{"id":"c4aa4797-0f0d-4b22-b49a-0379594e004b","arxiv_id":"1908.01783","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"low","formal_verification":"none","parameter_count":2,"one_line_summary":"A next-to-leading-logarithmic factorization and resummation for the soft drop groomed jet radius, including non-global and clustering logarithms, with predictions for the LHC and RHIC.","lead":"This paper computes the soft drop groomed jet radius at next-to-leading logarithmic accuracy in QCD, the observable that measures how far apart the two hard prongs of a groomed jet are. It shows the measurement is equivalent to a jet veto and uses that equivalence to resum logarithms, with a Monte Carlo treatment of non-global effects.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"All-order jet-veto equivalence assumes collinear-soft branches never cluster; clustering corrections are patched only at LL by a Monte Carlo tested at two loops, so a direct MC-vs-exact-soft-drop comparison is needed.","rationale":"The reader's weakest assumption and my concern coincide: Sec. 2.2's all-order proof relies on the absence of clustering among collinear-soft branches, which the paper's own Sec. 2.6 shows is false in the configurations generating Abelian clustering logarithms. That the proof is not exact is not by itself disqualifying—the formal machinery is designed to include clustering corrections—but the completeness of those corrections is the load-bearing point. The factorization in eq. (2.10) assumes the NGL and Abel clustering effects exponentiate as a product independent of the collinear and collinear-soft functions. The paper checks the first nontrivial coefficients at two loops and resums the leading series with a Monte Carlo, but this is an assumption rather than a proof. A direct numerical comparison of the MC's veto logic against the exact C/A soft-drop algorithm on the same final states would settle whether the MC correctly implements the observable to the claimed accuracy. Such a test is computationally simple and does not require new analytic work. Because the central claim depends on this, I recommend conditional acceptance pending this check. If the check passes, the ACCEPT verdict is appropriate; if it fails, the NLL resummation would need correction. This does not impugn the paper's honesty or the value of the framework; it identifies the precise step where the all-order argument has a gap.","tokens_in":25216,"tokens_out":17250,"duration_ms":191473,"concrete_test":"Generate final-state emissions with the paper's dipole Monte Carlo (Sec. 3.1) for fixed R, Rg, zcut, β and large-Nc. Feed the emitted particle list into an exact Cambridge/Aachen clustering plus soft-drop implementation (e.g., FastJet) and measure Rg. Compare this exact Rg distribution with the histogram H_t produced by the MC's own veto logic (Sec. 3.2) on identical events. Agreement within statistical precision over the full t range confirms the clustering treatment; a systematic difference reveals missing clustering configurations in the factorized resummation.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Section 2.2 proves the equivalence between the soft-drop groomed radius and an independent jet veto by induction over N collinear-soft branches, using the statement \"Due to angular ordering the collinear-soft branches Ji are not clustered together\" (θJi,Jj > θJi(j),J). This is not guaranteed by the collinear-soft power counting: two emissions at angles θ1, θ2 ~ Rg with azimuthal separation φ satisfy d12 < d1 whenever θ2^2 − 2θ1θ2 cos φ < 0, which is allowed phase space. In such configurations C/A clusters the two soft branches first, and the declustering tree tests the combined branch k12. Appendix A (eq. A.11) shows the resulting NNLO measurement contains an extra term Θ(θ1J−θ12)Θ(θ2J−θ12)[M1(k12)−M1(k1)M1(k2)] relative to the independent veto product. The paper absorbs such effects into the factorized NGL and Abelian clustering functions in eq. (2.10), resummed at LL and leading color by the Monte Carlo of Sec. 3. The factorization of these corrections as a multiplicative product is validated only at two loops (Figs. 3-4); if the corrections do not exponentiate in this form at higher orders, the NLL claim would miss terms. The MC's clustering rule in Sec. 3.2 implements the same no-clustering-before-hard-branch picture and has not been directly checked against the exact C/A soft-drop algorithm on its own generated phase space. Pythia agreement is encouraging but is not a controlled test of the factorization.