{"id":"039ccf22-f390-4973-952a-4400a83a5b12","arxiv_id":"2505.09686","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The authors deliver the first NNLO QCD plus NLO EW combination of predictions for polarised ZZ pairs at the LHC and validate them across five Monte Carlo codes and against ATLAS simulations.","lead":"This paper provides the most precise Standard Model predictions so far for pairs of Z bosons produced with defined polarizations at the Large Hadron Collider, combining two types of quantum corrections for the first time. The results give experimentalists better templates to search for signs of new physics in electroweak symmetry breaking.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The first-combination claim rests on an unpublished STRIPPER NNLO calculation whose polarised NNLO ingredients are not independently validated in this paper.","rationale":"The reader's weakest assumption is the same one I would flag: the STRIPPER NNLO QCD polarised calculation is unpublished and is the sole source of the NNLO rows that substantiate the 'first combination' headline. I agree with the CONDITIONAL verdict: the paper has substantial independent support at lower orders (four or more independent DPA codes agree at LO and NLO QCD; three at NLO EW; off-shell NNLO checked against Matrix; public Yoda data), and the ATLAS comparison is a useful external sanity check. The absence of PDF uncertainties is real but secondary, since it does not affect the novelty claim. The concern about STRIPPER is a verifiability gap rather than a demonstrated flaw; it can be closed by publication of the companion paper and/or an independent NNLO-polarised benchmark. No reason to reject; the conditional status is appropriate until the NNLO polarised machinery is independently checked.","tokens_in":33303,"tokens_out":6165,"duration_ms":69116,"concrete_test":"Release the companion calculation [116] and reproduce Table 2's LL, LT, TL, TT NNLO QCD fiducial cross sections (0.976(1), 2.107(2), 2.094(2), 10.63(1) fb) with an independent NNLO QCD implementation of the same DPA, or at minimum with the STRIPPER code run on the Eq. (2.11) setup after a public release. If the independent code disagrees with any polarised state beyond the quoted scale uncertainty (roughly 1-2%), the first-combination claim is not supported. The companion paper should also document the DPA singular-limit behaviour of the double-real and real-virtual contributions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of the paper (abstract; Sect. 1) is that this is the first combination of NNLO QCD and NLO EW corrections for polarised ZZ, and the numerical evidence for that claim is the NNLO rows of Tables 2 and 3 and the NNLO curves of Figs. 7 and 8. All of those numbers come exclusively from STRIPPER. Section 2.2 describes the STRIPPER polarised implementation only by reference to a companion paper that is 'in preparation' [116] and to two-loop amplitudes imported from VVamp [76]. The validation reported in the same section consists of an unpolarised, off-shell integrated comparison against Matrix and amplitude-level checks of polarised one-loop amplitudes against Recola. Neither check exercises the genuinely new ingredients of the NNLO-polarised calculation: the DPA-preserving treatment of double-real and real-virtual singular limits, the sector-improved subtraction for polarised projections, and the polarised two-loop amplitudes. Since the NNLO QCD corrections are large and helicity-dependent (+4% for TT, +10% for LL relative to NLO QCD), a mistake in any of these ingredients would shift the headline numbers by more than the quoted scale bands. This is not a demonstrated error, but a verifiability gap in the strongest claim. The unpolarised off-shell Matrix validation cannot constrain the polarised DPA projection at NNLO.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents Standard-Model predictions for the production of two polarised Z bosons decaying into four charged leptons at the 13 TeV LHC, using an ATLAS-like fiducial setup. It compares fixed-order and parton-shower-matched results from several independent Monte Carlo implementations based on the double-pole approximation, the narrow-width approximation, and the decay-chain approach, at LO, NLO QCD, NLO EW, and NNLO QCD accuracy, and studies NNLO QCD + NLO EW combinations, joint polarisation fractions, and comparisons with publicly available ATLAS Run-2 simulation predictions. The central claim is that this is the first combination of NNLO QCD and NLO EW corrections for polarised ZZ production and decay, setting a new perturbative-accuracy benchmark for polarised diboson measurements.","tokens_in":33551,"tokens_out":9241,"duration_ms":94238,"significance":"If the results hold, this paper provides a valuable community benchmark: a systematic comparison of polarisation-signal definitions, parameter-free SM predictions, a large set of integrated and differential results, public numerical data in Yoda format, and a direct comparison with the ATLAS modelling. The extensive cross-validation among several DPA codes at LO, NLO QCD, and NLO EW, and