{"id":"812f5fb0-444f-4b7e-b09f-2c895b27ee3c","arxiv_id":"hep-ph/0412400","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The authors extend their NLO QCD factorization calculation of exclusive radiative and electroweak penguin B decays to b to d transitions, giving Standard Model predictions for B to rho gamma, B to omega gamma and B to rho lepton pair alongside updated b to s results.","lead":"This paper computes Standard Model predictions at next-to-leading order for rare B meson decays into a photon or lepton pair plus a light vector meson, extending earlier work from b to s transitions to b to d transitions. It matters because these decays are sensitive probes of new physics in flavour-changing neutral currents, and the b to d modes offer an independent handle on the CKM unitarity triangle.","discovery_kind":"unclear","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The b→d rates and the |V_td/V_ts| < 0.21 bound scale with T1^ρ(0)^2, obtained by transporting the data-fitted T1^{K*}(0) = 0.28 through an assumed ratio F ∈ [0.75, 1.05]; the paper cannot tell whether the sum-rule discrepancy is normalization or SU(3) breaking.","rationale":"The paper is a careful NLO extension with new amplitudes explicitly given (Appendix A) and limitations stated. The reader correctly identified the form factor transport as the weakest link. The paper acknowledges it and uses a conservative F floor. The perturbative stability concern (C^(1) as large as Y^(u)) is also acknowledged via footnote 3 and the scale-dependence discussion. No unacknowledged structural flaw. The factor-of-two Belle tension is reported honestly. Verdict ACCEPT stands.","tokens_in":25838,"tokens_out":11265,"duration_ms":211233,"concrete_test":"An independent lattice determination of the ratio T1^ρ(0)/T1^{K*}(0) at the physical point, or a measurement of Br(B→ργ) at the current experimental sensitivity (the paper notes the theoretical rate saturates the current limit), would pin F. If F is found near 0.76, the central b→d rates drop by ~40% and the Eq. 34 bound weakens; if near 1.0, the predictions stand.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is NLO Standard Model expectations for b→d. The b→d rates (Eqs. 19, 20, 25, 26) and the CKM bound (Eq. 34) all scale with T1^ρ(0)^2, which is obtained by transporting the data-fitted T1^{K*}(0) = 0.28 (Eq. 18) through an assumed ratio F = T1^ρ/T1^{K*} ∈ [0.75, 1.05]. The paper explicitly cannot distinguish a normalization problem from an SU(3)-breaking problem in the sum-rule form factors (Section 3.1). If the resolution is SU(3) breaking, F ≈ 0.76 and the ρ rates are ~40% lower; if normalization, F ≈ 1.04. The bound Eq. 34 uses F > 0.7, which is more conservative than the stated range, but the resulting 0.21 is only marginally below the fit's upper edge (0.233), so the 'cuts into the fit range' statement is fragile: with F = 0.7 and the curly bracket at its lower edge 0.94, the bound relaxes to ~0.214. This is acknowledged, not hidden, but it means the b→d predictions are not parameter-free.","agreement_with_reader":"agree"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The manuscript extends the authors' earlier QCD-factorization analysis of exclusive radiative and electroweak penguin B decays from b→s to b→d transitions. At next-to-leading order in αs (with C9 at NNLL, including the recent three-loop mixing of [17,18]) it presents Standard Model expectations for B→K*γ, B→ργ, B→ωγ and for B→K*ℓ+ℓ− and B→ρℓ+ℓ−: CP-averaged branching fractions, partially integrated lepton-mass spectra, isospin asymmetries, direct CP asymmetries, forward-backward asymmetries and their zero positions. The new technical ingredients are the up-quark amplitudes T^(u)_a collected in Appendix A, the two-loop b→dγ* matrix element of [6,7], and the resulting bound |Vtd/Vts| < 0.21 (Eq. 34) from the current B→ρ0γ limit. The paper also compares its B→K*ℓ+ℓ− prediction with the first Belle partially integrated rate and discusses the constraints on (ρ̄, η̄) obtainable from B→ργ observables.","tokens_in":26211,"tokens_out":8273,"duration_ms":134473,"significance":"If the numbers hold, this paper supplies the reference Standard Model values against which b→d radiative and electroweak penguin searches at the B factories and at LHCb will be judged, in the same way that the authors' earlier b→s paper did for B→K*γ and B→K*ℓ+ℓ−. The explicit decomposition of the amplitudes in Tables 4 and 5 and the closed-form expressions in Appendix A (Eqs. 43–56) make the calculation reproducible and allow an independent check of the numerical results. The predictions are falsifiable and several are already confronted with data: the B→ρ0γ rate of Eq. (19) versus the current upper limit, the B→K*ℓ+ℓ− integral of Eq. (23) versus the Belle bin of Eq. (24), and the forward-backward zero positions of Eqs. (38) and (40). The error budget is presented honestly, with the dominant hadronic and CKM uncertainties separated, and the comparison with the closely related work of [15] and [16] is explicit and fair.","major_comments":[{"comment":"The branching fractions in Eqs. (19)–(20) are normalized to T1^ρ(0) = 0.21, but the text then states that the default value used in the rest of the analysis is T1^ρ(0) = 0.29 ± 0.04. These two choices are not equivalent: with 0.29 the central value of Eq. (19) becomes (0.29/0.21)^2 × 5.0×10^-7 ≈ 9.5×10^-7, which is about 2.4 times the experimental upper limit Br(B0→ρ0γ) < 0.4×10^-6 quoted in Table 6. The statement two paragraphs later that 'our theoretical result (19) already saturates the experimental bound' therefore holds only for the 0.21 normalization, not for the stated default. Since the b→d rates of Eqs. (19), (20), (25) and (26) and the discussion of Section 3.5 all rest on this input, the reader cannot tell which normalization underlies the quoted numbers. Please state explicitly which value of T1^ρ(0) is used for each equation, and reconcile the default with the experimental limit or explain why the default is retained despite it.","section":"Section 3.1, Eqs. (19)–(20)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Eq. (34) uses F > 0.7, whereas Section 3.1 states that 'we must assume 0.75 < F < 1.05 at least'. The weaker value is conservative, but the difference matters for the headline claim: with F = 0.7 and the curly bracket at its lower edge 0.94, the bound relaxes to about 0.20, which is only marginally below the upper edge 0.233 of the standard fit quoted in the text. The statement that the limit 'already cuts into the range' is thus fragile and depends on a choice of F that is not the one the paper argues for. In addition, the 'doubling the error on the input values of (ρ̄, η̄)' that produces the bracket 0.94–1.05 in Eq. (33) is introduced without justification. Please present the bound as an explicit function of F over the stated range, show the F = 0.75 case, and give the rationale for the error doubling.","section":"Section 3.5, Eq. (34)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The isospin asymmetry Δ(K*γ) is quoted as (5.8 +3.3−2.9)% with the Wilson coefficients evaluated at µ ≃ mb, and the text notes that this is smaller than the original calculation of [31], which used µ ≃ (mbΛQCD)^1/2. The argument for the scale choice is plausible, but the residual scale ambiguity is a factor-of-order-two effect on the central value and is not visible in the quoted error. Since the experimental number is (3.6 ± 3.8)%, the discriminating power of this prediction depends entirely on that choice. Please quote the value obtained at the alternative scale (mbΛQCD)^1/2 alongside the default, so that the reader can see the size of the ambiguity separately from the parameter errors of Table 2.","section":"Section 3.3, Eq. (27)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The 50% theoretical error assigned to the B→γ* form factors ξ^(Bγ*)_⊥,‖ dominates the error budget of the charged modes: it is the largest entry in Eqs. (20), (26) and (28) and controls the bands of Figs. 3 and 5. The assignment is a judgement call, and Appendix A.3 supports it only by noting that the QCD sum rule estimate of [28,29] is 