{"id":"d5b9c9a6-a6b5-42d2-82f9-733ff0389d82","arxiv_id":"2504.15056","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Branching fractions for B̄_s to charmed-strange mesons are predicted in the covariant light-front quark model; the s-wave rates match data, several p-wave channels look observable, and the D'_s1 rate overshoots experiment by about four times.","lead":"Using the covariant light-front quark model, the authors compute the form factors that control B̄_s decays into the charmed-strange mesons D_s, D*_s, D_s0, D_s1, D'_s1, and D_s2, and from them predict semileptonic and nonleptonic branching fractions. Several predicted p-wave channels are large enough to be searched for at LHCb or future e+e- colliders, and one predicted rate sits about four times above the measured value.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Untested zero-mixing assignment for D_s1(2460)/D_s1(2536) underlies the factor-of-four D'_s1 semileptonic excess; a mixing-angle scan is needed.","rationale":"The reader's weakest assumption identifies the same load-bearing concern: the zero-mixing heavy-quark-limit identification of the two axial-vector charm-strange mesons, Eq. (20). This is the most fragile step because the paper's most striking numerical result, the D'_{s1} semileptonic branching fraction that exceeds experiment by a factor of four, depends directly on it, and the authors flag the possibility of large mixing in Sect. III.C. The shared p-wave shape parameter beta is also a legitimate concern, but it affects all p-wave predictions globally rather than pinning down the single largest discrepancy. The paper otherwise has genuine strengths: it is a standard covariant LFQM application, all form-factor formulas are written out, the s-wave semileptonic rates agree with data, and the parameter count is modest. No fatal internal inconsistency was found. The reader's CONDITIONAL verdict remains appropriate; the condition should be a quantitative test of the mixing-angle and beta sensitivities before the D'_{s1} discrepancy is interpreted as a reason to remeasure. I therefore recommend no change to the reader's verdict.","tokens_in":19610,"tokens_out":4034,"duration_ms":37391,"concrete_test":"Recompute B(\\bar B_s\\to D_{s1}\\ell\\bar\\nu) and B(\\bar B_s\\to D'_{s1}\\ell\\bar\\nu) as functions of the axial-vector mixing angle \\theta, defining the physical states as superpositions of the P_1^{1/2} and P_1^{3/2} states used in Eq. (20). Use the present model's 3P1/1P1 form factors (or those of Ref. [2]) to build the mixed form factors, and scan \\theta over a physically motivated range, e.g., -30\\degree to +30\\degree, or use lattice/experimental constraints on the mixing angle. If no value of \\theta yields B(\\bar B_s\\to D'_{s1}\\mu\\bar\\nu) within 2\\sigma of (2.7\\pm0.7)\\times10^{-3} while keeping B(\\bar B_s\\to D_{s1}\\ell\\bar\\nu) consistent with existing limits, then the zero-mixing assumption is not the source of the discrepancy. If such a \\theta exists, the paper's headline claim requires a mixing-angle uncertainty band before the factor-of-four excess can be interpreted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's most notable number, B(\\bar B_s\\to D'_{s1}\\mu\\bar\\nu_\\mu)=11.1\\times10^{-3}, exceeds the measured (2.7\\pm0.7)\\times10^{-3} by a factor of four. This prediction rests on identifying the physical D_{s1}(2536) with the pure heavy-quark-limit eigenstate |P_1^{3/2}\\rangle and D_{s1}(2460) with |P_1^{1/2}\\rangle, Eq. (20). The authors themselves state in Sect. III.C that the charm quark is not heavy enough to guarantee this limit and that a relatively large mixing angle may exist. Under a nonzero