the agreement of the unpolarised off-shell NNLO QCD result with MATRIX, are genuine strengths. The main caveat is that the novel NNLO QCD polarised ingredients are documented only by reference to an unpublished companion paper, so the headline first-combination claim cannot be fully independently assessed from this manuscript alone.","major_comments":[{"comment":"The paper's central claim, the first NNLO QCD + NLO EW combination for polarised ZZ, rests entirely on the STRIPPER NNLO QCD numbers, which are documented only by a reference to an in-preparation companion paper [116], with two-loop amplitudes imported from VVamp [76]. The validation reported in Sect. 2.2 checks the unpolarised off-shell integrated cross section against MATRIX at NNLO QCD and checks polarised one-loop amplitudes against Recola; neither test exercises the genuinely new NNLO-polarised ingredients, namely the DPA-preserving treatment of double-real and real-virtual singular limits, the sector-improved subtraction for polarised projections, and the polarised two-loop amplitudes. Because the NNLO QCD corrections are large and helicity-dependent (+4% for TT and +10% for LL relative to NLO QCD, as quoted in Sect. 3.1), an error in any of these ingredients would shift the headline numbers by more than the quoted scale bands. This is a verifiability gap rather than a demonstrated error, but it is load-bearing for the main claim. Please include a technical description and at least one independent numerical check of the polarised NNLO ingredients in this manuscript, or make the companion paper available and cross-link the two papers explicitly.","section":"Sect. 2.2, STRIPPER paragraph; ref. [116]; Tables 2-3; Figs. 7-8"}],"minor_comments":[{"comment":"The caption of Table 2 should state explicitly that the NNLO QCD rows exclude the loop-induced gg contribution; currently this information appears only in a footnote of Table 1 and in the text of Sect. 3.2.","section":"Table 2 caption"},{"comment":"There is a typo in the list of scale variations: after \"(1, 1)\" a comma is missing before \"(1, 2)\".","section":"Eq. (2.10)"},{"comment":"The axis label in the panel is garbled (\"|ye+, ( + )|\") and should read \"|ye+ - ymu+mu-|\" as in the caption.","section":"Fig. 9(b)"},{"comment":"The text contains a duplicated word in \"The corrections reach up to ~25% for for small Delta-phi\" and a grammar error in \"more the truncated-shower Sherpa results\", which should be \"nor the truncated-shower Sherpa results\".","section":"Sect. 3.2"},{"comment":"The comparison with ATLAS simulations should state even more prominently that the ATLAS curves were constructed using MoCaNLO reweighting factors, so the agreement in Fig. 9 primarily validates the reweighting approximation and the polarisation modelling, not the NNLO QCD part of the predictions as an independent check.","section":"Sect. 3.4"}],"recommendation":"major_revision","confidential_remarks":"This is a well-executed multi-code comparison and a useful community resource, but the editor should note that the central NNLO QCD polarised numbers come from an unpublished companion paper (ref. [116]) by one of the coordinators. I recommend requesting the companion manuscript or a detailed technical appendix as part of the revision, because the current paper's headline claim cannot be fully checked from the material provided. The ATLAS comparison in Sect. 3.4 is not an independent external validation, since the ATLAS-simulation curves already incorporate MoCaNLO reweighting factors; the authors should make this limitation explicit in the revised text."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a solid, genuinely useful precision paper, and the first-combination claim is credible but not fully checkable in this manuscript. The genuinely new things are the NNLO QCD + NLO EW combination for polarised ZZ, the systematic comparison of DPA/NWA/BW signal definitions across several independent codes, and the matched/merged comparisons with ATLAS-style simulations.\n\nWhat earns credit: five independent DPA implementations agree at NLO QCD and NLO EW at the permille-to-percent level; the NWA/BW deviations from the DPA are quantified and explained; the ATLAS reweighting comparison is honest and informative; and the numerical results are released in Yoda format. The paper also openly flags the approximate nature of Sherpa nLO and the poor current modelling of the gg loop-induced channel. That is the right level of transparency.\n\nThe main soft spot is exactly the one the stress-test note identifies. The NNLO QCD rows in Tables 2 and 3, and the NNLO curves in Figs. 7 and 8, come exclusively from STRIPPER, and the polarised NNLO ingredients are delegated to an in-preparation companion paper [116]. The validations reported against Matrix and Recola exercise the unpolarised off-shell calculation and the polarised one-loop amplitudes, but not the genuinely new NNLO-polarised pieces: the DPA-preserving singular limits, the sector-improved subtraction for polarised projections, and the polarised two-loop amplitudes. Since the NNLO shifts are +4% for TT and +10% for LL, relative to NLO QCD, an error in those ingredients would shift the headline numbers by more than the quoted scale bands. This is a verifiability gap, not a demonstrated error, and the paper itself is explicit that the companion paper is in preparation.