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents a factorization-based resummation of the soft drop groomed jet radius R_g (equivalently θ_g = R_g/R) at next-to-leading logarithmic accuracy. The authors develop an SCET refactorization of the semi-inclusive jet function in the limit z_cut ≪ 1, θ_g ≪ 1, based on an asserted all-order equivalence between the soft drop declustering measurement and a jet veto in the angular region between the groomed and ungroomed jet boundaries. They compute the collinear and collinear-soft functions to NLO, compute the leading non-global logarithms and the leading Abelian Cambridge/Aachen clustering logarithms at NNLO, and resum these corrections at leading logarithmic accuracy in the large-N_c limit with a dipole Monte Carlo algorithm. The resulting NLL distributions are compared with Pythia 8 for LHC kinematics, and predictions are provided for STAR/RHIC kinematics. The paper openly states in Section 2.7 that the subleading non-global and clustering logarithms are not fully conclusive, and it describes the nonperturbative freezing of α_s used in the low-scale region.","tokens_in":25541,"tokens_out":9518,"duration_ms":101777,"significance":"If the framework is correct, this is the first NLL calculation of the soft drop groomed jet radius, an observable that is important for jet substructure and for heavy-ion applications. The paper's strengths are the explicit closed-form NLO collinear and collinear-soft functions, the explicit NNLO phase-space check in Appendix A, the transparent Monte Carlo algorithm for non-global and clustering logarithms, and the parameter-free comparison with Pythia 8. The main risk is the precise status of the claimed all-order jet-veto equivalence and the extent to which the Monte Carlo correctly captures the exact C/A clustering structure; the paper is candid about some of these limitations but not about all of them.","major_comments":[{"comment":"The induction proof of the all-order equivalence M_N = ∏_i M1(J_i) rests on the assertion that 'Due to angular ordering the collinear-soft branches J_i are not clustered together.' This assertion is not guaranteed by the collinear-soft power counting: two emissions with θ_1, θ_2 ~ R_g and azimuthal separation φ satisfy d_12 < d_1 whenever θ_2^2 - 2 θ_1 θ_2 cos φ < 0, so the C/A tree can cluster the two soft branches before either clusters with the hard branch. The authors' own NNLO calculation, eq. (A.11), contains the residual term Θ(θ_1J−θ_12)Θ(θ_2J−θ_12)[M1(k_12)−M1(k_1)M1(k_2)] relative to the independent-veto product. Thus the induction in Sec. 2.2 proves the equivalence only in the channel without mutual clustering, and the abstract's claim of an 'all order equivalence to a jet veto' overstates the result. Please qualify the equivalence as holding modulo C/A clustering corrections and state explicitly how the factors S^C/A_i,NGL and A^C/A_i,Abel in eq. (2.10) and the Monte Carlo of Sec. 3 absorb those corrections at the claimed accuracy.","section":"Sec. 2.2 / App. A"},{"comment":"The NLL claim depends on the Monte Carlo of Sec. 3 resumming the non-global and Abelian clustering logarithms with the same C/A clustering prescription as the exact soft drop algorithm. The only quantitative validation of the Monte Carlo is the small-t comparison with the two-loop coefficients in Figs. 3-4, and the Pythia comparison is not a controlled test of the factorization. I request either a direct comparison of the Monte Carlo's veto and clustering rule against an exact implementation of the C/A soft drop algorithm on Monte Carlo-generated phase space (for example at fixed order in the small-t region), or an explicit argument that the clustering rule in eq. (3.2) together with the veto prescription in Sec. 3.2 is exact at leading logarithmic accuracy for this observable. Without such a check, the statement that the resummation is at NLL, rather than at NLL for the global logs plus an assumed LL treatment of clustering effects, is not fully supported.","section":"Sec. 3"}],"minor_comments":[{"comment":"The text states that the impact of subleading NGLs and clustering logarithms is 'not yet conclusive' but then uses the leading-log treatment in the main predictions. This caveat should be repeated in the conclusions when the overall accuracy is summarized as NLL.","section":"Sec. 2.7"},{"comment":"In the bullet list at the end of Section 3.1, 'See App. 3.4' should read 'See Sec. 3.4'.","section":"Sec. 3.1"},{"comment":"The abbreviation 'f.c.' in eq. (2.51) is not defined; please spell out 'fixed-coupling' at first use.","section":"Eq. (2.51)"},{"comment":"The sentence 'Therefore, to we need to insert the constraint' contains a grammatical typo and should be corrected.","section":"Sec. 2.5"},{"comment":"The sentence 'We result is plotted as a function of θ_g' should read 'The result is plotted as a function of θ_g'.","section":"Fig. 2 caption"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper gives the first NLL treatment of the soft drop groomed jet radius R_g. The factorization theorem, the explicit NLO collinear and collinear-soft functions, the NNLO non-global and Abelian clustering coefficients, and the Monte Carlo resummation are all real additions; the MLL result of Larkoski et al. is cleanly recovered as a limit. The comparison to Pythia is honest, no parameters are fitted, and the paper openly names its main limitations. This is solid, careful work and deserves a serious referee.