{"id":"ea9967ab-1780-480d-a87b-425a10a2a1f6","arxiv_id":"2608.12182","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":10,"one_line_summary":"A revised light-cone sum rule calculation yields g_{D*D*pi}=5.71 GeV^-1 and g_{B*B*pi}=4.90 GeV^-1, with a static coupling ĝ=0.30±0.04.","lead":"This paper recalculates the strong couplings of heavy vector mesons to pions using light-cone sum rules, adding next-to-leading-order perturbative corrections and higher-twist effects. If correct, the new values sharpen inputs for models of exotic hadron molecules and for predictions of rare B* and D* decays.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The quoted couplings rest on the dimensionally inconsistent printed higher-twist sum rules (Eqs. 53 and 59) and so cannot be reproduced or verified as written.","rationale":"The paper is a serious LCSR calculation and the non-trivial NLO factorized kernel, the explicit continuum subtraction, and the transparent error budget deserve credit. The strongest prediction, however, is quantitative, and the printed equations feeding the numerics contain an internal dimensional inconsistency that the text does not mention. The reader's weakest_assumption focused on the two-dimensional duality-region shape, which the paper itself acknowledges and tabulates; I see that as a moderate, already-quantified systematic. The dimensional issue in Eqs. (53) and (59) is more directly load-bearing because it affects the twist-3 and twist-4 contributions used to produce the central values, and it is not flagged. I stress that this may be a typesetting or notational omission rather than a physics error; that is why the appropriate verdict remains conditional rather than reject or unverified. The concrete check above would settle it: an independent reduction of Eq. (48) through Eq. (51), or a comparison with the corresponding formula in Ref. [33], will show whether the missing factors exist. Until then, the quoted couplings and \\hat g should not be used as quantitative inputs. This agrees partially with the reader, whose rationale already noted the dimension mismatch but whose headline concern was the duality shape.","tokens_in":19695,"tokens_out":13319,"duration_ms":124723,"concrete_test":"Re-derive F_2P_NLP by applying the double spectral transform (51) and double Borel transform to Eq. (48), keeping all M^2, m_Q^2, and μπ factors explicit, and check whether Eq. (53) follows with every term of dimension GeV^2. Independently, take the m_Q → ∞ limit of Eq. (55) using Eq. (58) and compare term-by-term dimensions with Eq. (59). If a factor such as M^4 or 1/τ is missing, recompute Table II and the couplings; the twist-3 LO row (0.089 GeV for D*) will change by an O(1) amount and Eqs. (57) and (61) must be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central values depend on the sum rule (55), where all F terms must share the dimension GeV^2 fixed by F_LP in Eq. (44). In Eq. (53), φ4(u) is dimension GeV^2 because δ2π has GeV^2 (Eq. A9), so the first term is GeV^2; the second term, 1/(3mQ μπ) φσ3(1/2), is GeV^-2 because mQ μπ has dimension GeV^2 and φσ3 is dimensionless. These terms cannot be added. Eq. (59) has a related problem: with the scaling f_H* = \\hat f sqrt(mQ) in Eq. (58), fπ^2/\\hat f^2 has dimension GeV, the bracket terms have dimension GeV (or mixed if φ4 is taken dimensionless), and the prefactor 2/fπ leaves a result of dimension GeV, whereas g_H*H*π must be GeV^-1 and \\hat g is dimensionless. Unless factors of M^2, m_Q^2, or τ are missing, the numerical predictions 5.71, 4.90, and \\hat g=0.30 are not supported by the printed formulas. This is more load-bearing than the duality-shape uncertainty: the shape variation is tabulated in Table III and shows few-percent effects, whereas the twist-3 LO term is about 40% of the twist-2 LO contribution, so a missing dimensional factor would shift the central couplings beyond the quoted errors. The manuscript does not flag these dimensional inconsistencies.