Infrared Safe but Infinite: Soft-Gluon Divergences Inside the Physical Region

B.R. Webber; S. Catani

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Infrared Safe but Infinite: Soft-Gluon Divergences Inside the Physical Region

S. Catani, B.R. Webber

High Energy Physics - Phenomenology · Submitted 13 Oct 1997 · 26 references

Pith's verdict: The fixed-order mechanism is correct and cleanly derived; the resummation half is a double-logarithmic sketch, and the abstract's 'to all orders' slightly outruns Sect. 4.

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arXiv IDhep-ph/9710333 (version 1)

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CitationB.R. Webber, S. Catani. "Infrared Safe but Infinite: Soft-Gluon Divergences Inside the Physical Region." arXiv:hep-ph/9710333 (1997). https://pith.science/paper/LQGEMIPI

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Editor's note

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Short version: the fixed-order claim is right, and it is derived rather than asserted. The resummation half is a leading-log sketch, and the abstract leans on it harder than Sect. 4 supports. Neither problem is fatal, and the authors flag the second themselves in Sect. 5 — the classifier's 'no limitations found' is simply wrong on that point; they say plainly that single-logarithmic and double-sided cases remain to be done. So the reader's CONDITIONAL is the right call, and the stress-test's 'no unacknowledged load-bearing concern' holds up on my reading too. The one thing I would push back on is the abstract sentence [abstract:s1] claiming finiteness is restored after resummation to all orders; that is a DL statement about monotonic observables, not a general theorem, and it should read that way. Minor, but it is the sentence people will quote. The paper is also thin on how wide the dangerous region actually is — a practitioner wants to know how far from C = 3/4 or r = R to stay, and gets no number. Fair to call that out of scope for a letter, less fair for a paper whose stated motivation is phenomenological practice. The C-parameter case is the strongest part: A(3/4), A'(3/4), the explicit coefficient in Eq. 3.12, and h(3/4) = 146 ± 3 against EVENT is a real calculation with an independent numerical check, not a plausibility argument. The general step-to-ln^2(C − C0) mechanism in Eq. 2.9 is two lines from the plus-prescription and I could not break it. The Sudakov shoulder is a name for a structure that is genuinely there, not a coinage doing work it hasn't earned. This is for anyone doing event-shape fits or jet-shape measurements, and for anyone who has been taught that Sterman-Weinberg safety implies finite fixed-order coefficients — which is most of us. It is short, the argument is checkable, and the two worked examples are concrete. Send it out. I would cite it, and I would put the C-parameter section in front of a reading group.

Referee report

Significance

The paper identifies a genuine and previously under-emphasized failure mode of fixed-order QCD perturbation theory: infrared safety in the Sterman–Weinberg sense does not protect against divergences at interior critical points of the phase space. The general argument of Eq. (2.9) is short, clean, and correct, and the C-parameter example is worked analytically with a specified coefficient (Eq. 3.12) and cross-checked against an independent numerical program, which makes the prediction falsifiable rather than merely qualitative. The identification of the C = 3/4 point and of the cone boundary r = R as critical points is of direct practical use to anyone comparing fixed-order predictions with LEP or Tevatron data, and the named 'Sudakov shoulder' structure is a useful organizing concept. The paper is appropriately scoped as a letter: the general mechanism is established, and the all-order treatment is explicitly programmatic.

Major objections (3)