mixing angle, the D_{s1} and D'_{s1} form factors are linear combinations of the P_1^{1/2} and P_1^{3/2} form factors, so the two semileptonic rates shift in opposite directions. Because no mixing-angle scan or uncertainty band is provided, the factor-of-four discrepancy cannot currently be attributed to new-physics-requiring physics, to an LFQM form-factor error, or to the assumed zero-mixing identification. This directly affects the paper's suggestion that the measurement should be repeated, making it the single most load-bearing unsecured premise. A secondary but related fragility is the single shared shape parameter \\beta=0.3483 GeV for all four p-wave mesons, Eq. (23), which the authors concede may be too small.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper computes the \\bar{B}_s \\to D_{sJ} transition form factors (D_{sJ} = D_s, D_s^*, D_{s0}, D_{s1}, D'_{s1}, D_{s2}) in the covariant light-front quark model. The two axial-vector mesons are identified with the heavy-quark-limit eigenstates via Eq. (20), form factors are fitted to the pole forms of Eqs. (24)-(25) with parameters in Table I, and the results are used to predict semileptonic (\\bar{B}_s \\to D_{sJ}\\ell\\bar{\\nu}) and nonleptonic (\\bar{B}_s \\to D_{sJ}\\pi/K) branching fractions under naive factorization. The s-wave semileptonic predictions agree with experiment (D_s\\mu\\bar{\\nu}: 2.66e-2 vs (2.31 +/- 0.21)e-2; D_s^*\\mu\\bar{\\nu}: 5.11e-2 vs (5.2 +/- 0.5)e-2). The p-wave predictions scatter widely relative to the literature; notably \\bar{B}_s \\to D'_{s1}\\mu\\bar{\\nu} = 11.1e-3 exceeds the measured (2.7 +/- 0.7)e-3 by a factor of four. The paper concludes that \\bar{B}_s \\to D_{sJ}\\pi with J = 0, 1', 2 have sizable branching fractions and are promising LHC targets. The authors explicitly flag in Sects. III.C and III.D the fragility of the p-wave assumptions: zero axial-vector mixing despite a charm quark that may not be heavy enough, a single shared shape parameter \\beta = 0.3483 GeV for all four p-wave mesons that may be too small, and naive factorization over-predicting the measured s-wave nonleptonic channels by factors of 1.6-2.2.","tokens_in":19786,"tokens_out":14938,"duration_ms":115216,"significance":"The s-wave sector is a genuine success: the two semileptonic rates agree with experiment without being fitted, establishing that the form-factor machinery and standard inputs (masses, V_cb, \\tau_{B_s}) are reliable at the 10-15% level. The analytic expressions in Appendix A and the explicit fit parameters in Table I make the calculation essentially reproducible, and the comparisons in Tables II and III are careful and extensive. The significance of the p-wave sector is conditional. If the mixing and shape-parameter assumptions survive scrutiny, the paper supplies a complete set of LFQM predictions for channels testable at LHCb, including several at the 10^-3 level and a fourfold tension with the measured \\bar{B}_s \\to D'_{s1}\\mu\\bar{\\nu} rate that would be phenomenologically notable. At present, however, that tension is not interpretable: because the physical axial-vector states are mixtures of the |P_1^{1/2}\\rangle and |P_1^{3/2}\\rangle states, a nonzero mixing angle shifts the D_{s1} and D'_{s1} rates in opposite directions, and no scan over the mixing angle is given.","major_comments":[{"comment":"The identification of D_{s1}(2460) as the pure heavy-quark-limit eigenstate |P_1^{1/2}\\rangle and D_{s1}(2536) as |P_1^{3/2}\\rangle is load-bearing for every axial-vector prediction, in particular for the fourfold excess of the predicted \\bar{B}_s \\to D'_{s1}\\mu\\bar{\\nu} rate (11.1e-3) over the measured (2.7 +/- 0.7)e-3. The