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper revisits the light-cone sum rule (LCSR) calculation of the strong couplings g_{D*D*π} and g_{B*B*π}. It derives the hard-collinear factorization of the relevant correlation function at leading power through next-to-leading order in α_s, includes next-to-leading-power higher-twist contributions from two- and three-particle pion distribution amplitudes up to twist-4, matches the QCD-level double spectral representation to the hadronic dispersion relation, and performs a numerical analysis with Borel, threshold, factorization-scale, and duality-region-shape uncertainties. The quoted results are g_{D*D*π}=5.71^{+0.67}_{-0.53} GeV^{-1}, g_{B*B*π}=4.90^{+0.57}_{-0.44} GeV^{-1}, and a static coupling ĝ=0.30±0.04 extracted by fitting 1/m_H corrections. The manuscript also compares these values with previous LCSR, QCD sum rule, lattice, and experimental determinations.","tokens_in":20107,"tokens_out":13063,"duration_ms":127499,"significance":"If the calculation is correct, this would be one of the most complete LCSR determinations of the H*H*π couplings, with a documented error budget covering scale, Borel, threshold, and duality-shape systematics. The explicit NLO hard-collinear kernel, the treatment of the two-dimensional quark-hadron duality region, and the breakdown of twist contributions are valuable and potentially useful for applications to hadronic molecules and heavy-meson weak decays. The paper also honestly states its main truncations (asymptotic DA in the NLO density, omission of twist-3 NLO corrections). However, the claimed numerical predictions cannot be verified from the printed formulas because the higher-twist sum rules contain dimensionally inconsistent terms, and the static-limit expression used for the ĝ extraction has the same problem. The manuscript is therefore not yet in a publishable form.","major_comments":[{"comment":"The twist-3 term in Eq. (53) is dimensionally inconsistent and cannot be added to the other terms. With φ4(u) carrying dimension GeV² from Eq. (A9), the first term in Eq. (53) has dimension GeV². In the second term, however, φσ3 is dimensionless and 1/(3 m_Q μπ) has dimension GeV^{-2}, so the term has dimension GeV^{-2}. The same inconsistency appears in the integrand of Eq. (48), where the two terms inside the parentheses do not share a common dimension. Since Eq. (53) enters the central sum rule Eq. (55), and Table II assigns the twist-3 LO piece about 40% of the twist-2 LO value, the numerical results in Eq. (57) are not reproducible from the formulas as printed. Please correct the factors of m_Q and μπ (or supply the missing dimensionful prefactors) and recompute the numerical tables and central values.","section":"Section V, Eqs. (48) and (53)"},{"comment":"The static-limit expression in Eq. (59) has a dimension problem. Using f_H* = \\hat f sqrt(m_Q), the factor fπ²/\\hat f² has dimension GeV, the parenthesized sum has dimension GeV, and the outer bracket therefore has dimension GeV². Multiplied by the prefactor 2/fπ, the right-hand side has dimension GeV, whereas the left-hand side g_{H*H*π} should have dimension GeV^{-1}. The text further states that the bracket is exactly the dimensionless static coupling ĝ, which is also dimensionally impossible. Either the left-hand side should carry a factor f_{H*}^2, or a compensating power of m_Q (or τ) is missing. This undercuts the claimed analytic verification of HQSS and the extraction of ĝ=0.30±0.04 in Eq. (61), and it must be repaired before the numerical result can be trusted.","section":"Section VI, Eq. (59)"},{"comment":"The extraction of the static coupling ĝ is not an independent determination. Two of the four inputs to the fit in Eq. (60) are the values g_{D*Dπ}=14.1 and g_{B*Bπ}=30.0 taken from Ref. [33], and Eq. (59) is explicitly stated to be structurally identical to Eq. (5.10) of the same reference. The resulting ĝ=0.30±0.04 therefore largely re-states the earlier framework, so the comparison with LQCD and experiment in Table V should be framed accordingly. Please show what the fit gives when the Ref. [33] inputs are removed, or otherwise quantify how much of the final ĝ is contributed by the new finite-mass LCSR results.","section":"Section VI, Eqs. (60)-(62)"}],"minor_comments":[{"comment":"The