[§4, Eq. (4.2) and the sentence following it; §5, final paragraph] The derivation of Eq. (4.2) rests on the assumption, stated in the sentence immediately after that equation, that sigma^(inf)_-(C0) carries no soft-gluon singularities because the observable is always increased by soft emission. That assumption holds for the C-parameter but fails for the non-monotonic k_perp jet-shape case that the paper itself exhibits in Eq. (3.25), where both sides of the critical point are singular. The concluding sentence of §5 — that resummation 'should be sufficient to render any safe quantity finite and smooth throughout the physical phase space' — is therefore broader than what §4 establishes. I recommend either restricting that sentence to observables monotonic in soft emission, or stating explicitly that the non-monotonic case is argued by analogy rather than derived.
[§4, Eqs. (4.2)–(4.3); the phrase 'infinitely differentiable' in §4 and §5] The claim that the resummed distribution is infinitely differentiable at C = C0 is established here only at double-logarithmic accuracy: the exponent -(a/2) ln^2(C-C0) vanishes faster than any power, so all derivatives exist. But Eq. (3.12) shows that single-logarithmic terms are present with coefficients of the same parametric order as the DL ones, and in standard Sudakov resummation such terms exponentiate into a power prefactor (C-C0)^b whose k-th derivative diverges as C -> C0+ for k > b. The paper should either restrict the smoothness statement to DL accuracy, or give an argument that the single-logarithmic series does not reintroduce a branch point at C0. This matters because the shoulder is characterized as smooth, not merely finite, and that characterization is part of the abstract's second claim.
[§3.2, Eq. (3.25) and the paragraph following it] The smoothing of the double-sided singularity in the k_perp jet shape is supported only by reference to Fig. 11 of Ref. [24], which is listed as an unpublished preprint (RAL-97-026, hep-ph/9707338). Since this is the paper's only worked non-monotonic example and it is used to support the generality of the resummation claim, the section would be considerably stronger if it contained an independent argument — even a DL toy model showing the convolution of a shoulder and an inverted shoulder — or at minimum a sentence stating what in Ref. [24] establishes the result and under what assumptions.

Minor objections (15)

[§2, Eq. (2.9)] The left-hand side, sigma^(n+1)_+(C) - sigma^(n+1)_-(C0), compares distributions at different arguments, while the right-hand side is written in terms of the discontinuity at C0. Presumably the intended object is the limit of the difference as C -> C0+ minus the limit from below; please make the argument structure explicit so the equation can be read without reconstruction.
[§2 and §3.1; §3.5 and §4.4] The symbol C denotes a generic observable in §2 and the C-parameter in §3.1, and A(C) in Eqs. (3.5)–(3.6) is a different object from A(1) in Eq. (4.4). Renaming the generic observable (for example to O or y) and the DL coefficient would remove a genuine source of confusion for the reader.
[§3.1, Eq. (3.12)] The (1-delta) factor multiplying the DL term and the origin of the single-logarithmic coefficient (3C_F + 11/6 C_A - 1/3 N_f) are not explained. A sentence on where each piece comes from would let the reader check the single-logarithmic term, which is otherwise quoted without derivation.
[§3.1, Eqs. (3.11) and (3.15)] The EVENT numbers 230 +/- 10 and 146 +/- 3 are quoted without stating the statistics behind the errors, the Monte Carlo parameter settings, or the scale at which alpha_S is evaluated. It would also be useful to say whether h(3/4) is expected to be renormalization-scale dependent.
[§3.1, Eq. (3.14)] The text says the remainder is 'expected' to take the form h(C) = h(3/4) + O(delta ln delta). Please state whether this is a proven statement about the delta -> 0 limit or a fit ansatz used to extract h(3/4) from the Monte Carlo.
[§3.2, Eq. (3.24)] The sign of the divergence in psi^(2)_in is stated conditionally on a > 0 ('likely to be positive in most jet configurations'). Either state what fixes the sign in the cone case or present the result explicitly as conditional, since the direction of the effect is what an experimental comparison would test.
[§3.2, Eq. (3.16)] The definition of psi(r) leaves the jet-axis prescription (E_T-weighted centroid versus cone axis) and the normalization implicit. Both should be stated, since the critical-point structure depends on which axis is used.
[§3.2, paragraph on cone algorithms] The statement that collinear unsafety 'affects any perturbative calculation that involves more than 5 final-state partons' is specific enough to warrant a short justification or a pointer to the place in Ref. [23] where the counting is done.
[§4, Eq. (4.3) and Fig. 1] The dot-dashed curve uses the step approximation A(C) ≃ A(3/4) Theta(3/4 - C) in addition to the DL form factor; the caption should say so explicitly, and the scale at which alpha_S = 0.12 is evaluated should be given.
[§2, footnote on integrability] The statement that all these singularities are integrable in a neighbourhood of the critical point holds only if sigma^(n) itself is integrable there. Please state that condition explicitly rather than leaving it implicit.
[§4, paragraph on non-perturbative smearing] The argument that relying on hadronization smearing would require non-power-suppressed non-perturbative contributions is plausible but not demonstrated. A sentence on why hadronization cannot supply smearing of the required form would make the argument do the work the paper asks of it.
[Abstract] The phrase 'to any finite order of perturbation theory' is slightly imprecise: the divergence first appears at order n+1, where n is the order at which the step appears. 'At sufficiently high finite order' would be more accurate.
[References [13] and [24]] Ref. [13] is listed as 'in preparation' and Ref. [24] as a preprint. The C-parameter resummation at C = 0 is standard (Ref. [4]) so Ref. [13] is not load-bearing, but the reader cannot check either source; where possible, updated citations would help.
[§3.2, Eqs. (3.22)–(3.23)] The arrows in these equations should specify the direction of the limit (r -> R^- or r -> R^+), since the whole point of the surrounding discussion is the one-sided versus two-sided behaviour at r = R.
[§3.2, Eq. (3.27)] A numerical estimate of how small the slicing parameter epsilon must be for the unphysical ln(epsilon) dependence to cancel would make this practical observation usable by someone actually running a slicing calculation.

