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Resumming transverse observables for NNLO+PS matching in GENEVA

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper establishes the first beyond-leading-log resummation of a transverse-measure one-jettiness and uses it, together with N3LL qT resummation, to build NNLO+PS generators for Higgs production in b-bbar and c-cbar annihilation.

desk verdict New T1^pT NLL' resummation is real and honestly presented, but the validation stops short of demonstrating the evolution itself; still worth refereeing. read the letter →

arxiv 2505.14773 v1 pith:EPBMWXZG submitted 2025-05-20 hep-ph hep-ex

Alessandro Gavardi , Rebecca von Kuk , Matthew A. Lim This is my paper
classification hep-phhep-ex
keywords NNLO+PSmatchingtransverseobservablesqTresummationone-jettinessSCET-IIfactorisationheavy-quarkannihilationGENEVANLL'
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper builds event generators that reach next-to-next-to-leading-order accuracy matched to a parton shower (NNLO+PS) using resolution variables that are both transverse-momentum-like. It claims the first resummation beyond leading logarithm of a transverse-measure one-jettiness, denoted $T_1^{pT}$, and combines it with $q_T$ resummation at N3LL inside the GENEVA framework. The case study is Higgs boson production in heavy-quark annihilation, i.e. $b\bar b \to H$ and $c\bar c \to H$, where the Higgs transverse momentum spectrum is a key observable. If correct, the construction provides NNLO+PS predictions with a high-accuracy $q_T$ spectrum, a jet-resolution variable that matches naturally to $p_T$-ordered showers, and a first step toward NNLO+PS for colour-singlet production with an associated jet.

What carries the argument

The load-bearing object is the transverse one-jettiness $T_1^{pT}$ of eq. (18): emissions are assigned to a beam or jet region by the conical measure (an anti-$k_T$-like distance), and then weighted by $p_{T,i}$ in the beam region or by the boost-invariant broadening distance $R_{iJ}$ in the jet region. Because these measures are both of SCET-II type, the singular cross section factorises into hard, soft, beam and jet functions, eq. (21), with the one-loop soft function from ref. [61] and the winner-take-all axis equivalence from ref. [59] providing the required ingredients. The NLL' resummation is obtained by evolving these functions in virtuality and rapidity, solved analytically in Laplace space. On the $q_T$ side the machinery is the N3LL resummation from the SCETlib module with hybrid profile scales, and the GENEVA splitting mappings are chosen to preserve the colour-singlet four-momentum and the hardest-parton rapidity.

What would settle it

A concrete falsifier is a two-loop computation of the soft function for $T_1^{pT}$ with the conical measure: if the resulting NNLL correction does not match the structure implied by the one-loop-based evolution equations, the NLL' resummation is incorrect. A cheaper check is to compute the $T_1^{pT}$ spectrum at NLO$_1$ without assuming factorisation and test whether the nonsingular remainder vanishes linearly as $T_1^{pT}\to 0$ over the full phase space, not only at the validation point.

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Extended reading notes

Core claim

The central claim is that the generalised one-jettiness $T_1^{pT}$, defined by conical region assignment and a boost-invariant broadening measure in the jet region, is a SCET-II observable whose cross section factorises as in eq. (21), so its logarithmically enhanced terms can be resummed to NLL'. The paper presents that resummation for the first time and embeds it in GENEVA together with N3LL $q_T$ resummation from SCETlib, producing generators for $b\bar b \to H$ and $c\bar c \to H$. The parton-level $q_T$ spectrum of the generator agrees exactly with SCETlib, and the showered spectrum is indistinguishable from it within Monte Carlo error. Fixed-order validation against SusHi and MCFM supports the claimed NNLO normalisation, and the nonsingular $T_1^{pT}$ remnant is shown to vanish linearly in the small-$T_1^{pT}$ limit, as the claimed logarithmic accuracy requires.

Load-bearing premise

The argument assumes the SCET-II factorisation of eq. (21), with the conical measure and the winner-take-all jet axis, applies over all of phase space used by GENEVA; if soft-recoil or non-perturbative contributions are missed by that factorisation, the claimed NLL' accuracy of the 1/2-jet separation would fail.

