{"id":"c50c8eb8-8cfd-4386-91f4-9471c6bc3df9","arxiv_id":"2607.27367","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A new photon-tagged angular energy correlator in inclusive B→X_sγ factorizes at leading power into the standard shape function and a newly computed measured jet function, enabling angular tests of endpoint factorization.","lead":"This paper introduces a photon-tagged energy correlator for inclusive B decays, showing that its angular spectrum factorizes into known short-distance physics, the B-meson shape function, and a new calculable jet function. It offers a new way to measure angular energy flow in B→X_sγ and to test the leading-power description of endpoint decays.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Missing zero-bin subtraction in the one-loop measured jet function may contaminate the angular kernel with soft modes.","rationale":"The reader identified resolved-photon effects as the weakest assumption, but insofar as those are genuinely subleading power, that concern does not undermine the leading-power claim. A sharper internal issue is the treatment of the collinear/soft overlap in the one-loop measured jet function. The paper's factorization derivation separates collinear and soft sectors and explicitly keeps only the collinear contribution to the energy-flow measurement at leading power. Yet the partonic calculation of J_TEC integrates over the full real-emission phase space, including x→0 where the emitted gluon is soft. In SCET, such a configuration must be removed from the collinear matrix element by zero-bin subtraction; otherwise the angular kernel contains a leading-power contribution from modes that the paper itself argues are power suppressed in the physical measurement. This is not a disagreement with the factorization theorem's structure, but a concrete technical gap in the calculation of the new perturbative object that carries the angular information. Because the inclusive sum rule does not constrain the angular tail, the error would not be caught by the stated consistency check. A re-computation with zero-bin subtraction is a well-defined, decisive check. The verdict is therefore CONDITIONAL rather than ACCEPT: the central factorization may survive, but the one-loop kernel and the numerical benchmark as presented require verification.","tokens_in":25619,"tokens_out":34146,"duration_ms":416945,"concrete_test":"Recompute the one-loop real-emission contribution to J_TEC(s,τ) with the standard SCET zero-bin subtraction: take Eq. (52) and subtract the soft-limit contribution obtained by first rescaling the final-state gluon momentum by λ→0 in both the matrix element and the measurement, before performing the x integral. Compare the resulting finite kernel g_0(r) and cumulative G_0(R) in Eq. (77) with Eqs. (55) and (77). If G_0(R) differs by an O(1) amount at R ∼ 1 (for instance, if the large-r tail 2/r² is removed), then the migration fractions in Table I and the closure-test predictions change at the same order as the reported 3–16% effect, and the one-loop kernel in Eq. (69) is not the correct collinear measured jet function.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim, Eq. (45), rests on a leading-power collinear measured jet function J_TEC whose one-loop calculation is presented in Sec. IV. The definition in Eq. (43) is a collinear matrix element, but the explicit real-emission computation in Eq. (52) integrates x over the full range 0 ≤ x ≤ 1 with no zero-bin subtraction or collinear-mode restriction. In the region x→0 at fixed s, the emitted gluon has n·p_g ≈ s/Q ∼ Λ_QCD, n̄·p_g = xQ → 0, and p⊥ → 0: this is a soft mode, not a collinear one. Such a gluon belongs to the soft sector X_s of the BPS-decoupled theory. By the paper's own Eq. (27), soft particles contribute to the BTEC only at relative order Λ_QCD/Q; they should not appear inside the leading-power collinear jet function. This soft region generates the large-r tail of the angular kernel g(r) ∼ 2/r² for r = τ/s ≫ 1, and hence contributes to the cumulative boundary term G(R) in Eq. (77). Because the plus prescription makes ∫ dτ K(s,τ) = 0, the inclusive sum rule in Eq. (46) does not constrain this tail; the error is invisible in the inclusive projection and only affects the angular distribution, i.e., the very observable the paper proposes. Thus the benchmark migration fractions in Table I and the closure-test prediction in Sec. VI C may be artifacts of double-counted soft modes. The paper does not mention zero-bin subtraction, rapidity regulators, or any equivalent check of collinear/soft overlap for J_TEC.