sentence 'The duality region possesses a smooth border crossing across the diagonals 1 = s_2' should read 'across the diagonal s1 = s2'.","section":"Section IV, text after Eq. (43)"},{"comment":"The first relation in Eq. (60), g_{H*Hπ} = (2 m_H ĝ)/fπ (1+δ1/m_H), is dimensionless if ĝ is dimensionless, while the couplings quoted in Table V are given in GeV^{-1}. Please clarify the convention used for g_{H*Hπ} and g_{H*H*π} in these relations, or add the explicit factor that restores the correct mass dimension.","section":"Section VI, Eq. (60)"},{"comment":"In the definition of Model II, the phrase 'its second momenta2 is adopted' should read 'its second Gegenbauer moment a2 is adopted'.","section":"Section VI, Model for the pion DA"},{"comment":"The entry for LCSR [33], g_{D*D*π}=7.27 GeV^{-1}, is derived from g_{H*Hπ}/\\sqrt{m_{H*}m_H}; this should be stated directly in the table or its caption to avoid confusion with the directly computed couplings.","section":"Table V"}],"recommendation":"major_revision","confidential_remarks":"The dimensional inconsistencies in Eqs. (48), (53), and (59) are the main barrier to publication. If the authors can supply corrected expressions and recomputed numbers, the paper may be suitable for a revised submission; without such corrections, the central predictions should not be cited. The limited independence of the ĝ extraction from Ref. [33] should also be addressed explicitly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a genuine step forward in the LCSR program for the H*H*pi couplings. The NLO hard-collinear kernel, the NLO double spectral density, and the systematic twist-3/4 treatment are new relative to the earlier LO work, and the paper is honest about its error budget and its remaining truncations. The scale-independence check at O(alpha_s) is a real plus. That alone earns referee time.\n\nThe load-bearing problem is dimensional. In Eq. (53), F_NLP^2P adds (1/4)(1+m_Q^2/M^2) phi_4(1/2), which is GeV^2 because delta_2pi has GeV^2, to -1/(3 m_Q mu_pi) phi_sigma_3(1/2), which is GeV^-2. Those cannot be added. In Eq. (59), the bracket is claimed to equal the dimensionless static coupling, but with f_H* = \\hat f sqrt(m_Q) the prefactor f_pi^2/\\hat f^2 is GeV, the bracket is GeV, and the overall 2/f_pi makes the result GeV, not GeV^-1. The twist-3 term is not a small correction: Table II shows it is about 40% of the twist-2 LO piece. So the printed equations do not support the quoted 5.71, 4.90, or \\hat g = 0.30. The paper does not flag these inconsistencies.\n\nThere are softer issues too. The reduction from Eq. (39) to Eq. (41) is a black box; the NLO density uses only the asymptotic DA; and the static-coupling fit draws two of its four inputs from Ref. [33], so \\hat g = 0.30 partly restates that framework. The duality-region shape uncertainty, by contrast, is handled well and is minor.\n\nIf the dimensional slips are corrected and the intermediate algebra is supplied, ideally with a code or notebook, this could become a solid citable paper. As it stands, I would not use the central values quantitatively, and any referee should require the corrected formulas and a reproducibility check before the numbers enter phenomenology.\n\nMy recommendation: do not desk-reject, but send to a serious referee with a request for major revision focused on the dimensional consistency of Eqs. (48), (53), and (59), and on showing the reduction of the NLO double spectral density.","headline":"Real LCSR upgrade, but the printed sum rules mix GeV^2 with GeV^-2 (Eq. 53) and give the static coupling the wrong dimension (Eq. 59); the central values are unsupported as written.","tokens_in":20652,"tokens_out":7793,"would_cite":false,"duration_ms":72911,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.38.