\n\nA smaller, genuinely minor point: the headline numbers carry QCD-scale uncertainties but not PDF uncertainties. For a comparison paper that is acceptable, but for a paper offering reference predictions to ATLAS and CMS it should either appear or be explicitly postponed.\n\nWho this is for: LHC phenomenologists doing polarisation template fits, and the precision EW community. It deserves a serious referee. My recommendation: accept for peer review, and require that the companion paper be posted or that the STRIPPER NNLO validation be documented in the revision. I would cite it once that companion paper is available.","headline":"A solid, genuinely useful precision paper whose headline NNLO QCD + NLO EW combination for polarised ZZ is credible but rests on an unpublished STRIPPER calculation that the manuscript itself does not fully document.","tokens_in":34191,"tokens_out":1533,"would_cite":true,"duration_ms":18635,"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":"First combination of NNLO QCD and NLO electroweak corrections for polarised Z-boson pairs produced at the LHC, validated across independent Monte Carlo implementations.","keywords":["polarised Z-boson pairs","NNLO QCD","NLO electroweak corrections","double-pole approximation","narrow-width approximation","polarisation fractions","four-lepton final state","LHC phenomenology"],"falsifier":"Compute the NNLO QCD corrections to polarised ZZ production with an independent implementation (for example, a different subtraction scheme or a second set of two-loop amplitudes) and compare the LL, LT, TL, and TT fiducial cross sections in the ATLAS setup; disagreement beyond the quoted 7-point scale uncertainties would overturn the state-of-the-art claim. A direct differential check is the high-transverse-momentum tail of the LL distribution, where the additive combination stays positive while the multiplicative combination can become negative above roughly 250 GeV.","tokens_in":33124,"feed_emoji":"🎯","tokens_out":5706,"duration_ms":57458,"temperature":0.7,"pith_summary":"This paper establishes the most precise Standard-Model predictions to date for the production of pairs of polarised Z bosons decaying to four charged leptons at the LHC. It reports the first combination of next-to-next-to-leading-order (NNLO) QCD corrections with next-to-leading-order (NLO) electroweak corrections for polarised intermediate bosons, and validates the result across several independent Monte Carlo implementations that use different definitions of the polarised signal. If the claim is right, experimental polarisation analyses now have reference cross sections, differential distributions, and joint polarisation fractions with percent-level QCD-scale uncertainties, ready for direct comparison with Run-2 and Run-3 data.","feed_headline":"First NNLO+EW predictions for polarised Z pairs at the LHC","feed_subtitle":"Combining seven codes, the paper sets reference cross sections for polarised Z-boson pairs at the LHC.","key_machinery":"The load-bearing object is the polarisation projector used in the double-pole approximation (DPA) and narrow-width approximation (NWA): the sum over all polarisation states in each Z propagator numerator is replaced by the product of one specific polarisation vector with its conjugate, isolating the longitudinal or transverse state while all matrix-element numerators are evaluated with on-shell projected kinematics. On top of this, the NNLO QCD calculation uses sector-improved residue subtraction with two-loop helicity amplitudes, while the NLO EW calculations use dipole subtraction in the DPA. The paper combines the QCD and EW corrections additively and multiplicatively, which brackets the ambiguity of the combination.","core_discovery":"The central claim is that polarised Z-boson pair production can now be predicted at NNLO QCD + NLO EW accuracy, combining an NNLO QCD calculation based on the double-pole approximation with three independent NLO EW calculations. The paper shows that all polarisation states (LL, LT, TL, TT) can be defined consistently at this accuracy: different on-shell definitions agree within about one to three percent, NNLO QCD adds +4% to +10% depending on polarisation, and NLO EW corrections are negative, reducing the fiducial cross section by about seven to ten percent. The resulting best predictions reproduce the normalisation of ATLAS Run-2 simulations in most angular distributions and pin down the size of non-resonant and interference effects at the percent level.","pith_inferences":["The same additive or multiplicative combination of NNLO QCD and NLO EW corrections could be carried over to polarised WZ and WW production, where the separate ingredients already exist; the ZZ results suggest the correction pattern will depend strongly on polarisation state.","A testable consequence is that current event-generator reweighting