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a photon-tagged one-point energy correlator (BTEC) for the endpoint region of B → X_s γ. Restricting to the direct O_7 contribution, it derives a leading-power SCET factorization, Eq. (45), in which the double-differential spectrum is a convolution of the standard hard coefficient, the universal B-meson shape function, and a new measured quark jet function J_TEC. The one-loop J_TEC is computed explicitly, an angular plus prescription is defined, the inclusive sum rule (Eq. (46)) and the standard quark-jet renormalization are checked, and fixed-cut cumulatives are constructed. Using the BLNP shape function, an illustrative benchmark gives 3–16% migration above angular cuts, and a closure test of leading-power endpoint factorization is proposed.","tokens_in":25982,"tokens_out":18444,"duration_ms":213966,"significance":"The observable and the factorization claim are interesting and potentially important: if Eq. (45) is correct, the angular spectrum is determined at leading power by known perturbative coefficients and the universal shape function, with no new leading-power nonperturbative function. The paper is largely self-contained, and its explicit one-loop calculation, the verification of the inclusive sum rule, and the RG-consistency check are valuable technical steps. The proposed fixed-cut cumulatives and closure test are a sensible way to isolate angular information. However, the one-loop jet function computation contains an unsubtracted soft/collinear overlap that affects the very angular kernel on which the numerical benchmark and closure test rest; this must be addressed before the quantitative claims can be accepted.","major_comments":[{"comment":"The real-emission integral in Eq. (52) integrates x over 0≤x≤1 with no zero-bin subtraction. In the x→0 region at fixed s, the emitted gluon has n·p_g≃s/Q∼Λ_QCD, n̄·p_g=xQ→0, and p⊥→0: this is a soft mode, not a collinear one, and by the paper's own Eq. (27) such a particle contributes to the BTEC only at O(Λ_QCD/Q). After BPS decoupling, final-state soft gluons belong to the soft matrix element bS_B, not to the collinear J_TEC. This region generates the large-r tail of g(r)∼2/r² and contributes to G(R) in Eq. (77), hence to Table I and the closure test in Sec. VI C. The plus prescription and the inclusive sum rule in Eq. (46) do not remove this contamination because the sum rule only constrains ∫dτ J_TEC. A zero-bin subtraction (or an equivalent collinear-mode restriction) is required to define a purely collinear measurable jet function.","section":"Sec. IV, Eq. (52)"},{"comment":"There is an internal tension between the power counting in Sec. III F and the one-loop calculation in Sec. IV. Equation (35) states that soft transverse recoil produces an O(Λ²_QCD/τ) angular migration, which is power suppressed at τ∼s∼QΛ_QCD, and Eq. (36) replaces the transverse constraint by δ(p_Xn⊥). Yet the x→0 mode retained in Eq. (52) is precisely a quark recoiling against a soft gluon, giving the quark a small angle τ≃sx and the gluon a wide angle τ≃s/x. This is the same soft-recoil migration that Sec. III F classifies as a power correction. Including it at leading power in J_TEC therefore double-counts the soft sector and likely overstates the angular tail; the claimed leading-power prediction is not established until this overlap is removed and the numerical impact on G(R), Table I, and Δi(τc) in Eq. (91) is reassessed.","section":"Secs. III F and IV"}],"minor_comments":[{"comment":"Typo: “On can immediately check” should read “One can immediately check.”","section":"Sec. IV A"},{"comment":"Several occurrences of “sufficient” should be “sufficient”; there are also nonstandard DOI strings in Refs. [51] and [60] that should be corrected.","section":"Throughout"},{"comment":"The statement that the BLNP normalization N cancels in each normalized cumulative assumes the same α_s(μ_i) model, which is stated; this is fine for the illustrative benchmark, but the reader would benefit from an explicit note that the cancellation holds only for the normalized ratio, not for absolute rates.","section":"Sec. VI B"},{"comment":"The all-order extension of Eq. (72) is admittedly conjectural; a brief comment on the expected form of the τ-dependence of the two-loop counterterm would strengthen the presentation.","section":"Sec. V"}],"recommendation":"major_revision","confidential_remarks":"The zero-bin issue is the decisive point. It is technically fixable: the authors should perform a proper zero-bin subtraction for J_TEC, or demonstrate with an explicit calculation that the soft x→0 contribution is cancelled or is genuinely subleading after the plus prescription. If the subtraction removes most of the G(R) tail, the numerical benchmark and the closure-test interpretation will need substantial revision. I would not reject the paper, because the factorization framework and the inclusive sum-rule checks are promising, but the present quantitative claims are not reliable without this repair."