'not too different from the heavy quark limit'. Please make the basis quantitative, for instance by quoting the spread between the heavy-quark-limit value of Eq. (56) and the sum-rule result, or by demonstrating explicitly how the conclusions of Sections 3.3–3.4 change if the error is halved or doubled.","section":"Section 3.3, Section 3.4 and Appendix A.3","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The prefactor of Eq. (27) should be stated unambiguously: the quoted 5.8% follows for 0.28/T1^{K*}(0) with T1^{K*}(0) = 0.28, not for a multiplicative 0.28·T1^{K*}(0). Please make the intended 1/T1 dependence explicit.","section":"Eq. (27)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Because the ω hadronic parameters are set equal to those of the ρ, the statement that Br(B0→ωγ) equals Br(B0→ρ0γ) is an assumption rather than a prediction, and the same applies to the near-coincidence of the ω and ρ0 curves in Fig. 4. This is acknowledged in Section 2.2 but should also be flagged where the numbers are quoted.","section":"Section 2.2 and Section 3.1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The comparison with Belle halves an average of charged and neutral rates measured over 4 < q2 < 8 GeV2 and sets it against a theory integral over 4 < q2 < 6 GeV2, relying on the near-flatness of the spectrum. Please show the theory band on the same figure or quote the 4–8 GeV2 integral directly, so that the factor-of-two discrepancy is not an artifact of the bin matching.","section":"Section 3.2, Eq. (24)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The normalization of the transverse form factor is now taken from data via Eq. (18), but its q2 shape still comes from the Ball–Braun parameterization of Table 3. The shape uncertainty, which matters most at low q2 where the photon pole dominates, does not appear to be included in the band of Fig. 1; please state whether it is.","section":"Section 3.2 and Fig. 1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The abstract states that the B→ργ decays 'provide constraints on the CKM parameters (ρ̄, η̄)', whereas Section 3.5 makes clear that at present only an upper limit exists and that the asymmetry constraints are illustrative, assuming observations at the theoretical values with no experimental error. Consider softening the abstract to match.","section":"Abstract","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The caption should state the value of α used in each of the three panels, since panels (a) and (b) refer to B+ and B− respectively and the text discusses the default α = 94° only for the band.","section":"Fig. 7 caption","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The annihilation entries in Table 4 are given as central values only, although the text assigns them a 50% error that dominates the charged-mode predictions. A footnote referring to that error would make the table self-contained.","section":"Table 4","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The hadronic errors on q0^2 are strongly asymmetric (+0.45/−0.39 for ρ0) while the CKM errors are quoted as symmetric ±0.02; please explain the origin of the asymmetry or symmetrize the presentation.","section":"Eq. (40)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Reference [33] reads 'BELLE Colaboration Collaboration'; please correct the duplication.","section":"References","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"minor_revision","confidential_remarks":"The overlap with [15] and [16] is disclosed and discussed in the appropriate places, and the new material relative to the authors' earlier b→s paper is clearly delimited. The paper is within the journal's scope. The main revision I would insist on is the reconciliation of the T1^ρ(0) default with the normalization of Eqs. (19)–(20), since that inconsistency is visible to any careful reader and affects the numbers most likely to be quoted."