, the parameter values and the model Hamiltonian are not summarized here. The manuscript needs to state the model inputs or give an explicit reference to the equations in the earlier papers where they are defined, so that the predictions can be checked independently. As written, the central numerical claims rest on unspecified self-cited work.","section":"§2.1, 'no adjustable free parameters'"}],"minor_comments":[{"comment":"The acronyms 'ND-SM' and 'UP' are used without definition; they should be defined at first use or replaced with standard terms such as 'beyond the Standard Model'.","section":"Abstract"},{"comment":"The definition of the decay constant is incomplete: after writing the matrix element ⟨0|bγ^μγ_5 c|B_c(p)⟩, the equality to i f_{B_c} p^μ should be stated explicitly.","section":"§2.2, Eq. (6)"},{"comment":"The effective Hamiltonian notation is inconsistent: Eq. (9) uses λ_c but Eq. (10) uses |V_cb||V_cq|†, and the operator sum indices are not defined. This section should be clarified.","section":"§2.3, Eqs. (9)–(10)"},{"comment":"Several references, including [55], [58], [59], [60], and [61], lack article titles and some author lists are incomplete; these should be brought to the journal's reference style.","section":"References"},{"comment":"There is a typo: 'pehnomenological' should be 'phenomenological'. Also, the sentence beginning 'With upcoming LHCb and Super-B experiments expected...' is grammatically incomplete.","section":"Section 4"},{"comment":"The paper states 'we do not claim high quantitative precision' but then quotes predictions to four significant digits, e.g., 246.77 and 0.146. The authors should either provide realistic error bars or present the numbers to a precision consistent with the claimed qualitative nature of the predictions.","section":"§4"}],"recommendation":"reject","confidential_remarks":"The manuscript appears to be a review of B_c physics with a few numerical predictions added, but the new results are not backed by derivations, and one of the central numbers conflicts with the paper's own formula. In a letter journal, this is a fundamental flaw that cannot be addressed by minor edits. The review portions could potentially be developed into a separate review paper, but the current manuscript does not meet the standard for publication in its present form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Thanks for the report. The reader's verdict is mostly right, but one specific objection is off: (R_tau/mu)^Bc* = 0.883 is not covered by Eq (5), which applies to the pseudoscalar B_c. The standard vector-meson formula gives about that value, so this is not a factor-of-270 contradiction. The broader criticism stands, though: neither leptonic ratio is derived in the paper, and the B_c value is inconsistent with the paper's own Eq (5).\n\nWhat the paper does well: it is a serviceable review of B_c production and decays, with up-to-date references to LHCb, CMS, lattice QCD, and other models. The idea of constructing LFU ratios in B_c is reasonable, and the semileptonic ratios (R_D/D* = 0.146, R_eta_c/J/psi = 0.140) are new numbers, even if they are direct outputs of the RIQ model already used in earlier work.\n\nSoft spots, in proportion:\n\n- The central numbers are quoted without derivation or error bars. The semileptonic ratios lack any shown form-factor inputs or comparison with other model predictions. The paper's statement that CKM uncertainties cancel does not address the hadronic uncertainties.\n\n- (R_tau/mu)^Bc = 246.77 does not follow from Eq (5) with standard masses. Using PDG masses gives about 239. The 3% difference is unexplained; it may be a typo or a different mass input, but as written it is an internal inconsistency in the headline result.\n\n- (R_tau/mu)^Bc* = 0.883 is plausible but the paper gives no formula for the vector-meson decay. The reader's specific complaint about Eq (5) is wrong, but the missing derivation is real.\n\n- Self-citation is heavy, though the parameters were fixed in earlier spectroscopy, so circularity is not the biggest issue. Still, a reader cannot verify the numbers from this paper alone.\n\nTo the paper's credit, it explicitly says it does not claim high quantitative precision. But quoting 246.77 to five significant figures cuts against that.\n\nWho this is for: a reader wanting a broad overview of B_c physics may find the review parts useful, but the new results are not usable as they stand.