\n\nThe soft spot is the all-order equivalence to a jet veto. Section 2.2's induction proof leans on the statement that collinear-soft branches are never clustered together, due to angular ordering. That is not guaranteed by the collinear-soft power counting: two emissions at angles of order R_g can satisfy d_12 < d_1, so the C/A algorithm clusters them first. Appendix A actually shows this, since eq. (A.11) contains an extra term for the clustered configuration. The authors know this and absorb the correction into the NGL and Abelian clustering functions, resummed at LL and leading color by the Monte Carlo. But then the \"all order equivalence\" is really an equivalence up to corrections patched by an MC validated at two loops. The NLL claim is conditional on the exponentiated form of those corrections, and that is not fully closed.\n\nThe Pythia agreement is encouraging but not a controlled test of the factorization; the MC and Pythia share similar leading-log emission logic. A direct comparison of the MC clustering rule to the exact soft-drop algorithm on the same generated phase space would be the right way to close the gap. Power corrections near theta_g = 1 and the alpha_s freezing procedure are minor and are acknowledged.\n\nOverall, I trust the global-logarithm part of the calculation; the non-global/clustering sector is handled in the standard way but with a visible caveat. I would send this to peer review, asking the authors to confront the clustering assumption explicitly and to add the direct MC check. The paper is mainly for jet substructure and resummation practitioners, and it will be useful to them.","headline":"A genuinely new NLL calculation of the soft drop groomed jet radius, with an all-order equivalence claim that is slightly stronger than the proof supports; worth serious review.","tokens_in":26095,"tokens_out":3460,"would_cite":true,"duration_ms":38571,"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":"This paper proves an all-order equivalence between the soft drop groomed radius and a jet veto, which makes the observable predictable at next-to-leading-logarithmic accuracy.","keywords":["soft drop grooming","groomed jet radius","jet substructure","factorization theorem","resummation","non-global logarithms","Cambridge/Aachen clustering","jet veto"],"falsifier":"An explicit next-to-next-to-leading-order evaluation of the configuration in which two collinear-soft emissions have the smallest mutual distance and cluster before either joins the hard branch would settle the equivalence: if the soft drop measurement there differs from the independent-veto product $M_1(k_1)M_1(k_2)$, the factorized non-global logarithm and the $4/9$ clustering reduction would need revision. The experimental side of the same check is a high-statistics comparison of the resummed $\\theta_g$ distribution with LHC data at $p_T>600$ GeV and $z_{\\rm cut}=0.1$, $\\beta=0,1,2$.","tokens_in":25013,"feed_emoji":"📐","tokens_out":8552,"duration_ms":81603,"temperature":0.7,"pith_summary":"The paper claims that the radius of a soft-drop-groomed jet — the opening angle between the two branches that survive grooming — can be predicted at next-to-leading-logarithmic accuracy. The key move is a proof that, when the groomed radius and the soft threshold are small, the soft drop declustering procedure is equivalent, to all orders, to a jet veto on the region between the groomed and the original jet boundaries. That equivalence puts the observable inside an existing factorization theorem, so the large logarithms of the groomed radius, the jet radius, and the soft-drop threshold can be resummed. Non-global logarithms and clustering effects from the Cambridge/Aachen reclustering are resummed with a Monte Carlo algorithm, and the resulting distribution matches a parton-shower simulation.","feed_headline":"Groomed jet radius predicted at next-to-leading-log accuracy","feed_subtitle":"A new proof equates the groomed radius with a jet veto, taming clustering effects and matching parton showers.","key_machinery":"The load-bearing identity is the soft-drop/jet-veto equivalence: for angular-ordered collinear-soft branches $J_i$, the soft drop measurement function obeys $M_N=\\prod_i M_1(J_i)$, where $M_1$ keeps a branch inside the groomed radius $R_g$ or vetoes it if it lies outside and below the soft-drop threshold. This turns the groomed-radius measurement into independent veto constraints and is what separates the collinear and collinear-soft functions in the factorization. The paper carries the all-order resummation with a dipole Monte Carlo that implements the veto and the Cambridge/Aachen clustering rule, resumming the non-global and Abelian clustering logarithms at leading-logarithmic accuracy; fixed-order calculations of the first coefficients $S^{C/A}_{i,2}$ and $A^{C/A}_{i,2}$, including the $4/9$ reduction of the non-global logarithm from clustering, anchor the resummation at two loops.","core_discovery":"On the paper's own terms, the central result is a factorization theorem for the cumulative soft drop groomed jet radius $\\theta_g=R_g/R$ in the double-small limit $z_{\\rm cut}\\ll 1$, $\\theta_g\\ll 1$. The semi-inclusive jet function is refactorized into hard, soft, collinear, and collinear-soft functions, and the novel ingredient is the all-order equivalence proven in Section 2.2: measuring $\\theta_g$ is the same as vetoing every collinear-soft branch that lies outside the groomed-radius cone and above the threshold $z_{\\rm