-t","12.39.Hg"],"model":"deepseek-v4-flash","headline":"The paper's upgraded light-cone sum rule predicts the strong couplings $g_{D^*D^*\\pi}=5.71^{+0.67}_{-0.53}\\,\\text{GeV}^{-1}$ and $g_{B^*B^*\\pi}=4.90^{+0.57}_{-0.44}\\,\\text{GeV}^{-1}$, and a separated static coupling $\\hat{g}=0.30\\pm0.04$.","keywords":["light-cone sum rules","strong coupling constants","D*D*π coupling","B*B*π coupling","heavy quark spin symmetry","pion light-cone distribution amplitudes","hard-collinear factorization","higher-twist corrections"],"falsifier":"Vary the duality boundary shape parameter $\\alpha$ beyond the three values ($1/2,1,2$) the paper already scans, or evaluate the double dispersion integral with the alternative pole-resolving technique it cites: the off-diagonal NLO density changes by several percent under the existing scans, so a wider scan that moves $g_{D^*D^*\\pi}$ or $g_{B^*B^*\\pi}$ by more than the quoted $\\pm0.5$ to $\\pm0.7\\,\\text{GeV}^{-1}$ would falsify the duality ansatz. Independently, a lattice determination of the static coupling that separates $1/m_Q$ corrections by the same convention and returns $\\hat{g}$ above about $0.4$ would contradict the paper's central claim that the gap to experiment is heavy quark spin symmetry breaking rather than a defect of the sum rule.","tokens_in":19435,"feed_emoji":"⚛️","tokens_out":13533,"duration_ms":113712,"temperature":0.7,"pith_summary":"This paper sets out to determine the strong couplings $g_{D^*D^*\\pi}$ and $g_{B^*B^*\\pi}$ — the vertices that control how a pion interacts with a pair of heavy vector mesons — from light-cone sum rules, going beyond earlier leading-order treatments. The upgrade works on two fronts: the leading-power part of the correlation function is factorized through next-to-leading order in $\\alpha_s$, and the next-to-leading-power part is included at leading order by evaluating two- and three-particle pion distribution amplitudes up to twist-4. The paper obtains $g_{D^*D^*\\pi}=5.71^{+0.67}_{-0.53}\\,\\text{GeV}^{-1}$ and $g_{B^*B^*\\pi}=4.90^{+0.57}_{-0.44}\\,\\text{GeV}^{-1}$. Parametrizing the $1/m_H$ corrections and combining with the companion $H^*H\\pi$ couplings, it extracts the universal static coupling $\\hat{g}=0.30\\pm0.04$, which sits below lattice and experimental values because those extraction routes absorb positive heavy-quark mass corrections. If the calculation is right, these are the most complete light-cone sum rule values to date for couplings that feed the one-pion-exchange potentials of the $Z_c(4020)$ and $Z_b(10650)$ exotic candidates and the $H^*\\to\\pi$ transition form factors needed for rare weak decays of heavy vector mesons.","feed_headline":"Sum rules yield D*D*π and B*B*π couplings of 5.71 and 4.90","feed_subtitle":"The next-to-leading-order and higher-twist calculation also isolates the static coupling ĝ = 0.30, below lattice and experiment.","key_machinery":"The load-bearing object is the vacuum-to-pion correlation function $\\Pi_{\\mu\\nu}(p,q)$ of two local heavy-vector interpolating currents, whose hadronic double dispersion relation has a pole term proportional to $g_{H^*H^*\\pi}f_{H^*}^2$. The argument is carried by three pieces of machinery: the hard-collinear factorization formula at leading power, whose one-loop hard kernel $H^{(1)}_1$ is obtained by subtracting the operator renormalization factors (including the evanescent operator mixing $Z_{E1}$) from the bare QCD amplitude; the NLO double spectral density $\\rho^{(1)}(r,\\sigma)$, rewritten in variables $r=(\\hat{s}_2-1)/(\\hat{s}_1-1)$, $\\sigma=\\hat{s}_1+\\hat{s}_2-2$, where a localized $\\delta(r-1)$ term and a continuous logarithmic term of opposite signs make the result sensitive to the shape of the two-dimensional quark-hadron duality region $(s_1/s_*)^\\alpha+(s_2/s_*)^\\alpha\\le 1$ (the triangle, $\\alpha=1$, chosen as default); and the light-cone expansion of the heavy-quark propagator in a background gluon field, which generates the two- and three-particle higher-twist contributions. The final sum rule combines these into an expression for $g_{H^*H^*\\pi}f_{H^*}^2$ whose static limit reproduces the $H^*H\\pi$ sum rule, thereby verifying heavy quark spin symmetry.","core_discovery":"The central claim is that the $H^*H^*\\pi$ strong coupling can be extracted from a correlation function of two heavy-vector currents in a pion state once two systematic improvements are made: a hard-collinear factorization formula at leading power