{"id":"dc2dfd84-e27b-4608-8f16-78627fe7bdc7","arxiv_id":"2412.16095","paper_version":2,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Exact mixed QCD-EW corrections at order alpha_s alpha to neutral-current Drell-Yan production are computed and applied to distributions, the forward-backward asymmetry, and dressed leptons.","lead":"This paper reports a complete calculation of the combined strong and electroweak corrections to the Drell-Yan process, in which proton collisions produce a muon pair. The result covers the whole range of dimuon masses and is needed for percent-level precision predictions at the LHC.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Summary's 'no approximation' claim conflicts with the admitted neglect of top-mass effects in two-loop virtuals; if the induced error is not negligible, the exactness claim fails.","rationale":"The central claim, as stated by the reader, is that the O(alpha_s alpha) contribution is known exactly. The most load-bearing condition for that claim is therefore the absence of any approximation in the ingredients. The paper itself states an exception (top-mass neglect in two-loop virtuals), and the Summary's \"no approximation\" sentence is false as written. I considered the reader's candidate weakest assumption, the qT-subtraction abelianisation: that is indeed the most catastrophic potential failure mode, but it is supported by rcut stability, lepton-mass independence, and by agreement with the independent calculation of Ref. [55] in the qqbar channel (which contains the two-loop virtuals) after the Ref. [55] bug was fixed. So I do not regard that as the most load-bearing concern. The top-mass neglect is a definite, admitted omission with an unconvincing error estimate; its numerical impact is not quantified. The unresolved quark-photon 10% difference with Ref. [55] is a further stated limitation, but the channel is numerically small. A quantitative re-evaluation with exact mt would settle whether the exactness claim is merely over-worded or numerically wrong. Therefore I recommend CONDITIONAL acceptance pending that check and a corrected Summary.","tokens_in":23441,"tokens_out":12156,"duration_ms":113947,"concrete_test":"Recompute the two-loop virtual amplitude with exact top-mass dependence (or with the mt -> infinity and mt -> 0 limits) for representative phase-space points and re-evaluate the fiducial cross sections and AFB distributions with the resulting shift. If the shift is below the quoted scale uncertainties, the numerical results stand but the Summary must be corrected; if not, the central claim of exactness and the \"entire range\" statement require revision.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Section 2 states that in the two-loop virtual corrections \"we neglect top-mass effects\", while the Summary (Sec. 5) asserts \"Our calculation does not rely on any approximation\". These statements are incompatible. The two-loop virtual amplitude [56] is a central ingredient of the O(alpha_s alpha) result; neglecting mt introduces a scheme-dependent omission at that order. The error estimate in Sec. 2 (\"at the percent level of the computed correction\") is justified by the smallness of the bottom-quark density, but that argument does not apply to top-mass dependence in q qbar -> l+ l- amplitudes, which is not suppressed by bottom PDFs. Hence the size of the induced error is not demonstrated. This directly affects the strongest claim that the O(alpha_s alpha) contribution is known exactly and holds in the entire invariant-mass range. A secondary, unresolved factual issue is the 10% discrepancy with Ref. [55] in the quark-photon channel (Sec. 4, Table 2), which the authors state they cannot currently assess because channel uncertainties are not provided.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents the computation of the O(alpha_s alpha) mixed QCD-electroweak corrections to the neutral-current Drell-Yan process pp -> mu+ mu- + X, using massive muons, exact two-loop amplitudes, and a qT-subtraction formalism obtained by abelianising the NNLO QCD heavy-quark pair production results. The authors give phenomenological results for bare muons in the resonant and high-invariant-mass regions, for the forward-backward asymmetry, and for dressed leptons, including a comparison with the massless-lepton calculation of Ref. [55]. The calculation is a parameter-free Standard Model prediction: no observable is fitted, and all couplings, masses, and PDFs are taken from external sources. The main methodological inputs are the two-loop amplitudes of Ref. [56], one-loop amplitudes checked with OpenLoops and Recola, and the Matrix framework