Editorial extensions

If this is right

  • The $b\bar b \to H$ and $c\bar c \to H$ generators provide parton-level $q_T$ distributions at N3LL+NNLO accuracy, and the showered $q_T$ distribution agrees with the parton-level one to within Monte Carlo error.
  • Because both resolution variables are transverse, the matching is compatible with $p_T$-ordered showers without truncated showering, simplifying future GENEVA implementations.
  • The NLL' $T_1^{pT}$ resummation is a first step toward NNLO+PS matching for colour-singlet production in association with a hard jet; reaching NNLL' would require a two-loop soft function.
  • Applying the same generator construction to Drell-Yan would yield $W/Z$ production with N3LL+NNLO $q_T$ accuracy by construction, removing the need for a separate reweighting step.

Reading between the lines

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

  • The two-loop soft function for $T_1^{pT}$ could be computed with existing soft-function technology; whether its structure matches the one-loop-based NLL' prediction would give a sharp test of the factorisation beyond the validations shown.
  • The same transverse-measure construction could be carried over to $Z$+jet or $H$+jet processes, where the transverse one-jettiness may make $p_T$-ordered shower matching as natural as it is for the colour-singlet case; the paper notes the required resummation level but does not implement it.
  • The large (up to 40%) difference between spectrum and cumulant scale-setting conventions in the $b\bar b \to H$ transition region implies that phenomenological studies using this generator should state the scale-setting choice explicitly when quoting $q_T$ spectra.
  • A direct comparison of the full showered NNLO+PS prediction against an independent generator for the same process, rather than only fixed-order validation, would quantify the residual matching ambiguity from the new variable.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper reports a GENEVA implementation that uses two transverse resolution variables to build NNLO+PS generators for Higgs production in heavy-quark annihilation (bb->H and cc->H). The 0/1-jet separation is based on the colour-singlet transverse momentum qT, resummed at N3LL using SCETlib and its published profile-scale setup. The new element is the 1/2-jet separation variable T1^pT, a transverse-measure one-jettiness defined in Eq. (18), for which the authors construct a resummation at NLL' accuracy starting from the SCET-II factorisation in Eq. (21). Fixed-order validation is provided against SusHi and MCFM, the qT spectrum is compared with a standalone SCETlib run, and the logarithmic structure of the T1^pT singular cross section is checked in Fig. 3. Showered results are compared with parton-level results for rapidity, qT, and hardest-jet distributions.

Significance. If the accuracy claims are substantiated, the paper provides a valuable new tool and a methodological step: it is, to my knowledge, the first implementation of a transverse-measure one-jettiness resummation beyond LL inside an NNLO+PS framework, and the use of qT plus T1^pT may improve matching to transverse-momentum-ordered showers. The work also benefits from transparent discussion of scale-setting choices, a clear separation between resummed and fixed-order regions, and explicit validation of the qT interface. The main weakness is that the central novelty, the NLL' resummation of T1^pT, is not validated at the order where the NLL' evolution kernels actually contribute, and no uncertainty estimate is attached to the T1^pT predictions. These issues are fixable but need to be addressed before the claim can be accepted.