authors themselves state in Sect. III.C that the charm quark mass is not large enough and that a relatively large mixing angle may exist. Under a nonzero mixing angle the D_{s1} and D'_{s1} form factors become linear combinations of the |P_1^{1/2}\\rangle and |P_1^{3/2}\\rangle form factors, and the two semileptonic rates move in opposite directions. As it stands, the reader cannot tell whether the factor-of-four discrepancy is an artifact of the zero-mixing ansatz, a form-factor error, or a real effect, so the suggestion in Sect. III.C that the measurement be repeated is premature. Please provide a scan of the D_{s1} and D'_{s1} semileptonic rates versus the mixing angle, state the mixing angle needed to reproduce the experimental rate, and propagate that scan into the affected entries of Table II.","section":"Section III.C, Eq. (20)"},{"comment":"All four p-wave mesons are assigned the single shape parameter \\beta = 0.3483 GeV, fixed through f_{D_{s0}} = 74.4 MeV taken from the quark-model paper Ref. [4]; no measured input anchors the p-wave \\beta. The authors concede in Sect. III.D that this value may be too small and that their p-wave nonleptonic rates are consequently underestimated. The effect is severe for D_{s1}: \\bar{B}_s \\to D_{s1}\\pi is predicted at 4.39e-6, up to about two orders of magnitude below the other predictions listed in Table III (Refs. [33, 34, 3]). Because the small D_{s1} form factors in Table I result from near-cancellations, they are maximally sensitive to \\beta. Please add a sensitivity study varying the p-wave shape parameter (uniformly, and per meson if possible), and quote how the p-wave entries in Tables II and III change under that variation.","section":"Section III.A, Eq. (23), and Section III.D"},{"comment":"The headline claim that \\bar{B}_s \\to D_{sJ}\\pi with J = 0, 1', 2 are promising candidates for observation rests on naive factorization with a_1 = 1.02. The same framework over-predicts the measured s-wave channels by factors of about 1.6 (\\bar{B}_s \\to D_s\\pi: 4.62e-3 vs (2.98 +/- 0.14)e-3) and about 2.2 (\\bar{B}_s \\to D_s^*\\pi: 4.12e-3 vs (1.9^{+0.5}_{-0.4})e-3), as the authors acknowledge in the text. This implies an unquantified normalization uncertainty of order a factor of two that propagates directly into the absolute scale of the p-wave nonleptonic predictions on which the paper's conclusion rests. Please state an uncertainty on the nonleptonic predictions, for example by varying a_1 over a plausible range or by showing the sensitivity to the 1/N_c-suppressed amplitudes, and temper the corresponding conclusions accordingly.","section":"Section III.D, Eqs. (36)-(40)"}],"minor_comments":[{"comment":"Ref. [42] is listed as E. V. Linder, New Astron. Rev. 49, 93 (2005), arXiv:astro-ph/0404032, which is an astronomy/dark-energy review rather than a source for the \\bar{B}_s \\to D'_{s1} semileptonic prediction (0.8-1.0e-3) attributed to it in Table II. Please verify and replace this citation.","section":"Reference list, Ref. [42]"},{"comment":"All entries in Tables II and III are quoted without uncertainties. Once the mixing-angle scan and \\beta-sensitivity study requested above are performed, please propagate those uncertainties into the tabulated values so that the comparisons with experiment, in particular the D'_{s1} semileptonic channel, can be judged quantitatively.","section":"Tables II and III"},{"comment":"The concluding sentence repeats the abstract's claim that some branching fractions are sizable and promising without the caveats on axial-vector mixing and on naive factorization that are stated in Sects. III.C and III.D. I suggest carrying those caveats into the