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The paper

The paper claims

Infrared- and collinear-safe QCD observables can still be infinite at ordinary interior points of phase space, order by order, whenever a lower-order distribution has a step or kink there.

The reading

The Sterman–Weinberg criteria of infrared and collinear safety are usually read as a promise that the fixed-order perturbative coefficients of an observable are finite. Catani and Webber argue that this stronger reading is false. What safety actually guarantees is only that soft and collinear divergences cancel when the soft-gluon probability, a plus-distribution, acts on a sufficiently smooth test function. If the distribution at some order $n$ is not smooth at an accessible interior point $C_0$ — a step, or a discontinuous derivative — then the next order inherits a $+a/2$ times $[1/(1-z)]_+$ type convolution that produces a $+a/2$ times $[1/(1-z)]_+$ divergence, in practice a term going like $+a/2$ times $[1/(1-z)]_+$ evaluated at $C-C_0$, i.e. a double logarithm $+a/2$ times $[1/(1-z)]_+$ of $C-C_0$, and higher orders raise the power. They exhibit two real cases — the $C$-parameter in $e^+e^-$ annihilation, where the three-parton phase-space boundary sits at $C=3/4$, and the jet profile in hadron collisions, where the cone radius $R$ is a critical point — and then argue that summing soft-gluon terms to all orders removes the divergence and leaves a smooth, infinitely differentiable structure they name the Sudakov shoulder. If they are right, a whole class of observables that pass the standard safety test cannot be compared to fixed-order theory near their critical points, and the safety argument itself has to be restated at the level of resummed rather than fixed-order predictions.

What carries the argument

Three pieces carry the argument. First, the plus-prescription of Eq. (2.4), $dw/dz = a[ln(1/(1-z))/(1-z)]_+$, which is the only cancellation that safety guarantees and which is well behaved only on smooth test functions — this is the precise sense in which safety is weaker than finiteness. Second, the convolution of Eq. (2.6), $hat sigma^{(n+1)}(C) = int_0^C dy, hat sigma^{(n)}(C-y), (dw/dz)_{z=1-y} + ...$, together with its evaluated form Eq. (2.9), which converts a step or a kink in the lower-order distribution into a logarithmically enhanced, integrable singularity at the critical point. Third, the exponentiation of Eq. (4.2), $hat sigma^{(infty)}_+(C) - hat sigma^{(infty)}_-(C_0) = exp[-(a/2)ln^2(C-C_0)],[hat sigma^{(n_0)}_+(C_0) - hat sigma^{(n_0)}_-(C_0)]$, which turns the divergent series into a smooth interpolation across $C_0$ — the Sudakov shoulder. The name is chosen by analogy with the Sudakov form factor that suppresses the exclusive boundary $C to 0$ in Eq. (4.1); the difference is that at the boundary the exponential kills the cross section, whereas at an interior critical point it merely rounds off a step.