in experimental analyses introduces larger biases for observables that probe suppressed LL phase space than for TT, so data in the high-transverse-momentum and large-rapidity-separation region should discriminate.","The observed difference of about 13% between two resummation schemes in the lowest transverse-momentum bin of the LL state suggests that resummation-scheme uncertainty, rather than fixed-order scale variation, may dominate longitudinal-boson transverse-momentum predictions.","Because inclusive joint polarisation fractions shift by only a few percent between NLO and NNLO+EW, detecting new-physics effects through polarisation fractions will likely require differential observables or high-energy tails rather than inclusive rates."],"forward_implications":["Polarised ZZ fiducial cross sections are now available with roughly 1-3% QCD-scale uncertainties (about 2-4% when gluon-fusion loop-induced contributions are included), matching the level needed for current experimental template fits.","The LL polarisation mode receives the largest NNLO QCD correction (about +10%) and the largest shape distortions at high transverse momentum, so future generator predictions should target hard radiation for longitudinal bosons.","Approximate NLO multi-jet merging reproduces the NNLO QCD tails better than pure NLO-plus-shower matching, indicating that hard real radiation, not soft resummation, drives the higher-order QCD effects.","The comparison with ATLAS Run-2 shows that reweighting LO-merged samples by NLO corrections is adequate for angular shapes in the quark channel, but biases kinematic regions probing large rapidity separations and moderate-to-high transverse momenta.","Off-shell and polarisation-interference contributions remain at the percent level; treating them as an explicit separate template, as the paper recommends, would reduce ambiguity in future polarisation-fraction measurements."],"supporting_citations":[{"why":"Supplies the NNLO QCD calculation for polarised ZZ production used to obtain the NNLO rows and the combined predictions.","marker":"[116]"},{"why":"Provides the two-loop helicity amplitudes for quark-induced ZZ production that enter the NNLO QCD matrix elements.","marker":"[76]"},{"why":"Defines the DPA polarisation framework and supplies the NLO QCD and NLO EW predictions used as the electroweak component.","marker":"[15]"},{"why":"Used to validate the off-shell total cross section of the NNLO calculation against an independent code.","marker":"[77]"},{"why":"Demonstrates the NNLO QCD + NLO EW combination for off-shell diboson production, the scheme the paper extends to polarised final states.","marker":"[41]"},{"why":"The ATLAS Run-2 measurement and simulation that the final predictions are compared against.","marker":"[5]"},{"why":"Provides the exact NLO QCD matched-to-shower predictions used to assess parton-shower and resummation effects.","marker":"[22]"},{"why":"Provides the narrow-width-approximation and approximate-NLO matched and merged polarised predictions used in the comparison.","marker":"[21]"}],"fun_headline_variants":["Polarised Z pairs meet NNLO+EW for first time","New gold standard for polarised Z-boson pairs","NNLO+EW unites for polarised Z production","First combined QCD+EW order for polarised Z pairs","Polarised Z pairs get first NNLO+EW predictions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central result assumes that the NNLO QCD calculation for polarised ZZ production in the double-pole approximation is correct, even though its detailed derivation is not described here and is delegated to a companion paper; if that calculation carries an error in the polarised projection or in the subtraction, the quoted NNLO rows and the 'first combination' claim would shift.","fun_headline_variants_meta":{"raw":{"variants":["Polarised Z pairs meet NNLO+EW for first time","New gold standard for polarised Z-boson pairs","NNLO+EW unites for polarised Z production","First combined QCD+EW order for polarised Z pairs","Polarised Z pairs get first NNLO+EW predictions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000426,"raw_usage":{"total_tokens":2172,"prompt_tokens":925,"completion_tokens":1247,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":541,"completion_tokens_details":{"reasoning_tokens":1162}},"tokens_in":541,"tokens_out":1247,"duration_ms":9378,"temperature":1.0,"reasoning_tokens":1162,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:26:41.635380+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the NNLO QCD corrections to polarised ZZ production with an independent implementation (for example, a different subtraction scheme or a second set of two-loop amplitudes) and compare the LL, LT, TL, and TT fiducial cross sections in the ATLAS setup; disagreement beyond the quoted 7-point scale uncertainties would overturn the state-of-the-art claim. A direct differential check is the high-transverse-momentum tail of the LL distribution, where the additive combination stays positive while the multiplicative combination can become negative above roughly 250 GeV.","supporting_citations":[],"review_version":1}