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper introduces a photon-tagged one-point energy correlator (BTEC) for inclusive endpoint B→X_sγ and derives a leading-power factorization into the standard hard coefficient, the universal B-meson shape function, and a new measured quark jet function. The factorization derivation in Sec. III is self-contained and careful, and the one-loop computation is explicit, with the inclusive projection correctly reducing to the ordinary quark jet function. That is real progress and worth a serious look.\n\nThe main soft spot is the one-loop jet function in Sec. IV. The real-emission integral in Eq. (52) runs over the full range 0≤x≤1, and the x→0 region is soft, not collinear. In the BPS-decoupled theory used here, that region belongs to the soft sector, which the paper itself says contributes only at O(Λ_QCD/Q) to the measurement. No zero-bin subtraction or equivalent check appears. This soft region generates the large-r tail of g(r)~2/r^2 and therefore feeds the cumulative boundary term G(R) in Eq. (77). Because the angular plus prescription makes the inclusive sum rule blind to this tail, the benchmark migration fractions in Table I and the closure-test prediction in Sec. VI C could be contaminated by double-counted soft modes. This is not a cosmetic concern: the migration is the observable.\n\nThe paper is honest about its scope—resolved photons, the small-angle TMD regime, and the semileptonic extension are deferred—and the first-moment identity plus the bounded-cumulative discussion are nice. If the zero-bin issue is resolved (or if I am missing a subtle reason the tail is not double counting, which I do not see), the framework is a solid contribution. As it stands, I would send it to a referee who knows SCET overlap subtleties, but I would not cite the numerical results yet.","headline":"A genuinely new angular observable with a careful SCET derivation, but the one-loop jet function likely double-counts soft modes for lack of a zero-bin subtraction.","tokens_in":26493,"tokens_out":5584,"would_cite":false,"duration_ms":70255,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A photon-tagged energy correlator factorizes the leading-power angular structure of inclusive endpoint B→X_sγ decays into a known hard coefficient, the universal B-meson shape function, and a new measured quark jet function, with no new non","keywords":["B decays","B→X_sγ","energy correlator","factorization","shape function","measured jet function","endpoint kinematics","photon tagging"],"falsifier":"Compute the resolved-photon soft and jet functions in the same endpoint region and compare their contribution to the fixed-cut cumulative F_i(τ_c) with the direct term; any contribution that is not suppressed by Λ_QCD/Q falsifies the leading-power relation. Experimentally, an independently calibrated shape function propagated to multiple (Eγ, τ_c) bins that yields residuals Δ_i systematically larger than the estimated power corrections would also falsify the factorization.","tokens_in":25477,"feed_emoji":"🎯","tokens_out":6191,"duration_ms":64119,"temperature":0.7,"pith_summary":"The paper introduces a photon-tagged energy correlator (BTEC) that resolves how the recoiling hadronic system in inclusive endpoint B decay spreads in angle around the photon-defined axis. Its central aim is to prove that, at leading power and at the natural collinear angular scale, this angular spectrum is completely determined by the known hard coefficient, the same universal B-meson shape function that controls the ordinary photon spectrum, and a new perturbatively calculable measured quark jet function. The paper derives this factorization relation, computes the new jet function at one-loop accuracy, and verifies that integrating it over angle recovers the standard inclusive quark jet function. A sympathetic reader would care because the observable adds genuinely new angular information beyond the photon spectrum, provides a closure test of endpoint factorization, and could sharpen signal-background separation when energy-flow profiles differ.","feed_headline":"Photon-tagged energy flow factorizes in B decays","feed_subtitle":"The angular spectrum of B→X_sγ uses only known hard terms, the universal shape function, and one calculable jet kernel.","key_machinery":"The load-bearing objects are the photon-tagged one-point energy correlator (BTEC) and the measured quark jet function J_TEC^q(s,τ,μ). The BTEC assigns each hadron in the recoiling X_s system an energy weight E_a/E_X at the angular variable τ_a = Q²(1−n̂_J·n̂_a)/2, with the recoil axis n̂_J fixed exactly by the tagged photon. The proof uses a soft-collinear decoupling field redefinition to separate collinear and soft degrees of freedom, then shows that the measurement, the momentum-conservation constraints, and the soft matrix element reduce at leading power to a convolution of the hard coefficient, the shape function, and