abstract and conclusions, since the size of the p-wave rates is sensitive to both assumptions.","section":"Abstract and Conclusions"}],"recommendation":"major_revision","confidential_remarks":"The s-wave semileptonic results are solid, and the manuscript fits the scope of a QCD-phenomenology journal. The p-wave content, however, is largely a spectator-strange extension of the classic Cheng-Chua-Hwang analysis (Ref. [2]) with updated inputs, so the incremental novelty is moderate. I also recommend checking the reference list: Ref. [42] appears to cite an astronomy paper. My recommendation of major revision is driven by the unquantified axial-mixing and shared-\\beta assumptions, which the authors themselves flag as fragile; these are addressable with additional analysis within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a competent, fully-written-out LFQM computation of the B̄s→DsJ form factors and branching fractions for all six final states, with the two measured s-wave semileptonic modes reproduced nicely. The notable p-wave numbers, especially the 11.1×10⁻³ for B̄s→D′s1 μν̄ that is four times the measured value, rest on assumptions the authors themselves flag, and there are no uncertainties anywhere. Worth a serious referee, but the referee should push for a mixing-angle scan and error bars.\n\nWhat is new: not a huge amount—the channels have been computed before (Refs. [3,6,33,34,39,40,41,43] and others). The contribution is a covariant LFQM re-derivation with the full analytic form factors in the appendix, and a clean internal benchmark: B̄s→Ds μν̄ gives 2.66×10⁻² vs (2.31±0.21)×10⁻², and D∗s gives 5.11×10⁻² vs (5.2±0.5)×10⁻². That anchors the s-wave machinery. The form factors are also close to the B→DJ results from Cheng-Chua-Hwang, which is reassuring.\n\nSoft spots:\n- The factor-of-four D′s1 semileptonic excess is the paper's most interesting number, and it depends on Eq. (20): Ds1(2460) and Ds1(2536) treated as pure |P¹ᐟ²₁⟩ and |P³ᐟ²₁⟩. The authors concede the charm quark isn't heavy enough. Without a mixing-angle scan, you can't tell whether the discrepancy is real physics or just the eigenstate assumption. That's load-bearing.\n- All four p-wave mesons share β=0.3483 GeV, which the authors say may be too small. Every p-wave form factor inherits this number. Some nonleptonic p-wave modes come out below other predictions, and they say it's likely this beta.\n- No uncertainties in any table. The D′s1 discrepancy is quoted as a factor of four against (2.7±0.7)×10⁻³, but you can't assess significance without error bars on their numbers.\n- The nonleptonic s-wave rates overshoot data by ~50%; they blame naive factorization. That means the headline pionic p-wave rates are order-of-magnitude estimates.\n- Minor: Ref. [42] is a dark-energy review by Linder, cited for a B̄s→Ds0 branching fraction—clearly a citation mistake. Also they don't comment on the fifteenfold disagreement with Ref. [6] for B̄s→Ds1 eν̄e.\n\nNone of this is fatal to the core calculation. The s-wave semileptonic claim holds up, and the paper is honest about its own weaknesses.\n\nFor whom: heavy-flavor phenomenologists who want a self-consistent LFQM set of B̄s→DsJ predictions, and people planning LHCb searches for the pionic modes. It deserves peer review; I'd send it out with a request for a mixing-angle scan, uncertainties, and a corrected reference list.","headline":"Competent LFQM re-derivation of B̄s→DsJ rates, anchored by the s-wave semileptonic data, but the interesting p-wave numbers—especially the factor-of-four D′s1 excess—rest on an untested mixing assumption and a single shared beta, with no error