Extended reading notes

Core claim

The paper's central claim is that infrared and collinear safety, as formulated by Sterman and Weinberg, does not imply that the coefficients of the perturbative expansion are non-singular functions. The cancellation mechanism that safety guarantees is the plus-prescription of Eq. (2.4): real and virtual soft-gluon emissions combine into a distribution that is well behaved only when integrated against a test function that is smooth at $z=1$. The $(n+1)$-st order distribution is obtained by convolving the $n$-th order one with that distribution, Eq. (2.6), so if the $n$-th order has a step at an interior point $C_0$ the convolution diverges. Eq. (2.9) makes this quantitative: a jump $[hat sigma^{(n)}_+(C_0) - hat sigma^{(n)}_-(C_0)]$ generates a term $-a/2 ln^2(C-C_0)$ at order $n+1$, and further orders multiply the logarithm. For the $C$-parameter the step is at $C=3/4$, the largest value three partons can reach (the symmetric $x_1=x_2=x_3=2/3$ configuration), and the authors verify the predicted second-order behaviour $B_+(C) propto A(3/4)[(2C_F+C_A)(1-delta)ln^2 delta + ...]$ against the EVENT Monte Carlo, finding $B_-(3/4)=230 plus or minus 10$ and $h(3/4)=146 plus or minus 3$. For jet shapes the critical point is the cone radius $r=R$, giving single-logarithmic divergences in the cone algorithm and a double-sided singularity in the $k_perp$ algorithm. Finally, iterating the soft-gluon convolution and exponentiating gives Eq. (4.2), in which the step is suppressed by $exp[-(a/2)ln^2(C-C_0)]$ rather than the divergence being enhanced: the resummed distribution is finite, continuous and infinitely differentiable at $C_0$, the Sudakov shoulder.

Load-bearing premise

The resummation argument assumes the observable always increases when a soft gluon is emitted, so that only the step across the critical point needs exponentiating and the lower side carries no soft-gluon singularities; for the non-monotonic case, which the paper itself identifies in the $k_perp$ jet algorithm, no analytic resummation is given and the smoothing is asserted by analogy to a numerical figure in a cited preprint.

Editorial extensions

If this is right

Fixed-order predictions for the $C$-parameter distribution cannot be trusted in a neighbourhood of $C=3/4$; the second-order result already diverges as $ln^2(C-3/4)$ above the point, and each further order raises the power of the logarithm.
Jet-shape and jet-profile distributions in hadron collisions are unreliable near the cone radius $r=R$, with a single-logarithmic divergence in cone algorithms and a two-sided singularity in $k_perp$ algorithms.
Phase-space slicing calculations acquire an unphysical $ln s_{min}$ dependence, Eq. (3.27), that cancels only when the slicing parameter is taken sufficiently small.
Any use of an apparently safe observable to measure $alpha_S$ or test QCD requires first locating its critical points and either avoiding them or resumming the soft-gluon terms.
Because the fixed-order divergence is integrable, hadronization smearing could hide it — but only at the cost of non-perturbative corrections that scale logarithmically with $Q$ rather than as inverse powers, which would undermine the safety argument itself.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The argument generalizes into a practical recipe: for any candidate observable, compute the lowest order at which the distribution has a step or a discontinuous derivative, locate that point, and check whether it lies inside the accessible phase space. The paper effectively proposes this as a routine step before any fixed-order comparison with data.
The distinction the authors draw between a step (which diverges at the next order) and a kink (which diverges only in the derivative) suggests a hierarchy of severity that could be tabulated for the standard event-shape variables; thrust is the worked example of the milder case, with the cusp appearing at $C_0 = 1/3$.
If the Sudakov shoulder is real and smooth, its width is set by $a$ and $alpha_S$, so measuring the shoulder's shape near $C=3/4$ would be an independent handle on $alpha_S$ and on the colour factor combination $C_F + C_A/2$ that enters $A(1)$ — the authors note the shoulder would be twice as steep in an abelian theory.
The paper's own treatment of the non-monotonic $k_perp$ case is by analogy to a numerical figure in a cited preprint rather than by derivation, which leaves an opening: an analytic resummation of the double-sided singularity would test whether the smoothing mechanism really works when the observable is not monotonic in soft-gluon energy.