major comments (2)
  1. [Sec. V C, Fig. 3 and Sec. IV B] The nonsingular comparison in Fig. 3 validates only the O(alpha_s) singular terms of the factorised cross section in Eq. (21). The NLL' evolution kernels (the two-loop cusp anomalous dimension and the one-loop noncusp/rapidity anomalous dimensions entering Eqs. (26), (28), (33)-(36), and the solutions in Eqs. (37)-(42)) first affect the expanded spectrum at O(alpha_s^2): errors in these kernels leave the linear suppression of the nonsingular remainder in Fig. 3 unchanged. I therefore do not regard the NLL' claim as numerically established. Please add a validation that exercises the two-loop singular terms, for example by comparing the O(alpha_s^2) expansion of the resummed T1^pT spectrum with the exact two-loop singular contribution, or by an explicit analytic consistency check of the rapidity and virtuality RGEs against the known one-loop ingredients.
  2. [Sec. V C, Fig. 4 and Sec. IV B] The resummed T1^pT spectrum is shown without any uncertainty band, and the paper does not specify the central scales, profile functions, or variation procedure used for the T1^pT resummation. Unlike the qT case, where Appendix A gives the hybrid profile scales and a 36-point envelope, Section IV B leaves the natural scales mu_H, mu_B, mu_S, mu_J, nu_B, nu_S, nu_J and their transition to the fixed-order region unspecified. Since Eqs. (6)-(7) use this resummation to separate the 1- and 2-jet bins, the size of missing higher-order effects in the exclusive jet binning is currently unquantified. Please provide the T1^pT scale prescription and at least one uncertainty estimate (e.g. an envelope obtained by varying the profile transition points and the resummation scales).
minor comments (4)
  1. [Sec. V B, Fig. 2] Because GENEVA is interfaced directly to the SCETlib qT module, the agreement between GENEVA and SCETlib in Fig. 2 is primarily a consistency check of the integration and mapping, not an independent validation of the N3LL resummation itself; the text should state this explicitly to avoid an apparent circularity.
  2. [Sec. V A, Fig. 1] The MCFM comparison uses a different PDF set and different renormalisation/factorisation scales (CT14NNLO, mu_F=mH/4, mu_R=mH) from the rest of the paper; a brief explanation of why this specific setup is required for the comparison would help readers judge the strength of the fixed-order validation.
  3. [Sec. V C, Figs. 3 and 4] The captions of Figs. 3 and 4 do not specify axis labels or units; adding explicit axis labels (e.g. T1^pT in GeV) and legend entries would improve readability.
  4. [Appendix C, Eq. (C8)] The notation L0(k, mu/Q) is not defined in Appendix B, where L0 is introduced as a plus distribution of a dimensionless argument; please clarify the arguments and normalisation of the logarithms in this expression.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: the NLL' T1^pT resummation is built from external published SCET ingredients; the only self-citations fix interface and scale-setting conventions and do not force the central result.

full rationale

The paper's central new result, the NLL' resummation of the transverse-measure one-jettiness T1^pT, is not derived from the authors' own fitted or predicted quantities. The factorisation in eq. (21) and the one-loop soft function are taken from ref. [61]; the WTA-axis equivalence and broadening jet function from ref. [59]; the one-loop beam functions from refs. [65,66]; and the hard function from the standard one-loop QCD amplitude. These are external, parameter-free ingredients that do not assume the paper's target result. The qT N3LL component is obtained by directly interfacing SCETlib [31,58], with profile-scale choices adopted from the authors' earlier ref. [33] purely as a scale-setting convention. This is a minor self-citation, but it does not enter or force the T1^pT derivation. The external fixed-order benchmarks against SusHi and MCFM provide independent validation, and fig. 2 is explicitly a consistency and interface check of the Geneva wrapper against SCETlib, not a prediction generated from fitted parameters. Fig. 3 validates only the O(alpha_s) singular boundary terms of the T1^pT factorisation and does not exercise the NLL evolution kernels or profile-scale uncertainties; that is a validation gap and correctness risk, but not a circularity. No equation in the paper reduces to its own input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the established qT factorisation and on the SCET-II factorisation for T1^pT, with the profile-scale and cut choices serving as free parameters. No invented entities are introduced.