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"Bottom line: this is the reference calculation for exclusive b→d radiative and electroweak penguins at NLO, and the part that matters is genuinely new — the up-quark amplitudes T^(u)_a in Appendix A, the first NLO B→ρℓ+ℓ− rates (Eqs. 25, 26), and the forward-backward asymmetry zeros in Eq. 40. The b→s numbers are an update of the authors' own earlier work, useful but not the point. If you work on b→d rare decays, you will cite this. The machinery is standard QCD factorization and the new pieces are written out explicitly enough to check; the two-loop b→d vertex from Seidel and Asatrian et al. is folded in properly, and the numerical tables (4 and 5) let you see where each amplitude comes from. That transparency is worth something and is not universal in this literature. The paper is also candid about its own weak points: footnote 3 says outright that higher-order and power corrections are not quantified, the 50% annihilation error is stated, and the factor-of-two gap with the Belle B→K*ℓℓ rate is reported rather than buried. The form-factor story is the load-bearing soft spot, and the authors know it. T1^{K*}(0)=0.28 is fitted to B→K*γ data (Eq. 18) and then transported to ρ through an assumed ratio F∈[0.75,1.05]. They say plainly they cannot tell whether the sum-rule discrepancy is normalization or SU(3) breaking, so every b→d rate scales with a number they do not control. That is a real limitation, not a fatal one, and it is disclosed. One place where the prose outruns the number: Eq. 34's bound |Vtd/Vts|<0.21 is quoted as cutting into the standard-fit range, but the fit's upper edge is about 0.233 and the bound uses the conservative F>0.7 with the curly bracket at 0.94. Push those to their edges and you land near 0.214 — still inside, barely. The claim survives but it is marginal, and a sentence saying so would be more honest than 'already cuts into the range.' Minor: the ρ0–ω difference is not predicted because the ω hadronic parameters are copied from the ρ; the authors flag this, so treat any ρ0/ω comparison as unsupported. Audience: B-physics phenomenologists and anyone preparing b→d analyses for LHCb or Belle II. Worth a serious referee; the calculation deserves scrutiny on the form-factor transport and the power-correction truncation, not on its foundations.","headline":"A careful, honest NLO extension to b→d penguins; the new amplitudes and B→ρℓℓ rates are the real content, and the CKM bound is weaker than the text implies.","tokens_in":26846,"tokens_out":1035,"would_cite":true,"duration_ms":18622,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["12.38.Bx","13.20.He","12.15.Hh","14.40.Nd"],"model":"selfhosted/deepseek-v4.1-flash","headline":"The paper extends the QCD-factorization program for exclusive rare B decays from $b$ to $s$ transitions down to $b$ to $d$ transitions, supplying next-to-leading-order Standard Model reference values for $B to rho gamma$, $B to omega gamma$","keywords":["QCD factorization","rare B decays","electroweak penguins","b to d transitions","CKM unitarity triangle","B to rho gamma","forward-backward asymmetry","next-to-leading order"],"falsifier":"A measurement of $mathrm{Br}(B^0 to rho^0 gamma)$ well below the current limit, or a lattice determination of $T_1^rho(0)/T_1^{K^*}(0)$ outside the range $0.75$ to $1.05$, would move or break the $|V_{td}/V_{ts}| < 0.21$ bound and the $(bar rho, bar eta)$ constraints that follow from it.","tokens_in":27247,"feed_emoji":"⚛️","tokens_out":3887,"duration_ms":63188,"temperature":0.7,"pith_summary":"The authors want to give the same level of theoretical control to exclusive $b to d$ penguin decays that earlier work gave to $b to s$: $B to rho gamma$, $B to omega gamma$ and, for the first time at next-to-leading order, $B to rho ell^+ ell^-$. The obstacle had been a missing two-loop virtual correction to the $b to d gamma^*$ vertex from light-quark loops; with that piece now available, the decay amplitudes can be completed, and the paper's Appendix A writes down the new up-quark amplitudes $T^{(u)}_a$ that carry the $b to d$ specific physics. The payoff is a set of numbers a reader can compare to data: branching fractions, isospin asymmetries, direct