Original abstract

We show that QCD observables defined as infrared- and collinear-safe, according to the usual Sterman-Weinberg criteria, can nevertheless be infinite at accessible points inside phase space, to any finite order of perturbation theory. Infrared finiteness is restored after resummation of divergent terms to all orders. The resulting characteristic structure, which we call a Sudakov shoulder, represents an interesting new class of QCD predictions.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,944 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.40 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.44 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We show that QCD observables defined as infrared- and collinear-safe, according to the usual Sterman-Weinberg criteria, can nevertheless be infinite at accessible points inside phase space, to any finite order of perturbation theory. Infrared finiteness is restored after resummation of divergent terms to all orders. The resulting characteristic structure, which we call a Sudakov shoulder, represents an interesting new class of QCD predictions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show that QCD observables defined as infrared- and collinear-safe, according to the usual Sterman-Weinberg criteria, can nevertheless be infinite at accessible points inside phase space, to any finite order of perturbation theory.	result 0.92	0.92	0.90	asserted 1.00
s1	Infrared finiteness is restored after resummation of divergent terms to all orders.	result 0.90	0.68	0.15	asserted 1.00
s2	The resulting characteristic structure, which we call a Sudakov shoulder, represents an interesting new class of QCD predictions.	interpretation 0.88	0.85	0.17	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Predictions of the C-parameter distribution for αS = 0.12. Dashed: O(αS). Solid: O(α 2 S ). Dot-dashed: resummed. the three-parton upper limit C = 3 4 : A(C) C ∼ 3/4 ≃ A( 3 4 ) Θ( 3 4 − C) , (3.8) A( 3 4 ) = 32 243 π √ 3 M0 = 256 243 π √ 3 CF . (3.9) The derivative of A(C) is also finite at C = 3 4 − : in fact A ′ ( 3 4 ) = −8 3A( 3 4 ) . (3.10) The resulting first-order prediction in the vicinity of C = 3 4 is shown by the dashed curve in

**Figure 2.** Second-order prediction of the C-parameter distribution for C → 3 4 + . Points: EVENT Monte Carlo. Curve: Eqs. (3.12-3.15). Using Eq. (3.10), we see that the first term in the square bracket on the right-hand side of Eq. (3.12) is in complete agreement with Eq. (2.9) with a = (2CF + CA)αS(Q)/π. The second term in the square bracket is due to collinear but non-soft parton splitting: singlelogarithmic contributions of this type were neglected in the simplified discussion of Sect. 2, which was valid to double-logarithmic (DL) accuracy only. Comparing our analytic calculation with…

Figures reproduced from arXiv:hep-ph/9710333 by the authors.

References

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The Sudakov radiator for jet observables and the soft physical coupling
hep-ph 2018-07 conditional novelty 7.0 of 10

Closed-form NNLL Sudakov radiator for generic rIRC-safe jet observables, a soft physical coupling to O(alpha_s^3), and new analytic NNLL results for angularities and energy-energy-correlation moments.
NNLOPS accurate predictions for $W^+W^-$ production
hep-ph 2018-05 accept novelty 7.0 of 10

Reweighting a MiNLO W-pair event sample to a fully differential NNLO calculation yields the first NNLO-plus-parton-shower prediction for a four-particle final state, in agreement with ATLAS and CMS data.
aMCfast: automation of fast NLO computations for PDF fits
hep-ph 2014-06 accept novelty 7.0 of 10

An automated interface converts arbitrary NLO LHC cross sections into fast interpolating grids, validated to roughly 10^-4 accuracy on top-pair, photon+jet, dilepton+jet, Zbb, and W+charm production.
Combining Higher-Order Resummation with Multiple NLO Calculations and Parton Showers in GENEVA
hep-ph 2012-11 conditional novelty 7.0 of 10

A master formula multiplicatively matches N-jettiness resummation to fully differential NLO matrix elements and Pythia 8, giving a Monte Carlo formally accurate to relative O(alpha_s) at all jet resolutions.
NNLO corrections to event shapes in $e^+e^-$ annihilation
hep-ph 2007-11 conditional novelty 7.0 of 10

The authors present the first complete NNLO QCD corrections to six three-jet event shape distributions in e+e- annihilation, finding 5 to 20 percent corrections beyond NLO and a 30 to 50 percent reduction in scale unc...
Positive-weight moment matching at NNLO and beyond
hep-ph 2026-10 accept novelty 6.0 of 10

Maximum-entropy reweighting of a leading-order Pythia sample reproduces NNLO Drell-Yan and Z+jet moments with strictly positive event weights.
Heavy Jet Mass in Hadronic Higgs Decays
hep-ph 2026-07 conditional novelty 6.0 of 10

Heavy jet mass in hadronic Higgs decays is predicted at N³LL′ (dijet) plus NNLL (Sudakov shoulder) plus NNLO, with new analytic trijet-region logarithms for H→gg and H→q̄q.
Precise Predictions for Event Shapes in Hadronic Higgs Decays
hep-ph 2025-08 conditional novelty 6.0 of 10

First NNLO QCD predictions for six classical event-shape distributions and soft-drop thrust in hadronic Higgs decays, for both H to b bbar and H to gg channels.
Recoil-Safe Subtraction, Matching and Merging in e+e- to hadrons
hep-ph 2025-07 conditional novelty 6.0 of 10