free parameters (3)
  • Profile scale transition points (x1, x2, x3) = 0.1, 0.45, 0.8 (central); x2 varied 0.2-0.6
    Hybrid profile scales in Appendix A determine where resummation turns off; chosen by hand and varied for matching uncertainty.
  • Nonperturbative scale prescription mu* = mu*(x,y) = sqrt(x^2 + y^2)
    Freezes beam and soft scales at low b_T; a modelling choice from the literature (refs. [53,57]) not fitted to data.
  • Resolution cut values qcut_T and (T1^pT)^cut = 1 GeV for both; jet radius R = 0.4
    Technical slicing and jet definition choices used in the generator; qcut_T = 1 GeV is set small enough that missing power corrections are at the 0.2% level for the total cross section.
assumptions (5)
  • domain assumption The qT factorisation for colour-singlet production in SCET (eq. 11) holds at leading power, and the N3LL resummation from SCETlib is correct for b bbar H and c cbar H.
    Invoked in Sec. III and V.B; imported from SCETlib and ref. [33]. This is a well-established framework, but the paper adds no independent derivation.
  • domain assumption The generalised one-jettiness T1^pT admits the SCET-II factorisation of eq. (21) with the one-loop soft function of ref. [61].
    Sec. IV.A-B. If this factorisation is incomplete for the conical measure with WTA axis, the NLL' resummation is invalid.
  • domain assumption The winner-take-all axis is equivalent to the N-jettiness minimisation axis at one-loop, making the soft function recoil-free.
    Sec. IV.A, based on ref. [59]; needed to avoid additional transverse-momentum convolutions.
  • domain assumption Leading-power qT singular terms contain all the two-loop information used for the approximate NNLO; power corrections below qcut_T are negligible at qcut_T = 1 GeV.
    Sec. V.A; the paper drops fixed-order NNLO terms and relies on the singular approximation, validated against SusHi for the total cross section but not for all differential distributions.
  • domain assumption Hybrid profile scales (Appendix A) and the nonperturbative mu* prescription correctly deactivate resummation at large qT and cover the associated uncertainty.
    Used for qT resummation; standard choices from refs. [55-57] and SCETlib.

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Cite this review

Pith. "Pith review of Resumming transverse observables for NNLO+PS matching in GENEVA." pith.science (2026). https://pith.science/paper/EPBMWXZG

@misc{pith2026250514773,
  author       = {Pith},
  title        = {Pith review of: Resumming transverse observables for NNLO+PS matching in GENEVA},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EPBMWXZG}},
  note         = {Machine review of arXiv:2505.14773}
}
abstract

We study the use of higher-order resummation for transverse observables to achieve NNLO+PS matching within the GENEVA framework. In particular, we embed $q_T$ resummation for colour-singlet production at N$^3$LL obtained via soft-collinear effective theory and implemented in the library SCETlib within GENEVA. We also study for the first time the use of the generalised $N$-jettiness variable in parton shower matching, and achieve the resummation of the one-jettiness defined with transverse measures up to NLL$'$ accuracy. As a case study, we use these resummed calculations to construct a GENEVA NNLO+PS generator for Higgs boson production in heavy-quark annihilation (with beauty or charm-quarks in the initial state). The use of transverse measures facilitates the matching to showers ordered in transverse momentum, and opens the door to possible future extensions of this approach to the production of colour singlets in association with final-state jets.

Figures

Figures reproduced from arXiv: 2505.14773 by the authors.

Figure 1
Figure 1. FIG. 1: Comparison between MCFM and [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Nonsingular [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 5
Figure 5. FIG. 5: Higgs boson rapidity spectrum in [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figures from the paper (3 more)
Figure 7
Figure 7. Figure 7: FIG. 7: As in fig.6, but for [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Hardest jet rapidity spectrum in [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 10
Figure 10. Figure 10: FIG. 10: Parton-level Higgs boson [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Reference graph

Works this paper leans on

83 extracted references · 14 canonical work pages · cited by 1 Pith paper

  1. [1]

    Billis, B

    G. Billis, B. Dehnadi, M. A. Ebert, J. K. L. Michel, and F. J. Tackmann, Phys. Rev. Lett. 127, 072001 (2021), arXiv:2102.08039 [hep-ph]

    arXiv 2021

  2. [2]

    X. Chen, T. Gehrmann, E. W. N. Glover, A. Huss, B. Mistlberger, and A. Pelloni, Phys. Rev. Lett. 127, 072002 (2021), arXiv:2102.07607 [hep-ph]

    arXiv 2021

  3. [3]

    7 − 2π2 3 − 6 log 2 δ(k) + 6 + 8 log ν Q L0 k, µ Q # (C8) and J (1) g (k, µ, ν) =

    0 ≤ x ≤ x3/2 , 1 − 2(1 − x/x3)2 x3/2 < x≤ x3 , 1 x3 ≤ x , (A7) with x ≡ qT /mH controls the size of the variations, rang- ing from a factor of 2 for x = 0 to 1 for x ≥ x3. Note that both the resummation itself and the associated resum- mation uncertainty is deactivated for qT ≥ x3mH . The combined resummation uncertainty ∆res is calculated by enveloping 3...