for phase-space integration and subtraction.","tokens_in":23583,"tokens_out":7455,"duration_ms":70394,"significance":"If the result is correct, this is a milestone for precision Standard Model phenomenology: it provides the first complete computation of the mixed QCD-electroweak corrections to the neutral-current Drell-Yan process over the full invariant-mass range, including two-loop virtual effects. The paper contains several strong internal and external checks: pointwise agreement between OpenLoops and Recola, stable rcut extrapolations for two lepton masses, reproduction of NNLO QCD and NLO EW benchmark results, and a documented collaboration with the authors of Ref. [55] to identify and fix a bug in the independent massless calculation. These checks support the credibility of the central claim. The main caveat is that the Summary's assertion that the calculation 'does not rely on any approximation' is not literally consistent with the treatment of top-mass effects in the two-loop virtual corrections, as discussed below. The residual small discrepancy in the quark-photon channel also deserves a more explicit treatment, but it does not appear to affect the main quantitative conclusions.","major_comments":[{"comment":"The Summary's opening statement that 'Our calculation does not rely on any approximation and holds in the entire range of dilepton invariant masses' is not consistent with Sec. 2, where the authors state that in the two-loop virtual corrections 'we neglect top-mass effects.' The accompanying error estimate, based on the smallness of the bottom-quark density, applies only to bottom-initiated channels; top-mass effects in the two-loop virtual corrections to q qbar -> l+ l- are not suppressed by the bottom PDF, so the percent-level estimate does not cover the actual source of the approximation. Since the claim of exactness over the full m_mumu range is the paper's headline result, please either quantify the neglected top-mass dependence (for example by computing a representative two-loop virtual contribution with and without m_t) or reformulate the Summary to state that the calculation is complete at O(alpha_s alpha) except for the treatment of m_t in the two-loop virtual amplitude.","section":"Summary (Sec. 5) and Sec. 2"},{"comment":"The comparison with the massless calculation of Ref. [55] leaves the quark-photon channel unresolved: the present result, sigma^(1,1) = -0.231(9) pb, is about 10% larger than the corresponding result of Ref. [55], and the authors write that they cannot assess the significance because Ref. [55] does not provide per-channel uncertainties. Since this comparison is one of the main validation pillars of the calculation, please report the uncertainty on the q-gamma contribution in a way that allows an assessment (including the numerical result of Ref. [55]), or provide an additional independent check of this channel. The small absolute size of the channel means this is not a reason to doubt the main results, but it should be resolved or explicitly carried as an uncertainty in the Summary.","section":"Sec. 4, Table 2"}],"minor_comments":[{"comment":"Reference [6] is incomplete: it lists the title of the CMS W-mass measurement but has no arXiv identifier or DOI; please complete the entry.","section":"References"},{"comment":"The notation dsigma^(0,1)_γγ,m_l=0 on the left-hand side and dsigma^(0,1)_γγ,m_l on the right-hand side is confusing; please define explicitly that the latter is the massive-theory result and that the logarithmic term is the scheme-compensation contribution from the photon PDF.","section":"Sec. 4, Eq. (14)"},{"comment":"In the bottom-left panel (quark-gluon channel), the tick labels on the horizontal axis appear garbled in the manuscript and are not readable; please regenerate the figure.","section":"Fig. 7"},{"comment":"The label 'NNLOMIX' is used inconsistently: the text defines it as including only mixed QCD-EW corrections on top of LO, but the figure legend appears to use the same label for the full NLOQCD+NLOEW+NNLOMIX prediction. Please clarify the notation in the figure caption.","section":"Sec. 3.3 and Fig. 5"},{"comment":"The Summary reports only the quark-gluon discrepancy with Ref. [55] as disappearing after the bug fix, but does not mention the residual quark-photon discrepancy discussed in Sec. 4; please add a sentence for completeness.","section":"Sec. 5"}],"recommendation":"minor_revision","confidential_remarks":"The technical achievement is very strong and the cross-checks are unusually thorough. I would not block this paper. The requested changes are local: qualify the 'no approximation' claim, quantify or explicitly document the top-mass treatment, and provide a more complete statement about the residual quark-photon discrepancy. The paper's central result is sound and represents an important step forward for precision Drell-Yan phenomenology."