The Alaric shower is matched to NLO matrix elements and merged to five jets in e+e- to hadrons, with new analytic subtraction terms validated against Catani-Seymour subtraction.
Drell-Yan lepton-pair production: $q_T$ resummation at N$^3$LL accuracy and fiducial cross sections at N$^3$LO
hep-ph 2021-03 accept novelty 6.0 of 10

The authors deliver the first N3LL+N3LO QCD prediction for the Drell-Yan transverse-momentum spectrum and the first N3LO fiducial cross sections for Z/gamma* production at the LHC.
Matching NNLO to parton shower using N$^3$LL colour-singlet transverse momentum resummation in GENEVA
hep-ph 2021-02 conditional novelty 6.0 of 10

Using the dilepton transverse momentum as the zero-jet resolution variable lets GENEVA combine N3LL resummation with NNLO and Pythia8, and the showered predictions reproduce LHC 13 TeV Drell-Yan data.
Fiducial $q_T$ resummation of color-singlet processes at N$^3$LL+NNLO
hep-ph 2020-09 conditional novelty 6.0 of 10

A public, process-generic SCET-based qT-resummation framework delivers N3LL+NNLO fiducial predictions for color-singlet processes, with new results for diphoton and Z-gamma production and an analysis of photon-isolati...
Scale and isolation sensitivity of diphoton distributions at the LHC
hep-ph 2020-09 conditional novelty 6.0 of 10

Switching from smooth-cone to matched-hybrid isolation and from a diphoton-mass to an average-transverse-momentum scale brings NNLO diphoton predictions into agreement with 8 TeV ATLAS data within scale uncertainties.
Accurate single- and double-differential resummation of colour-singlet processes with MATRIX+RadISH: $W^+W^-$ production at the LHC
hep-ph 2020-04 accept novelty 6.0 of 10

A MATRIX+RadISH interface produces NNLO+N3LL transverse-momentum spectra for W+W- production at the LHC, plus NNLO+NNLL leading-jet and jet-vetoed spectra, with fiducial cuts.
Top-quark pair production at the LHC: Fully differential QCD predictions at NNLO
hep-ph 2019-06 accept novelty 6.0 of 10

Fully differential NNLO QCD predictions for top-quark pair production at the LHC, computed with qT subtraction and validated against an independent calculation at the percent level.
Joint resummation of two angularities at next-to-next-to-leading logarithmic order
hep-ph 2018-06 conditional novelty 6.0 of 10

The authors jointly resum logarithms of two angularities to NNLL accuracy, match to NLO, and validate the single-angularity factorization against Event2, showing the winner-take-all axis removes recoil sensitivity.
NLO predictions for Higgs boson pair production with full top quark mass dependence matched to parton showers
hep-ph 2017-03 accept novelty 6.0 of 10

Full NLO QCD di-Higgs production with exact top quark mass dependence is matched to parton showers in POWHEG and MG5_aMC@NLO, and the shower effects are found to be smaller than the failure of the heavy-top approximat...
NNLO QCD corrections to jet production in deep inelastic scattering
hep-ph 2017-03 accept novelty 6.0 of 10

Full NNLO QCD corrections to inclusive single-jet and di-jet production in deep inelastic scattering are computed, and they bring the HERA jet data into substantially better agreement than NLO while cutting the theory...
$W^+W^-$ production at the LHC: fiducial cross sections and distributions in NNLO QCD
hep-ph 2016-05 accept novelty 6.0 of 10

The first fully differential NNLO QCD predictions for W+W- production with leptonic decays at the LHC, including off-shell effects and spin correlations, are presented for 8 and 13 TeV.
Precise QCD predictions for the production of a Z boson in association with a hadronic jet
hep-ph 2015-07 accept novelty 6.0 of 10

A fully differential next-to-next-to-leading-order QCD calculation of Z boson plus jet production at the LHC finds corrections of about 1% over NLO, with residual scale uncertainty near 1%.
Higgs boson production in association with a jet at NNLO using jettiness subtraction
hep-ph 2015-05 conditional novelty 6.0 of 10

A complete NNLO QCD calculation of Higgs-plus-jet production via jettiness subtraction agrees with an independent subtraction calculation and adds small quark-initiated channels.
Wgamma and Zgamma production at the LHC in NNLO QCD
hep-ph 2015-04 accept novelty 6.0 of 10