CP asymmetries, lepton-mass spectra, and forward-backward asymmetries with their zero crossings. The authors also show that the existing upper limit on $B^0 to rho^0 gamma$ already constrains $|V_{td}/V_{ts}| < 0.21$, and that the asymmetries in $B to rho gamma$, taken together, carve out a region of the $(bar rho, bar eta)$ plane nearly orthogonal to the standard fit. The authors are explicit about two soft spots: the $B to K^*$ tensor form factor must be reduced below its QCD sum rule value to match data, and the Belle measurement of the partially integrated $B to K^* ell^+ ell^-$ rate sits about a factor of two above their prediction.","feed_headline":"Rare b→d penguin decays get full NLO predictions","feed_subtitle":"Next-to-leading-order QCD factorization yields reference rates, asymmetries, and a |Vtd/Vts| bound below 0.21.","key_machinery":"The machinery is QCD factorization for exclusive decays: the hadronic matrix element is written as a form-factor term $xi_a C_a^{(i)}$ plus a hard-scattering term involving the $B$ meson light-cone distribution amplitude and the light-meson distribution amplitude, with the transverse and longitudinal amplitudes separated. The objects that carry the argument are the coefficient functions $C_7^{(i)}$ and $C_{9,a}^{(i)}(q^2)$, which package the short-distance physics and are split into a top-quark sector $i = t$ and an up-quark sector $i = u$ weighted by the CKM ratio $lambda_u^{(d)}/lambda_t^{(d)} = -R_{ut} e^{i alpha}$. The new content is the up-sector amplitude $T_a^{(u)}$, whose two-loop correction from light-quark loops $C^{(1)}$ turns out to be as large as the one-loop function $Y^{(u)}(q^2)$ and largely cancels its imaginary part, and the power-suppressed annihilation amplitude $Delta T_perp^{(u)}$ that is enhanced by the large Wilson coefficient $C_2$ and dominates the charged-mode transverse amplitude. Because the up-sector amplitudes enter with a different weak phase, the interference terms produce the isospin and CP asymmetries and shift the forward-backward zero differently for $B$ and $bar B$.","core_discovery":"The central claim is that exclusive radiative and electroweak penguin decays of $B$ mesons to $K^*$, $rho$ and $omega$ are now computable at next-to-leading order in $alpha_s$ for both $b to s$ and $b to d$ at once, within QCD factorization at leading power in $1/m_b$, with weak annihilation included at leading order and the numerically relevant $1/m_b$ annihilation and hard-spectator corrections added. Concretely the paper delivers: $mathrm{Br}(B^0 to rho^0 gamma) = (5.0 pm 0.5) times 10^{-7}$ and $mathrm{Br}(B^+ to rho^+ gamma) = (10.3^{+1.5}_{-1.2}) times 10^{-7}$ for a reference tensor form factor $T_1^rho(0) = 0.21$; partially integrated rates $int_1^6 dq^2, dmathrm{Br}(B^0 to rho^0 ell^+ ell^-)/dq^2 = 4.2^{+0.6}_{-0.4} times 10^{-9}$ and $9.6^{+1.5}_{-1.1} times 10^{-9}$ for the charged mode; direct CP asymmetries $A_{CP}(rho^0 gamma) = (-10.4^{+1.6}_{-2.4}|_{mathrm{CKM}}{}^{+3.0}_{-3.6}|_{mathrm{had}})%$ and $A_{CP}(rho^+ gamma) = (-10.7^{+1.5}_{-2.0}{}^{+2.6}_{-3.7})%$; isospin asymmetries $Delta(rho gamma) = (-4.6^{+5.4}_{-4.2}{}^{+5.8}_{-5.6})%$ and $Delta(K^* gamma) = 0.28, T_1^{K^*}(0), (5.8^{+3.3}_{-2.9})%$; and forward-backward zero positions around $q^2 = 3.6$ to $4.5 , mathrm{GeV}^2$ for the four $B to rho ell^+ ell^-$ modes, distinguishable between $B$ and $bar B$ because the up-quark amplitude now carries a large absorptive part. The authors' own framing of why this matters is that $b to d$ penguins are the cleanest place to look for new flavour-changing neutral currents, and that the $B to rho gamma$ observables give a determination of the apex of the unitarity triangle independent of the standard fit.","pith_inferences":["The factor-of-two gap between the Belle partially integrated $B to K^* ell^+ ell^-$ rate and the prediction points, if it persists, to a tension between the tensor form factor preferred by $B to K^* gamma$ and the longitudinal form factor $A_0$ preferred by the dilepton rate, which would be a concrete handle on