cut}\\theta_g^{\\beta}p_T$. Because the veto constraint is independent for each branch, the measurement function factorizes into a product of single-branch constraints, and the resulting non-global and Cambridge/Aachen clustering logarithms can be resummed at leading-logarithmic accuracy by a Monte Carlo algorithm in the large-$N_c$ limit. With canonical scale choices the framework reproduces the earlier modified-leading-log result at leading accuracy and goes beyond it; the resummed distribution agrees with the parton-shower comparison for $\\beta=0,1,2$.","pith_inferences":["If the equivalence is as general as the proof indicates, other groomed observables that fix only the declustering angle — groomed jet mass, groomed angularities — should admit the same veto mapping, unifying their resummations.","Event generators with recoil or with emissions that are not angularly ordered could expose the numerical size of the power corrections the factorization drops, especially when two collinear-soft branches sit close together.","The $\\beta=0$ (mMDT) case, where the groomed jet shrinks most and hadronization shifts are smallest, is the cleanest place for data to discriminate NLL resummation from the earlier modified-leading-log result."],"forward_implications":["The groomed radius distribution becomes a resummed, perturbatively controlled observable that can be compared with LHC and RHIC data at next-to-leading-logarithmic accuracy.","All jet-veto resummation technology, including non-global logarithms and clustering corrections, transfers to soft-drop groomed substructure through the proven equivalence.","Quark-versus-gluon jet fractions and logarithms of the original jet radius are included systematically beyond leading order through the flavor-dependent refactorization.","The framework is extendable beyond NLL and can be matched to fixed-order calculations, so the accuracy of the groomed-radius prediction is not a dead end."],"supporting_citations":[{"why":"defines the soft drop grooming algorithm and the groomed radius $R_g$ that is the subject of the paper.","marker":"[4]"},{"why":"supplies the dipole Monte Carlo technique for resumming non-global logarithms that the paper adapts to the groomed-radius veto.","marker":"[50]"},{"why":"provides the analysis of Abelian clustering logarithms and their exponentiation used to identify the clustering corrections.","marker":"[53]"},{"why":"is the direct predecessor that resums non-global and clustering effects for groomed multi-prong jet shapes.","marker":"[58]"},{"why":"establishes the effective-field-theory refactorization of jet processes from which the collinear and collinear-soft functions are taken.","marker":"[70]"},{"why":"supplies the jet-veto resummation results on which the equivalence argument leans.","marker":"[75]"},{"why":"provides the parton-shower Monte Carlo used as the baseline for the numerical comparison.","marker":"[82]"}],"fun_headline_variants":["Soft drop jet radius at NLL: veto equivalence proof","Groomed radius resummed via jet veto equivalence","NLL accuracy for groomed jet radius, Pythia8 matched","Taming non-global logs in groomed jet radius","New factorization for soft drop groomed radius"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument requires that the soft wide-angle emissions inside a jet are angularly ordered, so that no two such emissions cluster together before either clusters with the hard core; if that ordering fails at the required accuracy, the claimed identity between soft drop and a jet veto breaks down.","fun_headline_variants_meta":{"raw":{"variants":["Soft drop jet radius at NLL: veto equivalence proof","Groomed radius resummed via jet veto equivalence","NLL accuracy for groomed jet radius, Pythia8 matched","Taming non-global logs in groomed jet radius","New factorization for soft drop groomed radius"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000322,"raw_usage":{"total_tokens":1801,"prompt_tokens":923,"completion_tokens":878,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":539,"completion_tokens_details":{"reasoning_tokens":797}},"tokens_in":539,"tokens_out":878,"duration_ms":9522,"temperature":1.0,"reasoning_tokens":797,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T15:03:55.680101+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"An explicit next-to-next-to-leading-order evaluation of the configuration in which two collinear-soft emissions have the smallest mutual distance and cluster before either joins the hard branch would settle the equivalence: if the soft drop measurement there differs from the independent-veto product $M_1(k_1)M_1(k_2)$, the factorized non-global logarithm and the $4/9$ clustering reduction would need revision. The experimental side of the same check is a high-statistics comparison of the resummed $\\theta_g$ distribution with LHC data at $p_T>600$ GeV and $z_{\\rm cut}=0.1$, $\\beta=0,1,2$.","supporting_citations":[{"cited_title":"Resummation of jet-veto logarithms in hadronic processes containing jets","cited_arxiv_id":"1210.1906","evidence_quote":"supplies the jet-veto resummation results on which the equivalence argument leans."}],"review_version":1}