Complete NNLO QCD corrections raise the Wγ cross section by 19 to 26 percent and the Zγ cross section by 8 to 18 percent, improving agreement with ATLAS data.
A Precise Determination of $\alpha_s$ from the C-parameter Distribution
hep-ph 2015-01 conditional novelty 6.0 of 10

Fitting the C-parameter distribution at N3LL-prime accuracy to 404 bins of LEP/SLD data gives alpha_s(m_Z) = 0.1123 +/- 0.0015 and Omega_1 = 0.421 +/- 0.063 GeV, confirming thrust/C-parameter universality of the leadi...
C-parameter Distribution at N${}^3$LL$^\prime$ including Power Corrections
hep-ph 2014-11 conditional novelty 6.0 of 10

The C-parameter distribution in electron-positron annihilation is computed with N3LL-prime resummation plus a renormalon-free power correction, reaching about 2.5 percent perturbative uncertainty at Q = mZ.
Weak corrections to Higgs hadroproduction in association with a top-quark pair
hep-ph 2014-07 accept novelty 6.0 of 10

The first calculation of weak next-to-leading-order corrections to pp -> ttH finds them at the few-percent level inclusively but around 8 percent in boosted kinematics, comparable to QCD scale uncertainties there.
Phenomenology of event shapes at hadron colliders
hep-ph 2010-01 conditional novelty 6.0 of 10

Matched NLO plus NLL predictions for dijet event shapes at hadron colliders are presented for the first time, with uncertainty bands and systematic comparisons to parton showers.
Event shapes and jet rates in electron-positron annihilation at NNLO
hep-ph 2009-04 accept novelty 6.0 of 10

The paper publishes complete next-to-next-to-leading-order perturbative QCD coefficients for six event-shape observables and four jet-rate definitions in electron-positron annihilation, including soft-gluon subtractio...
Triphoton production at hadron colliders in NNLO QCD
hep-ph 2020-10 conditional novelty 5.0 of 10

A fully differential NNLO QCD calculation of triphoton production, with an on-the-fly two-loop amplitude, brings theory into agreement with ATLAS 8 TeV data and predicts large corrections up to 100 TeV.
MiNNLO$_{\rm PS}$: Optimizing $2\to 1$ hadronic processes
hep-ph 2020-06 accept novelty 5.0 of 10

Three prescriptions (untruncated matching, low-scale PDF evolution, and a local shower recoil scheme) bring MiNNLO_PS predictions for Higgs and Drell-Yan production into few-permille to few-percent agreement with fixe...
Diphoton production at the LHC: a QCD study up to NNLO
hep-ph 2018-02 accept novelty 5.0 of 10

NNLO QCD corrections to LHC diphoton production raise the NLO cross section by about 40 percent, and smooth-cone isolation reproduces standard-cone results once isolation is tight.
Jet production in the CoLoRFulNNLO method: event shapes in electron-positron collisions
hep-ph 2016-06 conditional novelty 5.0 of 10

A general local-subtraction method reproduces published NNLO event-shape distributions in electron-positron annihilation and yields the first NNLO prediction for the jet cone energy fraction.
Vector boson production at hadron colliders: transverse-momentum resummation and leptonic decay
hep-ph 2015-07 accept novelty 5.0 of 10

NNLL+NNLO transverse-momentum resummation for W and Z production now retains the full leptonic decay with spin correlations, together with an explicit, general prescription for how the boson's transverse momentum is a...
Handbook of LHC Higgs Cross Sections: 3. Higgs Properties
hep-ph 2013-07 accept novelty 5.0 of 10

The LHC Higgs Cross Section Working Group's third handbook sets the state-of-the-art Standard Model and MSSM Higgs production and decay predictions at 125-126 GeV with quantified theory uncertainties, and adds a first...
Hadronic top-quark pair-production with one jet and parton showering
hep-ph 2011-10 conditional novelty 5.0 of 10

Matching the NLO top-pair-plus-jet calculation to parton showers roughly halves the predicted Tevatron top forward-backward asymmetry, and the entire shift comes from the low transverse-momentum region of the top pair.
Combination of electroweak and QCD corrections to single W production at the Fermilab Tevatron and the CERN LHC
hep-ph 2009-07 conditional novelty 5.0 of 10

Combining NLO electroweak and NLO QCD corrections for single W production yields a conservative theoretical accuracy of about 2% (standard cuts) and about 5% (high tails) at the Tevatron and LHC.
Physics at a 100 TeV pp collider: Standard Model processes
hep-ph 2016-07 accept novelty 4.0 of 10