where the heavy-quark expansion is failing.","Because the charged-mode predictions lean on the annihilation amplitude and the $B to gamma^*$ form factors $xi_perp^{(B gamma^*)}, xi_parallel^{(B gamma^*)}$, a future lattice or sum-rule determination of those form factors at $q^2 approx 0$ would convert the largest hadronic error bar in this paper into a genuine test.","The same formalism applied with $delta_{qd} to delta_{qs}$ would generate the corresponding spectator-charge terms for $B_s to phi ell^+ ell^-$, which the appendix flags in passing but does not compute.","If the direct CP asymmetry in $B to rho gamma$ were measured far from the predicted $-10%$, the circle in the $(bar rho, bar eta)$ plane would move rather than shrink, so the asymmetry is a sharper discriminant of new phases in $b to d gamma$ than of the CKM angle itself."],"forward_implications":["The existing experimental upper limit on $B^0 to rho^0 gamma$ translates into $|V_{td}/V_{ts}| < 0.21$ for form-factor ratio $F > 0.7$, a bound that already cuts into the range $0.204^{+0.029}_{-0.046}$ obtained from the standard unitarity-triangle fit.","A measurement of $mathrm{Br}(B^0 to rho^0 gamma)$ near the current limit, combined with the $B to K^* gamma$ rate, fixes $|V_{td}/V_{ts}|$ up to the form-factor ratio $F = T_1^rho(0)/T_1^{K^*}(0)$.","Simultaneous measurement of the branching fraction, isospin asymmetry and direct CP asymmetry in $B to rho gamma$ determines $(bar rho, bar eta)$ from a circle intersection that is nearly orthogonal to the standard fit, giving a genuinely independent cross-check.","The location of the forward-backward asymmetry zero in $B to rho ell^+ ell^-$ measures the real part of the $b to d$ coefficient $C_9$, and the $B$ versus $bar B$ splitting of that zero measures the phase of the up-sector amplitude.","Once the CKM elements and the $b to s$ coefficients $C_9, C_{10}$ are known, the $B to rho ell^+ ell^-$ observables become constraints on the $b to d$ coefficients $C_9^d, C_{10}^d$, which new-physics scenarios with non-minimal flavour violation can shift in magnitude and phase."],"supporting_citations":[{"why":"Supplies the entire next-to-leading-order formalism for $B to K^* ell^+ ell^-$ that this paper transports to $b to d$, including the operator basis, the amplitude decomposition, and the annihilation topologies.","marker":"[3]"},{"why":"Provides the two-loop virtual correction to the $b to d ell^+ ell^-$ transition whose absence had blocked the $B to rho ell^+ ell^-$ prediction.","marker":"[6]"},{"why":"Independent computation of the same two-loop $b to d gamma^*$ matrix element, used as cross-check on the new up-sector amplitudes.","marker":"[7]"},{"why":"Source of the QCD sum rule form factors $V, A_1, A_2, T_1$ and their $q^2$ parametrizations, which set the normalization of every branching fraction quoted.","marker":"[26]"},{"why":"Origin of the isospin-asymmetry calculation in $B to K^* gamma$ and of the power-suppressed hard-spectator and annihilation corrections that this paper extends and re-evaluates at scale $m_b$.","marker":"[31]"},{"why":"Source of the $1/m_b$ power corrections to the transverse amplitude and of the endpoint-cutoff treatment used for the quark-loop function in the hard-spectator term.","marker":"[35]"},{"why":"Supplies the CKM inputs $bar rho, bar eta, R_{ut}, alpha$ and the standard-fit range of $|V_{td}/V_{ts}|$ against which the new bound is compared.","marker":"[20]"},{"why":"Provides the experimental upper limits on $B^0 to rho^0 gamma$, $B^+ to rho^+ gamma$ and $B^0 to omega gamma$ from which the $|V_{td}/V_{ts}|$ bound is derived.","marker":"[10]"},{"why":"Provides the Belle partially integrated $B to K^* ell^+ ell^-$ rate in the $4$ to $8 , mathrm{GeV}^2$ bin that the theoretical prediction is compared against.","marker":"[14]"}],"fun_headline_variants":["b→d penguins join b→s at NLO in QCD factorization","NLO QCD factorization now covers B→ργ and B→ρℓ⁺ℓ⁻","B→ργ CP asymmetries come out near −10% at NLO","Forward-backward zeros sit at 3.6–4.5 GeV² in B→ρℓℓ","Caveat: NLO b→d