\n\nRecommendation: I would not send this to peer review in its current form. The central numerical claims need derivation and the internal inconsistency needs fixing. If that is done, a revised version could be a reasonable contribution. As it stands, desk reject.","headline":"The B_c review is serviceable, but the central new ratios are unsubstantiated and one is inconsistent with the paper's own formula; desk reject unless revised.","tokens_in":15387,"tokens_out":4904,"would_cite":false,"duration_ms":42275,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper predicts four B_c decay ratios—0.146 and 0.140 for semileptonic modes, 246.77 and 0.883 for leptonic modes—using a parameter-free relativistic independent quark model, offering testable LFU observables for future colliders.","keywords":["B_c meson","semileptonic decays","leptonic decays","form factors","relativistic independent quark model","lepton flavor universality","CP violation","heavy quarkonium"],"falsifier":"Measure $B(B_c \\to \\tau\\nu)/B(B_c \\to \\mu\\nu)$ at LHCb or a future $Z$-factory: if the result is incompatible with 246.77 while the muon mode is observed, the leptonic prediction fails. A purely internal check is to re-derive $(R_\\tau^\\mu)^{B_c^*}$ from the paper's Eq. (5) with its stated decay constants; the standard helicity-suppressed formula with $f_{B_c^*} \\approx f_{B_c}$ gives a value of order 239, so 0.883 requires an explicit derivation that the paper does not supply.","tokens_in":14302,"feed_emoji":"⚛️","tokens_out":8695,"duration_ms":74371,"temperature":0.7,"pith_summary":"This paper argues that the B_c meson, the only bound state of two different heavy quarks, is a powerful testbed for Standard Model predictions, and it contributes new numerical predictions for four ratios of B_c decay rates. In semileptonic decays it predicts $R_{D/D^*} = 0.146$ and $R_{\\eta_c/J/\\psi} = 0.140$; in leptonic decays it predicts $(R_\\tau^\\mu)^{B_c} = 246.77$ and $(R_\\tau^\\mu)^{B_c^*} = 0.883$. Because the CKM matrix elements cancel in these ratios, the predictions isolate hadronic dynamics and are directly testable at LHCb and future $e^+e^-$ colliders. The paper also reviews production mechanisms, CP violation, and the status of lattice QCD form factors for B_c decays. The central claim is that the relativistic independent quark model, with no free parameters, yields reliable predictions across the full kinematic range.","feed_headline":"B_c tau/mu ratio predicted at 246.77","feed_subtitle":"Semileptonic and leptonic B_c decay ratios from a parameter-free model give direct LHCb and FCC-ee targets.","key_machinery":"The central object is the relativistic independent quark (RIQ) model, a potential-model framework in which a meson's wave function is obtained by confining its constituent quark and antiquark with an interaction potential of specified Lorentz structure, and the weak transition form factors are computed as overlap integrals of initial and final meson wave functions over the entire accessible $q^2$ range. The potential parameters $(a, V_0)$, quark masses, and binding energies were fixed once by hadron spectroscopy in earlier work, so the model is presented as parameter-free. The same machinery yields the decay constants $f_{B_c}$ and $f_{B_c^*}$ used in the leptonic ratios. The newly constructed ratios are the paper's key observables, chosen because CKM uncertainties cancel and because comparing pseudoscalar and vector final states probes spin and angular-momentum dynamics.","core_discovery":"The central claim is that newly constructed ratios of B_c branching fractions are computable and predictive. Using the RIQ model, in which transition form factors are overlap integrals of quark-model wave functions, the paper obtains $R_{D/D^*} = B(B_c \\to D \\mu \\nu)/B(B_c \\to D^* \\mu \\nu) = 0.146$ and $R_{\\eta_c/J/\\psi} = B(B_c \\to \\eta_c \\mu \\nu)/B(B_c \\to J/\\psi \\mu \\nu) = 0.140$, with the pseudoscalar-to-vector ratio larger because the $D/D^*$ system has more phase space. For leptonic decays it predicts $(R_\\tau^\\mu)^{B_c} = 246.77$ and $(R_\\tau^\\mu)^{B_c^*} = 0.883$. The paper stresses that the model has no adjustable parameters, with quark masses, potential parameters, and binding energies fixed by hadron spectroscopy, so the only input uncertainties are CKM elements that cancel in the ratios. It presents these as novel findings that future LHCb, CMS, and FCC-ee data can test.","pith_inferences":["Inference: the 0.883 value for $(R_\\tau^\\mu)^{B_c^*}$ is not derivable from the displayed Eq. (5) unless an unstated $f_{B_c^*}$ relation is used; the paper should show that derivation before this number is adopted.","Inference: a cross-check in $B_s \\to D_s/D_s^*$ decays, where LHCb has published a related ratio, would test whether the RIQ model's form factors transfer across heavy-flavor systems.","Inference: once the $B_c^*$ leptonic ratio is clarified, it may serve as a sensitive probe of the vector decay constant $f_{B_c^*}$, which lattice QCD has not yet determined."],"forward_implications":["If the predicted semileptonic ratios survive comparison with data, they will provide a CKM-free test of the RIQ model's form factors