At 100 TeV, photon-initiated and electroweak-boson-initiated channels grow to rival quark-antiquark annihilation for multi-TeV Drell-Yan and diboson production, and electroweak splittings appear in multi-TeV jets at t...
The strong coupling constant: State of the art and the decade ahead
hep-ph 2022-03 accept novelty 3.0 of 10

Seven independent classes of measurement converge on a strong coupling alpha_s(m_Z) = 0.1179 +/- 0.0009, and the paper lays out what each class would need to reach per-mille precision within a decade.
Event shapes in e+e- annihilation and deep inelastic scattering
hep-ph 2003-12 accept novelty 3.0 of 10

Event-shape observables in e+e- and DIS become calculable once large logarithms are resummed and non-perturbative 1/Q corrections are modelled, and the resulting fits are broadly consistent across observables and proc...
QCD resummation for hadronic final states
hep-ph 2015-05 accept novelty 2.0 of 10

The review consolidates the direct-QCD resummation program: soft and collinear factorization, NLL event-shape resummation via Caesar, non-global logarithms, and groomed jet substructure, with the factorization-breakin...
Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning
hep-ph 2017-09 accept novelty 1.0 of 10

The review argues that infrared-and-collinear-safe observables plus grooming (modified mass drop / soft drop) give theoretically controlled jet substructure predictions, and surveys the machine-learning methods now ap...

How later papers used it

63 later papers cite it

Evidence: some. 62 of the citing papers share no author with it, and 4 of those carry a confident label from Pith's citation classifier.

Pith read 37 of the 87 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

3 later papers by other authors are listed below: 3 used its data or values.

Uses its data or values 3 papers

Used the values calculated in this paper, including b_02=43.3122 and b_12=-115.499, and fit the rest of the coefficients to EVENT2 output.

Accuracy and Precision in Collider Event Shapes (2016) · 0.98 · paraphrased: the licence does not allow quoting
Used the known value of the leading-order differential cross section for the C-parameter at its maximum value from this paper.

Covariantizing Phase Space (2020) · 1.00 · paraphrased: the licence does not allow quoting
Used the values calculated in this paper, including b_02=43.3122 and b_12=-115.499, and fit the rest of the coefficients to EVENT2 output.

C-parameter Distribution at N${}^3$LL$^\prime$ including Power Corrections (2014) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

61 arXiv papers cite this in 85 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 73 sentences without a confident label

Uses its data or values 3 papers

We use the value predicted by exponentiation in Ref. [ref] .

Accuracy and Precision in Collider Event Shapes · Nonsingular Terms · 0.87
In fact, using the known value of the leading-order differential cross section for the $C$-parameter at its maximum value [ref] , where [equation] the value of the differential cross section at a general value $C$ is [equation] Here, $Ω$ is the region of phase space where the $C$-parameter takes values between $C$ and $3/4$.

Covariantizing Phase Space · Introduction · 1.00
We use the values calculated in Ref. [ref] , , $b_02=43.3122$, and $b_12 = - 115.499$ and fit the rest of the coefficients to EVENT2 output.

C-parameter Distribution at N${}^3$LL$^\prime$ including Power Corrections · Nonsingular Terms · 0.99

Compares with it 1 paper

We also note that the Sudakov shoulder effect [ref] is observed around $p_T^A$ = 30 GeV from the distribution as in the scalar Higgs case [ref] .

Pseudoscalar Higgs plus jet production at Next-to-Next-to-Leading Order in QCD · Phenomenology · 0.89

Cites it as background 6 papers

These logarithms were identified by Catani and Webber [ref] in 1997, and a systematically improvable method to compute and resum these logarithms was developed in 2022 [ref] .

NNLL Resummation of Sudakov Shoulder Logarithms in the Heavy Jet Mass Distribution · Conclusions · 0.93
This is the Sudakov shoulder first identified by Catani and Webber in 1997 [ref] .

Heavy Jet Mass in Hadronic Higgs Decays · Introduction · 0.84
It is well known [ref] that in the case of symmetric (or nearly-symmetric) cuts fixed-order calculations are affected by perturbative (soft-gluon) instabilities at higher orders.

Drell-Yan lepton-pair production: $q_T$ resummation at N$^3$LL accuracy and fiducial cross sections at N$^3$LO · Introduction · 0.80

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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