bars.","tokens_in":20619,"tokens_out":3468,"would_cite":true,"duration_ms":29110,"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":"The paper argues that covariant light-front quark-model form factors predict sizable $\\bar{B}_s\\to D_{sJ}\\pi$ branching fractions for $J=0,1',2$, and semileptonic rates that match the measured $D_s$ and $D_s^*$ channels.","keywords":["B_s meson decays","D_sJ mesons","covariant light-front quark model","transition form factors","semileptonic decays","nonleptonic decays","axial-vector meson mixing","branching fractions"],"falsifier":"Measure $\\mathcal{B}(\\bar{B}_s\\to D'_{s1}\\mu\\bar{\\nu}_\\mu)$ and $\\mathcal{B}(\\bar{B}_s\\to D_{s1}\\mu\\bar{\\nu}_\\mu)$ at the LHC or a future $e^+e^-$ collider. If the $D'_{s1}$ rate stays near the current $(2.7\\pm0.7)\\times10^{-3}$ while $D_{s1}$ comes out near the paper's $2.67\\times10^{-3}$, the pure-eigenstate identification of the axial-vector mesons is ruled out; a recomputation with a nonzero $^3P_1$-$^1P_1$ mixing angle fitted to both channels would then settle which form factors are correct.","tokens_in":19161,"feed_emoji":"⚛️","tokens_out":8875,"duration_ms":75538,"temperature":0.7,"pith_summary":"The paper aims to show that the covariant light-front quark model can compute the full set of $\\bar{B}_s\\to D_{sJ}$ transition form factors, for $D_{sJ}=D_s,D_s^*,D_{s0},D_{s1},D'_{s1},D_{s2}$, and that the resulting semileptonic and nonleptonic branching fractions are reliable enough to guide searches. The s-wave semileptonic predictions match the measured $\\bar{B}_s\\to D_s\\mu\\bar{\\nu}_\\mu$ and $\\bar{B}_s\\to D_s^*\\mu\\bar{\\nu}_\\mu$ rates, while the p-wave pionic channels $\\bar{B}_s\\to D_{sJ}\\pi$ with $J=0,1',2$ come out near $10^{-3}$, which the authors argue puts them within reach of the LHC and future $e^+e^-$ colliders. The most striking number is $\\mathcal{B}(\\bar{B}_s\\to D'_{s1}\\mu\\bar{\\nu}_\\mu)=11.1\\times10^{-3}$, about four times the measured value, a discrepancy the paper attributes to the need for a remeasurement rather than to a failure of the model. If these predictions hold, the decays become a useful laboratory for non-perturbative QCD and for the internal structure of the $D_{sJ}$ states.","feed_headline":"B_s to D_sJ pionic decays predicted within LHC reach","feed_subtitle":"The pionic channels with J=0,1',2 land near 10^-3, and the semileptonic D_s and D_s* rates match experiment.","key_machinery":"The engine of the calculation is the covariant light-front quark model, in which a meson is described by a momentum-space Gaussian wave function whose width (shape parameter $\\beta$) is fixed by fitting the meson decay constant; the relativistic spin structure is handled through the Melosh rotation, which keeps the wave functions Lorentz invariant. The paper uses $f_{\\bar{B}_s}=230.3$ MeV, $f_{D_s}=249.9$ MeV, $f_{D_s^*}=272$ MeV, and $f_{D_{s0}}=74.4$ MeV to obtain $\\beta_{\\bar{B}_s}=0.6209$ GeV and a shared $\\beta=0.3483$ GeV for all four p-wave mesons. The transition matrix elements are reduced to form factors parametrized by the fitted forms of Eq. (24) or Eq. (25). For the two axial-vector mesons, the paper imposes the heavy-quark-limit identification of Eq. (20), treating $D_{s1}$ as the $j^P=1/2^+$ state and $D'_{s1}$ as the $3/2^+$ state, with the $^3P_1$-$^1P_1$ mixing angles fixed at their heavy-quark-limit values. That identification, together with the shared p-wave $\\beta$, carries the p-wave predictions.","core_discovery":"Within the covariant light-front quark model, the paper derives form factors for all six $\\bar{B}_s\\to D_{sJ}$ transitions from a single set of constituent quark masses and Gaussian wave functions, fixes each meson's