  4. [4]

    X. Chen, T. Gehrmann, E. W. N. Glover, A. Huss, P. F. Monni, E. Re, L. Rottoli, and P. Torrielli, Phys. Rev. Lett. 128, 252001 (2022), arXiv:2203.01565 [hep-ph]

    arXiv 2022

  5. [5]

    X. Chen, P. Jakubˇ c ´ ık, M. Marcoli, and G. Stagnitto, (2025), arXiv:2505.10618 [hep-ph]

    arXiv 2025

  6. [6]

    Alioli, C

    S. Alioli, C. W. Bauer, C. Berggren, A. Hornig, F. J. Tackmann, et al. , JHEP 1309, 120 (2013), arXiv:1211.7049 [hep-ph]

    arXiv 2013

  7. [7]

    P. F. Monni, P. Nason, E. Re, M. Wiesemann, and G. Zanderighi, JHEP 05, 143 (2020), arXiv:1908.06987 [hep-ph]

    arXiv 2020

  8. [8]

    J. M. Campbell, S. H¨ oche, H. T. Li, C. T. Preuss, and P. Skands, Phys. Lett. B 836, 137614 (2023), arXiv:2108.07133 [hep-ph]

    arXiv 2023

Show all 83 references
  1. [9]

    B. K. El-Menoufi, C. T. Preuss, L. Scyboz, and P. Skands, (2024), arXiv:2412.14242 [hep-ph]

    2024

  2. [10]

    Dasgupta, F

    M. Dasgupta, F. A. Dreyer, K. Hamilton, P. F. Monni, G. P. Salam, and G. Soyez, Phys. Rev. Lett. 125, 052002 (2020), arXiv:2002.11114 [hep-ph]

    2020 arXiv

  3. [11]

    van Beekveld et al

    M. van Beekveld et al. , (2024), arXiv:2406.02661 [hep- ph]

    2024 arXiv

  4. [12]

    Herren, S

    F. Herren, S. H¨ oche, F. Krauss, D. Reichelt, and M. Schoenherr, JHEP 10, 091 (2023), arXiv:2208.06057 [hep-ph]

    2023 arXiv

  5. [13]

    H¨ oche, F

    S. H¨ oche, F. Krauss, and D. Reichelt, (2024), arXiv:2404.14360 [hep-ph]. 15

    2024 arXiv

  6. [14]

    Alioli, C

    S. Alioli, C. W. Bauer, C. Berggren, F. J. Tackmann, and J. R. Walsh, Phys. Rev. D92, 094020 (2015), arXiv:1508.01475 [hep-ph]

    2015 arXiv

  7. [15]

    I. W. Stewart, F. J. Tackmann, and W. J. Waalewijn, Phys. Rev. Lett. 105, 092002 (2010), arXiv:1004.2489 [hep-ph]

    2010 arXiv

  8. [16]

    Alioli, A

    S. Alioli, A. Broggio, S. Kallweit, M. A. Lim, and L. Rot- toli, Phys. Rev. D 100, 096016 (2019), arXiv:1909.02026 [hep-ph]

    2019 arXiv

  9. [17]

    Alioli, A

    S. Alioli, A. Broggio, A. Gavardi, S. Kallweit, M. A. Lim, R. Nagar, D. Napoletano, and L. Rottoli, JHEP 04, 254 (2021), arXiv:2009.13533 [hep-ph]

    2021 arXiv

  10. [18]

    Alioli, A

    S. Alioli, A. Broggio, A. Gavardi, S. Kallweit, M. A. Lim, R. Nagar, D. Napoletano, and L. Rottoli, JHEP 04, 041 (2021), arXiv:2010.10498 [hep-ph]

    2021 arXiv

  11. [19]

    Alioli, A

    S. Alioli, A. Broggio, A. Gavardi, S. Kallweit, M. A. Lim, R. Nagar, and D. Napoletano, Phys. Lett. B 818, 136380 (2021), arXiv:2103.01214 [hep-ph]

    2021 arXiv

  12. [20]

    Cridge, M

    T. Cridge, M. A. Lim, and R. Nagar, Phys. Lett. B 826, 136918 (2022), arXiv:2105.13214 [hep-ph]

    2022 arXiv

  13. [21]