rates assume leading-power 1/m_b and T₁^ρ(0)=0.21"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The $b to d$ branching fractions and the $|V_{td}/V_{ts}|$ bound rest on carrying the $B to K^*$ tensor form factor, fixed to $T_1^{K^*}(0) = 0.28$ from $B to K^* gamma$ data, over to $B to rho$ through a ratio assumed to lie between $0.75$ and $1.05$.","fun_headline_variants_meta":{"raw":{"variants":["b→d penguins join b→s at NLO in QCD factorization","NLO QCD factorization now covers B→ργ and B→ρℓ⁺ℓ⁻","B→ργ CP asymmetries come out near −10% at NLO","Forward-backward zeros sit at 3.6–4.5 GeV² in B→ρℓℓ","Caveat: NLO b→d rates assume leading-power 1/m_b and T₁^ρ(0)=0.21"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":2894,"prompt_tokens":1264,"completion_tokens":1630,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":1517}},"tokens_in":1264,"tokens_out":1630,"duration_ms":14217,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":1517,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-29T16:28:49.509134+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"A measurement of $mathrm{Br}(B^0 to rho^0 gamma)$ well below the current limit, or a lattice determination of $T_1^rho(0)/T_1^{K^*}(0)$ outside the range $0.75$ to $1.05$, would move or break the $|V_{td}/V_{ts}| < 0.21$ bound and the $(bar rho, bar eta)$ constraints that follow from it.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the entire next-to-leading-order formalism for $B to K^* ell^+ ell^-$ that this paper transports to $b to d$, including the operator basis, the amplitude decomposition, and the annihilation topologies."},{"cited_title":"Analytic two-loop virtual corrections to $b --> d l^+ l^-$","cited_arxiv_id":"hep-ph/0403185","evidence_quote":"Provides the two-loop virtual correction to the $b to d ell^+ ell^-$ transition whose absence had blocked the $B to rho ell^+ ell^-$ prediction."},{"cited_title":"Virtual- and bremsstrahlung corrections to b -> d l+ l- in the standard model","cited_arxiv_id":"hep-ph/0312063","evidence_quote":"Independent computation of the same two-loop $b to d gamma^*$ matrix element, used as cross-check on the new up-sector amplitudes."},{"cited_title":"Exclusive Semileptonic and Rare B-Meson Decays in QCD","cited_arxiv_id":"hep-ph/9805422","evidence_quote":"Source of the QCD sum rule form factors $V, A_1, A_2, T_1$ and their $q^2$ parametrizations, which set the normalization of every branching fraction quoted."},{"cited_title":"Isospin Breaking in B -> K^* gamma Decays","cited_arxiv_id":"hep-ph/0110078","evidence_quote":"Origin of the isospin-asymmetry calculation in $B to K^* gamma$ and of the power-suppressed hard-spectator and annihilation corrections that this paper extends and re-evaluates at scale $m_b$."},{"cited_title":"Forward-backward and isospin asymmetry for B -> K* l+ l- decay in the standard model and in supersymmetry","cited_arxiv_id":"hep-ph/0212158","evidence_quote":"Source of the $1/m_b$ power corrections to the transverse amplitude and of the endpoint-cutoff treatment used for the quark-loop function in the hard-spectator term."},{"cited_title":"CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories","cited_arxiv_id":"hep-ph/0406184","evidence_quote":"Supplies the CKM inputs $bar rho, bar eta, R_{ut}, alpha$ and the standard-fit range of $|V_{td}/V_{ts}|$ against which the new bound is compared."},{"cited_title":"Search for the Radiative Penguin Decays B+ -> rho+ gamma, B0 -> rho0 gamma, and B0 -> omega gamma","cited_arxiv_id":"hep-ex/0408034","evidence_quote":"Provides the experimental upper limits on $B^0 to rho^0 gamma$, $B^+ to rho^+ gamma$ and $B^0 to omega gamma$ from which the $|V_{td}/V_{ts}|$ bound is derived."},{"cited_title":"Measurement of the Differential $q^2$ Spectrum and Forward-Backward Asymmetry for $B \\to K^{(*)} \\ell^+ \\ell^-$","cited_arxiv_id":"hep-ex/0410006","evidence_quote":"Provides the Belle partially integrated $B to K^* ell^+ ell^-$ rate in the $4$ to $8 , mathrm{GeV}^2$ bin that the theoretical prediction is compared against."}],"review_version":1}