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is the real thing. The paper delivers exact O(alpha_s alpha) corrections to neutral-current Drell-Yan with full off-shell kinematics and massive muons, and it extends the earlier Letter [54] with the FB asymmetry in the CMS 8 TeV setup, dressed-lepton results, the massless extrapolation, and a channel-by-channel comparison with the independent calculation of Ref. [55]. The two-loop amplitudes and master integrals were published before, so the novelty is not the amplitude; it is the complete hadronic implementation and the phenomenological map. That is still a substantial piece of work.\n\nThe cross-checks are what make it believable: one-loop amplitudes agree pointwise between OpenLoops and Recola, the rcut extrapolation is stable for the muon mass and for a 1 GeV lepton mass, NNLO QCD and NLO EW channels reproduce known results, and the earlier quark-gluon discrepancy with Ref. [55] vanished once the other group fixed its bug. The qT subtraction coefficients are imported from heavy-quark pair production by abelianisation, so there is a methodological dependency on published work, but the paper is transparent about that and the numerical checks give no reason to distrust it.\n\nThe main flaw is in the text, not the math. The Summary states \"Our calculation does not rely on any approximation,\" while Sec. 2 says top-mass effects are neglected in the two-loop virtual corrections. Those two statements do not square. The error estimate in Sec. 2, based on the small bottom-quark density, applies to bottom-initiated channels, not to the q qbar annihilation channel where top quarks also enter via loops. The actual numerical impact may well be small, but the paper does not demonstrate that directly, and the \"no approximation\" claim is too strong as written. This is a minor revision issue: soften the claim or supply a direct estimate.\n\nThe unresolved 10% difference with Ref. [55] in the q-gamma channel is a loose end, but that channel contributes about -0.23 pb out of a ~1900 pb cross section; it cannot affect any physical conclusion. The authors are right to flag it rather than paper over it.\n\nWho gets value: anyone doing precision DY phenomenology, PDF fits at large x, or weak mixing angle extraction. It deserves a serious referee and, after the wording fix, publication.","headline":"Exact mixed QCD-EW corrections to NC Drell-Yan, well cross-checked and phenomenologically important; the Summary overclaims 'no approximation' given the admitted top-mass neglect, but that is a wording fix, not a fatal flaw.","tokens_in":24186,"tokens_out":3033,"would_cite":true,"duration_ms":27978,"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":"The complete mixed QCD-electroweak correction to neutral-current Drell-Yan production is now computed exactly, without pole approximation, over the full dilepton-mass range.","keywords":["Drell-Yan process","mixed QCD-electroweak corrections","NNLO","qT subtraction","forward-backward asymmetry","effective weak mixing angle","dressed leptons","LHC precision physics"],"falsifier":"Perform an independent calculation of the $O(\\alpha_s \\alpha)$ neutral-current Drell-Yan cross section in the same fiducial setup using a local infrared-subtraction method instead of $q_T$ slicing; if the $r_{\\rm cut}\\to 0$ limit differs from the abelianised prediction by more than the quoted Monte Carlo uncertainties, in particular in the quark-antiquark or quark-gluon channels, then the imported coefficient is incomplete. A sharper version is to compute the pure-soft region of the double-real and real-virtual amplitudes at fixed lepton mass and check analytically that the abelianised counterterm cancels all $\\ln r_{\\rm cut}$ and constant terms.","tokens_in":23216,"feed_emoji":"⚛️","tokens_out":10674,"duration_ms":92758,"temperature":0.7,"pith_summary":"This paper reports the complete computation of the mixed strong-electroweak corrections, the term of order $O(\\alpha_s \\alpha)$, to the neutral-current Drell-Yan process, in which a lepton pair is produced through an off-shell photon or $Z$ boson in hadron collisions. The calculation is performed without any pole approximation and is claimed to hold across the entire range of dilepton invariant masses, from the $Z$ resonance to multi-TeV tails. The result matters for precision Standard Model studies because Drell-Yan data anchor measurements of the $W$ mass, the effective weak mixing