carried to next-to-leading order in $\\alpha_s$, with the one-loop hard-matching kernel computed and its scale dependence shown to cancel against the pion distribution amplitude; and next-to-leading-power contributions evaluated at leading order from two- and three-particle pion distribution amplitudes up to twist-4. After matching the QCD spectral representation to the hadronic double dispersion relation and performing a double Borel transformation, the paper predicts $g_{D^*D^*\\pi}=5.71^{+0.67}_{-0.53}\\,\\text{GeV}^{-1}$ and $g_{B^*B^*\\pi}=4.90^{+0.57}_{-0.44}\\,\\text{GeV}^{-1}$, with a dominant twist-2 leading-order term, a twist-3 correction around 40% of it, a negligible twist-4 term, and next-to-leading-order corrections near 10% that carry opposite signs in the charm and bottom channels. The paper further claims that heavy quark spin symmetry breaking can be isolated by parametrizing the $1/m_H$ corrections, yielding the static coupling $\\hat{g}=0.30\\pm0.04$ with correction parameters $\\delta_1=1.24\\pm0.55$ GeV and $\\delta_2=0.46\\pm0.43$ GeV, and that the systematically larger lattice and experimental values of $\\hat{g}$ are explained by those extractions absorbing the positive power corrections.","pith_inferences":["Because $\\hat{g}$ and the correction parameters $\\delta_i$ are strongly anti-correlated in the combined fit, adding an external constraint on any one of them — for instance a lattice value of the static coupling — would shrink the error ellipsoid substantially without any new sum-rule input; the paper does not perform this exercise.","The opposite signs of the NLO corrections in the charm and bottom channels arise from a delicate balance between the localized and continuous parts of the NLO spectral density at the chosen central scales; evaluating both channels at a common scale (say $\\mu=m_c$) would show whether the sign difference is a physical mass effect or an artifact of scale choice.","The duality-shape sensitivity lives entirely in the off-diagonal NLO density, so adopting the alternative systematic treatment of double dispersion integrals cited in the paper would provide a direct, independent cross-check of the dominant systematic uncertainty.","A lattice calculation of the $H^*H^*\\pi$ vertex at unphysical kinematics with controlled extrapolation, rather than of the static coupling alone, would test the paper's central values without relying on the intermediate $1/m_H$ parametrization whose parameters are so strongly correlated."],"forward_implications":["In the strict heavy-quark limit the new sum rule reduces analytically to the same static expression as the $H^*H\\pi$ coupling, so the framework self-consistently verifies heavy quark spin symmetry; the finite-mass deviations are then attributed to $1/m_H$ breaking rather than to a defect of the method.","The extracted $\\hat{g}=0.30\\pm0.04$ is systematically below lattice and experimental extractions, which the paper attributes to those extractions absorbing positive $1/m_Q$ corrections; the gap is therefore presented as a measure of heavy quark spin symmetry breaking rather than a contradiction.","The improved $g_{D^*D^*\\pi}$ and $g_{B^*B^*\\pi}$ values directly enter the one-pion-exchange potential, shifting predicted binding energies for exotic threshold candidates such as $Z_c(4020)$ and $Z_b(10650)$.","The couplings set the residue of the $H^*$ pole in the $H^*\\to\\pi$ transition form factor, providing input that will be needed to interpret the as-yet-unobserved weak decays of $B^*$ and $D^*$ mesons at future heavy-flavor runs.","Within the quoted errors the central values are stable against Borel mass, threshold, and factorization scale variations, and the twist-4 contribution is tiny, which the paper takes as support for the truncation of the operator product expansion."],"supporting_citations":[{"why":"Establishes the original light-cone sum rule for $H^*H^*\\pi$ and supplies the leading-order double spectral density that this paper upgrades.","marker":"[24]"},{"why":"Provides the companion $H^*H\\pi$ couplings and the static-limit sum rule used to verify heavy quark spin symmetry