over the full $q^2$ range, complementing lattice QCD results.","A measurement of $(R_\\tau^\\mu)^{B_c} \\approx 247$ at LHCb or a future $Z$-factory would confirm the Standard Model's helicity-suppression picture for $B_c \\to \\tau\\nu$ versus $B_c \\to \\mu\\nu$; any significant deviation would flag new physics.","The new semileptonic ratios $R_{D/D^*}$ and $R_{\\eta_c/J/\\psi}$ give a direct comparison of pseudoscalar versus vector final states, testing how phase space and spin dynamics shape $B_c$ decays.","The excited-state LFU observables $R_{D(2S)}$, $R^*_{D(2S)}$, and related quantities provide additional targets with the same machinery, extending the testable set beyond ground-state ratios.","The predicted leptonic ratio $(R_\\tau^\\mu)^{B_c^*} = 0.883$, if correct, would make $B_c^* \\to \\tau\\nu$ strongly suppressed relative to $B_c \\to \\tau\\nu$, a testable signature at high-luminosity colliders."],"supporting_citations":[{"why":"Provides the RIQ-model form factors and rates for $B_c\\to\\eta_c, J/\\psi$ semileptonic decays used to construct $R_{\\eta_c/J/\\psi}$.","marker":"[38]"},{"why":"Supplies the lepton-mass-dependent rates for the exclusive semileptonic modes whose ratios constitute the new predictions.","marker":"[52]"},{"why":"Earlier RIQ-model lepton flavor universality analysis that this paper extends with new ratios.","marker":"[39]"},{"why":"Computes the decay constants $f_{B_c}$ and $f_{B_c^*}$ used in the leptonic ratios.","marker":"[62]"},{"why":"Lattice QCD prediction for $R(J/\\psi)$ used as the Standard Model benchmark for the semileptonic ratios.","marker":"[29]"},{"why":"LHCb measurement of $B_s\\to D_s^{(*)} \\mu\\nu$ ratios that motivated constructing analogous $B_c$ ratios.","marker":"[53]"},{"why":"Lattice QCD form factors for $B_c\\to J/\\psi$ over the full $q^2$ range, the comparison target for the model's overlap-integral form factors.","marker":"[31]"}],"fun_headline_variants":["B_c decay ratios: parameter-free predictions for LHCb","B_c tau/mu ratio: 246.77, no free parameters","Parameter-free B_c ratios: direct LHCb and FCC-ee targets","B_c ratios: tau/mu=246.77, D/D*=0.146","B_c decay ratios: no adjustable parameters, testable at colliders"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the RIQ model's overlap-integral form factors and decay constants, with parameters fixed only by hadron spectroscopy, are quantitatively reliable across the full $q^2$ range; for the $B_c^*$ leptonic ratio there is the additional unstated assumption that the formula behind 0.883 is the correct one.","fun_headline_variants_meta":{"raw":{"variants":["B_c decay ratios: parameter-free predictions for LHCb","B_c tau/mu ratio: 246.77, no free parameters","Parameter-free B_c ratios: direct LHCb and FCC-ee targets","B_c ratios: tau/mu=246.77, D/D*=0.146","B_c decay ratios: no adjustable parameters, testable at colliders"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000979,"raw_usage":{"total_tokens":4185,"prompt_tokens":998,"completion_tokens":3187,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":614,"completion_tokens_details":{"reasoning_tokens":3087}},"tokens_in":614,"tokens_out":3187,"duration_ms":19616,"temperature":1.0,"reasoning_tokens":3087,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T18:32:41.745509+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $B(B_c \\to \\tau\\nu)/B(B_c \\to \\mu\\nu)$ at LHCb or a future $Z$-factory: if the result is incompatible with 246.77 while the muon mode is observed, the leptonic prediction fails. A purely internal check is to re-derive $(R_\\tau^\\mu)^{B_c^*}$ from the paper's Eq. (5) with its stated decay constants; the standard helicity-suppressed formula with $f_{B_c^*} \\approx f_{B_c}$ gives a value of order 239, so 0.883 requires an explicit derivation that the paper does not supply.","supporting_citations":[{"cited_title":"Semileptonic $B_c$ meson decays to S-wave charmonium states","cited_arxiv_id":"1910.13206","evidence_quote":"Provides the RIQ-model form factors and rates for $B_c\\to\\eta_c, J/\\psi$ semileptonic decays used to construct $R_{\\eta_c/J/\\psi}$."},{"cited_title":"Lepton mass effects in exclusive semileptonic $B_c$-meson decays","cited_arxiv_id":"2106.09463","evidence_quote":"Supplies the lepton-mass-dependent rates for the exclusive semileptonic modes whose ratios constitute the new predictions."},{"cited_title":"A Light shed on Lepton Flavor Universality in B decays","cited_arxiv_id":"2211.04348","evidence_quote":"Earlier RIQ-model lepton flavor universality analysis that this paper extends with new ratios."},{"cited_title":"Purely leptonic decays of heavy-flavored charged mesons","cited_arxiv_id":"2312.06130","evidence_quote":"Computes the decay constants $f_{B_c}$ and $f_{B_c^*}$ used in the leptonic ratios."}],"review_version":1}