angle, and proton parton distribution functions, and because percent-level corrections of this kind are needed to interpret high-luminosity LHC measurements. The mixed corrections are small for inclusive fiducial rates, around $-0.4\\%$ for bare muons, but they reach several percent in kinematical regions, notably with a nontrivial shape distortion around the $Z$ peak and a correction growing to about $-5\\%$ in the high-mass tail.","feed_headline":"Exact mixed QCD-electroweak correction now covers all Drell-Yan masses","feed_subtitle":"The mixed strong-electroweak piece for muon-pair production is now exact, reshaping the Z peak and the high-mass tail.","key_machinery":"The load-bearing mechanism is the transverse-momentum ($q_T$) subtraction identity $\\mathrm{d}\\sigma^{(1,1)}=H^{(1,1)}\\otimes \\mathrm{d}\\sigma_{\\rm LO}+[\\mathrm{d}\\sigma_R^{(1,1)}-\\mathrm{d}\\sigma_{\\rm CT}^{(1,1)}]$, which splits the mixed correction into an infrared-finite hard coefficient $H^{(1,1)}$, a real-emission piece regulated by a cut $r_{\\rm cut}$ on $q_T/m_{\\mu\\mu}$, and a counterterm that cancels the $r_{\\rm cut}\\to 0$ divergence. The new element is that $H^{(1,1)}$ and the counterterm are not derived from scratch; they are obtained by abelianising the NNLO QCD heavy-quark pair-production results, a route that works because the Drell-Yan final state is colour neutral, so final-state radiation is purely QED and the soft-parton structure simplifies. The two-loop virtual amplitude enters exactly, reduced to master integrals and evaluated through series expansions of the differential-equation method with the vector-boson masses kept complex in the complex-mass scheme.","core_discovery":"The paper establishes that the $O(\\alpha_s \\alpha)$ contribution to the neutral-current Drell-Yan cross section $pp\\to \\mu^+\\mu^-+X$ can be evaluated exactly, with no pole approximation and no restriction on the dilepton invariant mass, combining the exact two-loop virtual amplitude with all real-radiation and subtraction pieces. For bare muons in a standard 13.6 TeV fiducial setup, the mixed correction is $-0.4\\%$ of the Born cross section, but the invariant-mass distribution shows a nontrivial pattern: nearly zero at the $Z$ peak, about $+4\\%$ below the peak and $-2\\%$ above it, where the simple factorised product of QCD and electroweak corrections fails. In the high-mass region above 150 GeV the correction becomes increasingly negative, reaching about $-5\\%$ at 2 TeV, a size comparable to the statistical precision expected at the high-luminosity LHC. The forward-backward asymmetry receives mixed-correction shifts that are larger than the pure QCD shifts and grow with the rapidity of the dilepton system, which is relevant for future extractions of $\\sin^2\\theta_{\\rm eff}$. The calculation also extends to dressed leptons, using the muon mass as a physical regulator of final-state collinear singularities, and the results can be extrapolated to the massless limit; comparison with an independent massless-lepton calculation agrees after a bug in the comparison calculation was corrected.","pith_inferences":["Editorial inference: if the abelianised $q_T$-subtraction route is as complete as the $r_{\\rm cut}$ and lepton-mass checks suggest, the same method should supply $O(\\alpha_s \\alpha)$ corrections for other colourless electroweak final states, such as diboson or Higgs production, once the corresponding two-loop amplitudes become available.","Editorial inference: the demonstration that a finite lepton mass can regulate final-state collinear QED singularities and then be extrapolated away suggests a general recipe for non-collinear-safe observables in other processes: compute with massive leptons, apply the recombination prescription, then take $m_\\ell\\to 0$ and adjust the photon-PDF scheme, avoiding ad hoc photon-isolation requirements","Editorial inference: the failure of the factorised ansatz below the $Z$ peak implies that shower-based predictions relying on multiplicative QCD $\\times$ EW corrections should be benchmarked against the exact result bin by bin before claiming few-permille accuracy in the resonant region."],"forward_implications":["Exact mixed QCD-electroweak corrections can now be included in Standard Model reference predictions across the full dilepton-mass range, removing a previously uncontrolled approximation in precision Drell-Yan phenomenology.","For bare muons, the mixed correction shifts the invariant-mass distribution by about $+4\\%$ below the $Z$ peak and $-2\\%$ above it, with an almost flat $-0.4\\%$ effect on the fiducial cross section, and the factorised QCD $\\times$ EW ansatz fails below