and to fit the $1/m_H$ corrections.","marker":"[33]"},{"why":"Supplies the master spectral-representation formulas used to construct the NLO double density and the higher-twist densities.","marker":"[31]"},{"why":"Provides the soft-collinear effective theory one-loop matching framework, the operator renormalization factors including the evanescent mixing $Z_{E1}$, and the NLO evolution of the pion moments.","marker":"[36]"},{"why":"The NLO light-cone sum rule technique and the basis for using the asymptotic pion distribution amplitude in the NLO spectral density.","marker":"[30]"},{"why":"The alternative systematic treatment of double dispersion integrals over duality regions against which the triangular-region choice is benchmarked.","marker":"[46]"},{"why":"Supplies the lattice QCD value of the second Gegenbauer moment $a_2$ used in the two twist-2 pion distribution amplitude models.","marker":"[51]"},{"why":"Provides the conformal-expansion expressions for the two- and three-particle higher-twist pion distribution amplitudes and their scale dependence.","marker":"[55]"},{"why":"Gives the $1/m_Q$ parametrization of the couplings used to extract $\\hat{g}$, $\\delta_1$, and $\\delta_2$.","marker":"[56]"}],"fun_headline_variants":["Twist-4 sum rules give D*D*π=5.71, B*B*π=4.90","Static π coupling ĝ=0.30 from LCSR, below lattice","NLO sum rules refine D*D*π and B*B*π couplings","LCSR sharpen D*D*π and B*B*π couplings","Hard-collinear sum rules isolate static ĝ=0.30 in π couplings"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that the continuum contribution to the double dispersion integral is modeled by a two-dimensional quark-hadron duality region of a specific boundary shape (the triangle, $\\alpha=1$) with effective thresholds $s_0$; the paper itself notes it is unclear whether the triangular-region argument carries over to the off-diagonal part of the NLO spectral density, so if that ansatz fails the NLO and higher-twist contributions shift beyond the quoted errors.","fun_headline_variants_meta":{"raw":{"variants":["Twist-4 sum rules give D*D*π=5.71, B*B*π=4.90","Static π coupling ĝ=0.30 from LCSR, below lattice","NLO sum rules refine D*D*π and B*B*π couplings","LCSR sharpen D*D*π and B*B*π couplings","Hard-collinear sum rules isolate static ĝ=0.30 in π couplings"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001095,"raw_usage":{"total_tokens":4692,"prompt_tokens":1183,"completion_tokens":3509,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":799,"completion_tokens_details":{"reasoning_tokens":3392}},"tokens_in":799,"tokens_out":3509,"duration_ms":26444,"temperature":1.0,"reasoning_tokens":3392,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:16:32.626184+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Vary the duality boundary shape parameter $\\alpha$ beyond the three values ($1/2,1,2$) the paper already scans, or evaluate the double dispersion integral with the alternative pole-resolving technique it cites: the off-diagonal NLO density changes by several percent under the existing scans, so a wider scan that moves $g_{D^*D^*\\pi}$ or $g_{B^*B^*\\pi}$ by more than the quoted $\\pm0.5$ to $\\pm0.7\\,\\text{GeV}^{-1}$ would falsify the duality ansatz. Independently, a lattice determination of the static coupling that separates $1/m_Q$ corrections by the same convention and returns $\\hat{g}$ above about $0.4$ would contradict the paper's central claim that the gap to experiment is heavy quark spin symmetry breaking rather than a defect of the sum rule.","supporting_citations":[{"cited_title":"$D^*D\\pi$ and $B^*B\\pi$ couplings in QCD","cited_arxiv_id":"hep-ph/9410280","evidence_quote":"Establishes the original light-cone sum rule for $H^*H^*\\pi$ and supplies the leading-order double spectral density that this paper upgrades."},{"cited_title":"Perturbative QCD Correction to the Light-Cone Sum Rule for the $B^*B\\pi $ and $D^*D\\pi$ Couplings","cited_arxiv_id":"hep-ph/9903421","evidence_quote":"The NLO light-cone sum rule technique and the basis for using the asymptotic pion distribution amplitude in the NLO spectral density."}],"review_version":1}