    Alioli, G

    S. Alioli, G. Billis, A. Broggio, A. Gavardi, S. Kallweit, M. A. Lim, G. Marinelli, R. Nagar, and D. Napoletano, JHEP 06, 205 (2023), arXiv:2212.10489 [hep-ph]

    2023 arXiv

  14. [22]

    Alioli, G

    S. Alioli, G. Billis, A. Broggio, A. Gavardi, S. Kallweit, M. A. Lim, G. Marinelli, R. Nagar, and D. Napoletano, JHEP 05, 128 (2023), arXiv:2301.11875 [hep-ph]

    2023 arXiv

  15. [23]

    I. W. Stewart, F. J. Tackmann, and W. J. Waalewijn, Phys. Rev. D 81, 094035 (2010), arXiv:0910.0467 [hep- ph]

    2010 arXiv

  16. [24]

    Alioli, A

    S. Alioli, A. Broggio, and M. A. Lim, JHEP 01, 066 (2022), arXiv:2111.03632 [hep-ph]

    2022 arXiv

  17. [25]

    Alioli, C

    S. Alioli, C. W. Bauer, A. Broggio, A. Gavardi, S. Kall- weit, M. A. Lim, R. Nagar, D. Napoletano, and L. Rot- toli, Phys. Rev. D 104, 094020 (2021), arXiv:2102.08390 [hep-ph]

    2021 arXiv

  18. [26]

    P. F. Monni, E. Re, and P. Torrielli, Phys. Rev. Lett. 116, 242001 (2016), arXiv:1604.02191 [hep-ph]

    2016 arXiv

  19. [27]

    Bizon, P

    W. Bizon, P. F. Monni, E. Re, L. Rottoli, and P. Tor- rielli, JHEP 02, 108 (2018), arXiv:1705.09127 [hep-ph]

    2018 arXiv

  20. [28]

    Gavardi, M

    A. Gavardi, M. A. Lim, S. Alioli, and F. J. Tackmann, JHEP 12, 069 (2023), arXiv:2308.11577 [hep-ph]

    2023 arXiv

  21. [29]

    I. W. Stewart, F. J. Tackmann, J. R. Walsh, and S. Zu- beri, Phys. Rev. D 89, 054001 (2014), arXiv:1307.1808

    2014 arXiv

  22. [30]

    P. Cal, M. A. Lim, D. J. Scott, F. J. Tackmann, and W. J. Waalewijn, JHEP03, 155 (2025), arXiv:2408.13301 [hep-ph]

    2025

  23. [31]

    Nason, JHEP 11, 040 (2004), hep-ph/0409146

    P. Nason, JHEP 11, 040 (2004), hep-ph/0409146

    2004 arXiv

  24. [32]

    M. A. Ebert, J. K. L. Michel, F. J. Tack- mann, et al. , DESY-17-099 (2018), webpage: http://scetlib.desy.de

    2018

  25. [33]

    Buonocore, M

    L. Buonocore, M. Grazzini, J. Haag, L. Rottoli, and C. Savoini, Phys. Rev. D 106, 014008 (2022), arXiv:2201.11519 [hep-ph]

    2022 arXiv

  26. [34]

    P. Cal, R. von Kuk, M. A. Lim, and F. J. Tackmann, Phys. Rev. D 110, 076005 (2024), arXiv:2306.16458 [hep- ph]

    2024 arXiv

  27. [35]

    Biello, A

    C. Biello, A. Sankar, M. Wiesemann, and G. Zanderighi, Eur. Phys. J. C 84, 479 (2024), arXiv:2402.04025 [hep- ph]

    2024 arXiv

  28. [36]

    Bishara, U

    F. Bishara, U. Haisch, P. F. Monni, and E. Re, Phys. Rev. Lett. 118, 121801 (2017), arXiv:1606.09253 [hep- ph]

    2017 arXiv

  29. [37]

    J. C. Collins and D. E. Soper, Nucl. Phys. B 193, 381 (1981), [Erratum: Nucl.Phys.B 213, 545 (1983)]

    1981

  30. [38]