the resonance.","In the high-mass region the correction becomes more negative with invariant mass, reaching about $-5\\%$ at 2 TeV, a shift comparable to the expected high-luminosity LHC statistical precision that should be accounted for in new-physics searches and PDF fits.","Future template extractions of $\\sin^2\\theta_{\\rm eff}$ from the forward-backward asymmetry need to include these corrections: the mixed shifts in the asymmetry are larger than the NLO QCD shifts and increase with dimuon rapidity.","Dressed-lepton predictions can be extrapolated to the massless-lepton limit, providing a benchmark for calculations and event generators that treat photon radiation with different recombination prescriptions."],"supporting_citations":[{"why":"Supplies the exact two-loop mixed QCD-EW amplitudes for the neutral-current Drell-Yan process used in the purely virtual part.","marker":"[56]"},{"why":"Defines the master integrals onto which the two-loop amplitudes are reduced.","marker":"[57]"},{"why":"Provides the $q_T$ subtraction identity that splits the correction into hard coefficient, real contribution, and counterterm.","marker":"[88]"},{"why":"Provides the NNLO QCD heavy-quark pair-production results from which the mixed $H^{(1,1)}$ and counterterm are obtained by abelianisation.","marker":"[89–91]"},{"why":"Supplies the abelianisation procedure and its application to electroweak corrections that turns the QCD subtraction terms into mixed QCD-EW ones.","marker":"[38, 92]"},{"why":"Provides the initial-state soft/collinear and purely collinear ingredients needed for the mixed correction.","marker":"[39]"},{"why":"The companion letter reporting first results of the exact mixed correction; this paper gives the detailed phenomenological study and extensions.","marker":"[54]"},{"why":"The independent massless-lepton mixed QCD-EW calculation used for the dressed-lepton comparison in the massless limit.","marker":"[55]"},{"why":"Implements the semi-analytic differential-equations method used to evaluate the master integrals with complex masses.","marker":"[60]"},{"why":"Defines the complex-mass scheme that keeps the $W$ and $Z$ masses and widths complex-valued throughout the computation.","marker":"[87]"}],"fun_headline_variants":["Exact mixed QCD-EW correction now spans all Drell-Yan masses","Mixed QCD-EW corrections exact for all dilepton masses","Z peak, high mass: exact mixed QCD-EW Drell-Yan corrections","Exact mixed QCD-EW shifts Drell-Yan asymmetry and mass tail","Non-trivial pattern: exact mixed QCD-EW for Drell-Yan"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the transverse-momentum subtraction hard coefficient and counterterm, imported from heavy-quark pair-production results by abelianisation, contain every soft and collinear contribution specific to the colourless muon-pair final state, a point the paper tests with $r_{\\rm cut}$ and lepton-mass stability rather than by an independent derivation.","fun_headline_variants_meta":{"raw":{"variants":["Exact mixed QCD-EW correction now spans all Drell-Yan masses","Mixed QCD-EW corrections exact for all dilepton masses","Z peak, high mass: exact mixed QCD-EW Drell-Yan corrections","Exact mixed QCD-EW shifts Drell-Yan asymmetry and mass tail","Non-trivial pattern: exact mixed QCD-EW for Drell-Yan"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000736,"raw_usage":{"total_tokens":3289,"prompt_tokens":944,"completion_tokens":2345,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":560,"completion_tokens_details":{"reasoning_tokens":2242}},"tokens_in":560,"tokens_out":2345,"duration_ms":15626,"temperature":1.0,"reasoning_tokens":2242,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T10:47:30.572089+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Perform an independent calculation of the $O(\\alpha_s \\alpha)$ neutral-current Drell-Yan cross section in the same fiducial setup using a local infrared-subtraction method instead of $q_T$ slicing; if the $r_{\\rm cut}\\to 0$ limit differs from the abelianised prediction by more than the quoted Monte Carlo uncertainties, in particular in the quark-antiquark or quark-gluon channels, then the imported coefficient is incomplete. A sharper version is to compute the pure-soft region of the double-real and real-virtual amplitudes at fixed lepton mass and check analytically that the abelianised counterterm cancels all $\\ln r_{\\rm cut}$ and constant terms.","supporting_citations":[{"cited_title":"Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering","cited_arxiv_id":"1604.08581","evidence_quote":"Defines the master integrals onto which the two-loop amplitudes are reduced."}],"review_version":1}