shape parameter from its decay constant, and then feeds the form factors into semileptonic and factorized nonleptonic decay amplitudes. The central quantitative claims are that the s-wave semileptonic rates $\\mathcal{B}(\\bar{B}_s\\to D_s\\mu\\bar{\\nu}_\\mu)=2.66\\times10^{-2}$ and $\\mathcal{B}(\\bar{B}_s\\to D_s^*\\mu\\bar{\\nu}_\\mu)=5.11\\times10^{-2}$ agree with the measured central values, that the pionic modes $\\bar{B}_s\\to D_{sJ}\\pi$ with $J=0,1',2$ have branching fractions around $10^{-3}$ and should be observable, and that $\\bar{B}_s\\to D'_{s1}\\mu\\bar{\\nu}_\\mu$ is predicted at $11.1\\times10^{-3}$, far above the current experimental $(2.7\\pm0.7)\\times10^{-3}$. The paper treats the axial-vector states $D_{s1}(2460)$ and $D_{s1}(2536)$ as pure heavy-quark-limit eigenstates $|P_1^{1/2}\\rangle$ and $|P_1^{3/2}\\rangle$, respectively, and notes that this approximation is the most likely source of error for the $D'_{s1}$ channel.","pith_inferences":["The paper leaves implicit that a nonzero $^3P_1$-$^1P_1$ mixing angle would shift both the $D_{s1}$ and $D'_{s1}$ form factors; fitting that angle to the two measured semileptonic channels is a direct extension that could resolve the $D'_{s1}$ discrepancy.","Because a single shared $\\beta=0.3483$ GeV is imposed on all four p-wave mesons, the paper's underpredicted nonleptonic $D_{s1}\\pi$ rate could be tested by refitting $\\beta$ separately for each p-wave meson to its own decay constant.","If the $D'_{s1}$ semileptonic discrepancy survives remeasurement, comparing the muon and tau modes of the same transition would help separate form-factor effects from possible new physics, though the paper does not explore that comparison.","The same form factors can be recycled directly for other $b\\to c\\ell\\bar{\\nu}$ transitions in heavy-light systems, so the method's reliability is testable across a broader set of decays beyond $\\bar{B}_s\\to D_{sJ}$."],"forward_implications":["The s-wave semileptonic channels $\\bar{B}_s\\to D_s\\mu\\bar{\\nu}_\\mu$ and $\\bar{B}_s\\to D_s^*\\mu\\bar{\\nu}_\\mu$ are predicted at $2.66\\times10^{-2}$ and $5.11\\times10^{-2}$, matching the measured values.","The pionic nonleptonic modes $\\bar{B}_s\\to D_{sJ}\\pi$ with $J=0,1',2$ have branching fractions near $10^{-3}$, making them promising for observation at the LHC and future $e^+e^-$ colliders.","The prediction $\\mathcal{B}(\\bar{B}_s\\to D'_{s1}\\mu\\bar{\\nu}_\\mu)=11.1\\times10^{-3}$ exceeds the measured $(2.7\\pm0.7)\\times10^{-3}$, which the paper argues warrants repeating the measurement.","The p-wave form factors come out close to the corresponding $B\\to D_J$ form factors in the heavy-quark limit, supporting the underlying spectator-quark picture.","For the four measured s-wave nonleptonic channels $\\bar{B}_s\\to D_s^{(*)+}\\pi^-/K^-$, the predictions overshoot the data, which the paper interprets as a sign of deviation from naive factorization."],"supporting_citations":[{"why":"Supplies the covariant light-front formalism, zero-mode treatment, and Gaussian wave functions on which all form-factor calculations rest.","marker":"[1]"},{"why":"Provides the $B\\to D_J$ form factors and the heavy-quark-limit axial-vector mixing angles that the paper adopts and compares against.","marker":"[2]"},{"why":"Offers comparison predictions for $\\bar{B}_s\\to D_{s1}\\ell\\bar{\\nu}$ and nonleptonic rates that the paper uses to benchmark its p-wave results.","marker":"[3]"},{"why":"Is the source of $f_{D_s^*}$ and $f_{D_{s0}}$ used to fix the shape parameters of the vector and p-wave mesons.","marker":"[4]"},{"why":"Supplies the tensor-meson form-factor formalism and inputs used for the $D_{s2}$ channels.","marker":"[5]"},{"why":"Provides the meson masses, $\\bar{B}_s$ lifetime, CKM input, and experimental branching fractions used as inputs and as comparison data.","marker":"[29]"},{"why":"Supplies $f_{\\bar{B}_s}=230.3$ MeV, which fixes the $\\bar{B}_s$ shape parameter.","marker":"[30]"},{"why":"Provides comparison semileptonic and pionic branching fractions, including a close prediction for the $D'_{s1}$ semileptonic rate.","marker":"[34]"}],"fun_headline_variants":["Pionic B_s decays to D_sJ predicted at LHC reach","B_s to D_sJ pionic branching fractions near 10^-3","Light-front model yields LHC-accessible B_s to D_sJ rates","New predictions for B_s to D_sJ pionic and semileptonic decays","Pionic D_sJ channels from B_s decays predicted observable"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the two axial-vector mesons are exactly the unmixed heavy-quark-limit states $|P_1^{1/2}\\rangle$ and $|P_1^{3/2}\\rangle$, with no $^3P_1$-$^1P_1$ mixing; the paper itself concedes that the charm quark may not be heavy enough for this to hold.","fun_headline_variants_meta":{"raw":{"variants":["Pionic B_s decays to D_sJ predicted at LHC reach","B_s to D_sJ pionic branching fractions near 10^-3","Light-front model yields LHC-accessible B_s to D_sJ rates","New predictions for B_s to D_sJ pionic and semileptonic decays","Pionic D_sJ channels from B_s decays predicted observable"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001109,"raw_usage":{"total_tokens":4668,"prompt_tokens":1037,"completion_tokens":3631,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":653,"completion_tokens_details":{"reasoning_tokens":3532}},"tokens_in":653,"tokens_out":3631,"duration_ms":20280,"temperature":1.0,"reasoning_tokens":3532,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T11:36:21.259236+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $\\mathcal{B}(\\bar{B}_s\\to D'_{s1}\\mu\\bar{\\nu}_\\mu)$ and $\\mathcal{B}(\\bar{B}_s\\to D_{s1}\\mu\\bar{\\nu}_\\mu)$ at the LHC or a future $e^+e^-$ collider. If the $D'_{s1}$ rate stays near the current $(2.7\\pm0.7)\\times10^{-3}$ while $D_{s1}$ comes out near the paper's $2.67\\times10^{-3}$, the pure-eigenstate identification of the axial-vector mesons is ruled out; a recomputation with a nonzero $^3P_1$-$^1P_1$ mixing angle fitted to both channels would then settle which form factors are correct.","supporting_citations":[{"cited_title":"(6) The explicit form of h′ P is given by h′ P =(M ′2 − M ′2 0) √ x1x2 Nc 1√ 2~M ′ 0 ϕ′, (7) where ϕ′ is the light-front momentum distribution amplitude for an s-wave mes on","cited_arxiv_id":null,"evidence_quote":"Supplies the covariant light-front formalism, zero-mode treatment, and Gaussian wave functions on which all form-factor calculations rest."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the $B\\to D_J$ form factors and the heavy-quark-limit axial-vector mixing angles that the paper adopts and compares against."},{"cited_title":"(9) The explicit forms of h′ M and ω′ M can be found in Appendix A","cited_arxiv_id":null,"evidence_quote":"Offers comparison predictions for $\\bar{B}_s\\to D_{s1}\\ell\\bar{\\nu}$ and nonleptonic rates that the paper uses to benchmark its p-wave results."},{"cited_title":"(19) In the above equation, ˆN ′(′′) 1 = x1(M ′(′′)2 − M ′(′′)2 0 ), and h′(′′) P can be found in Eq","cited_arxiv_id":null,"evidence_quote":"Is the source of $f_{D_s^*}$ and $f_{D_{s0}}$ used to fix the shape parameters of the vector and p-wave mesons."},{"cited_title":"0 × 10−2[35], 2","cited_arxiv_id":null,"evidence_quote":"Supplies the tensor-meson form-factor formalism and inputs used for the $D_{s2}$ channels."}],"review_version":1}