J_TEC^q. The measured jet function, defined as a cut collinear matrix","core_discovery":"The paper's central claim is that the double-differential spectrum d²Γ_BTEC/(dEγ dτ) for the direct-photon contribution to B→X_sγ obeys a leading-power factorization: 2Γ_γ^(0)|VtbVts*|² Hγ(mb,μ) P− ∫_0^{P+} dω J_TEC^q(P−[P+−ω],τ,μ) bS_B(ω,μ), plus power corrections. Here Hγ is the standard hard coefficient, bS_B is the universal B-meson shape function already present in the inclusive photon spectrum, and J_TEC^q is a new measured quark jet function. The paper shows that the angular measurement acts only on the collinear sector at leading power, so no new nonperturbative function enters; all new angular dependence is carried by J_TEC^q, which the paper computes at one loop as a distribution i","pith_inferences":["Editorial inference: because the one-loop angular kernel is finite and analytic, higher-order and resummed versions of J_TEC^q could turn the boundary logarithm ln(s/τ_c) into a precision probe of angular ordering in inclusive B decay, which the one-dimensional photon spectrum cannot access.","Editorial inference: the one-tag construction is not specific to radiative B decay; any inclusive process with a fixed reference axis, such as a tagged Z or Higgs recoil, could be treated with the same measured-jet-function formalism and the same closure test.","Editorial inference: the proposed closure test is insensitive to corrections that mimic a shape-function shift; designing a minimal set of (Eγ, τ_c) bins that breaks that degeneracy would make the test substantially stronger, but the paper does not quantify such a design.","Editorial inference: if resolved-photon effects turn out not to be subleading, the BTEC data would not simply invalidate the factorization relation but would provide a first map of those subleading soft and jet functions, converting the proposed closure test into a discovery channel for them."],"forward_implications":["The double-differential BTEC spectrum is predictable at leading power once the B-meson shape function is calibrated from the ordinary photon spectrum; no additional nonperturbative function needs to be fitted.","Integrating the measured jet function over angle exactly recovers the standard inclusive quark jet function, so the ordinary photon-energy spectrum is reproduced as the zeroth angular moment.","Bounded cumulatives with a fixed angular cut τ_c ~ QΛ_QCD remain valid leading-power observables even though the pointwise spectrum fails at τ ~ Λ_QCD², making the prediction testable without resolving the nonperturbative small-angle region.","An illustrative one-loop benchmark places 3–16% of the normalized energy flow outside fixed cuts τ_c = 2–4 GeV², with larger migration at lower photon energy where the recoil jet is broader.","The same measured jet function and leading shape function appear in the semileptonic endpoint analogue, enabling a consistency test of shape-function universality before inclusive |Vub| applications."],"fun_headline_variants":["BTEC factorizes B→X_sγ energy flow","New correlator resolves B decay angular structure","B-decay energy flow: no new functions needed","Photon-tagged B decays: one-loop jet kernel","B→X_sγ angular spectrum from known inputs"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is that the direct-photon (O7) channel is the only leading-power contribution in the endpoint region, so resolved-photon contributions—where the photon couples to light partons—are suppressed by a power of Λ_QCD/Q; if that premise fails, the angular spectrum requires new nonperturbative soft and jet functions.","fun_headline_variants_meta":{"raw":{"variants":["BTEC factorizes B→X_sγ energy flow","New correlator resolves B decay angular structure","B-decay energy flow: no new functions needed","Photon-tagged B decays: one-loop jet kernel","B→X_sγ angular spectrum from known inputs"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000186,"raw_usage":{"total_tokens":1204,"prompt_tokens":825,"completion_tokens":379,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":569,"completion_tokens_details":{"reasoning_tokens":303}},"tokens_in":569,"tokens_out":379,"duration_ms":4153,"temperature":1.0,"reasoning_tokens":303,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T08:41:17.371648+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the resolved-photon soft and jet functions in the same endpoint region and compare their contribution to the fixed-cut cumulative F_i(τ_c) with the direct term; any contribution that is not suppressed by Λ_QCD/Q falsifies the leading-power relation. Experimentally, an independently calibrated shape function propagated to multiple (Eγ, τ_c) bins that yields residuals Δ_i systematically larger than the estimated power corrections would also falsify the factorization.","supporting_citations":[],"review_version":1}