    J. C. Collins and D. E. Soper, Nucl. Phys. B 197, 446 (1982)

    1982

  31. [39]

    J. C. Collins, D. E. Soper, and G. F. Sterman, Nucl. Phys. B 250, 199 (1985)

    1985

  32. [40]

    Catani, D

    S. Catani, D. de Florian, and M. Grazzini, Nucl. Phys. B 596, 299 (2001), arXiv:hep-ph/0008184

    2001 arXiv

  33. [41]

    de Florian and M

    D. de Florian and M. Grazzini, Nucl. Phys. B 616, 247 (2001), arXiv:hep-ph/0108273

    2001 arXiv

  34. [42]

    Collins, Foundations of perturbative QCD , Vol

    J. Collins, Foundations of perturbative QCD , Vol. 32 (Cambridge University Press, 2013)

    2013

  35. [43]

    C. W. Bauer, S. Fleming, and M. E. Luke, Phys. Rev. D 63, 014006 (2000), hep-ph/0005275

    2000 arXiv

  36. [44]

    C. W. Bauer, S. Fleming, D. Pirjol, and I. W. Stewart, Phys. Rev. D 63, 114020 (2001), hep-ph/0011336

    2001 arXiv

  37. [45]

    C. W. Bauer and I. W. Stewart, Phys. Lett. B 516, 134 (2001), hep-ph/0107001

    2001 arXiv

  38. [46]

    C. W. Bauer, D. Pirjol, and I. W. Stewart, Phys. Rev. D 65, 054022 (2002), hep-ph/0109045

    2002 arXiv

  39. [47]

    C. W. Bauer, S. Fleming, D. Pirjol, I. Z. Rothstein, and I. W. Stewart, Phys. Rev. D 66, 014017 (2002), hep- ph/0202088

    2002

  40. [48]

    Becher and M

    T. Becher and M. Neubert, Eur. Phys. J. C 71, 1665 (2011), arXiv:1007.4005 [hep-ph]

    2011 arXiv

  41. [49]

    M. G. Echevarria, A. Idilbi, and I. Scimemi, JHEP 07, 002 (2012), arXiv:1111.4996 [hep-ph]

    2012 arXiv

  42. [50]

    J.-Y. Chiu, A. Jain, D. Neill, and I. Z. Rothstein, JHEP 05, 084 (2012), arXiv:1202.0814 [hep-ph]

    2012 arXiv

  43. [51]

    Y. Li, D. Neill, and H. X. Zhu, Nucl. Phys. B 960, 115193 (2020), arXiv:1604.00392 [hep-ph]

    2020 arXiv

  44. [52]

    J.-y. Chiu, A. Jain, D. Neill, and I. Z. Rothstein, Phys. Rev. Lett. 108, 151601 (2012), arXiv:1104.0881 [hep-ph]

    2012 arXiv

  45. [53]

    M. A. Ebert and F. J. Tackmann, JHEP 02, 110 (2017), arXiv:1611.08610 [hep-ph]

    2017 arXiv

  46. [54]

    M. A. Ebert, J. K. L. Michel, I. W. Stewart, and F. J. Tackmann, JHEP 04, 102 (2021), arXiv:2006.11382 [hep- ph]

    2021 arXiv

  47. [55]

    Billis, F

    G. Billis, F. J. Tackmann, and J. Talbert, JHEP 03, 182 (2020), arXiv:1907.02971 [hep-ph]

    2020 arXiv

  48. [56]

    Ligeti, I

    Z. Ligeti, I. W. Stewart, and F. J. Tackmann, Phys. Rev. D 78, 114014 (2008), arXiv:0807.1926 [hep-ph]

    2008 arXiv

  49. [57]

    Abbate, M

    R. Abbate, M. Fickinger, A. H. Hoang, V. Mateu, and I. W. Stewart, Phys. Rev. D 83, 074021 (2011), arXiv:1006.3080 [hep-ph]

    2011 arXiv

  50. [58]

    Lustermans, J

    G. Lustermans, J. K. L. Michel, F. J. Tackmann, and W. J. Waalewijn, JHEP03, 124 (2019), arXiv:1901.03331 [hep-ph]

    2019 arXiv

  51. [59]

    Billis, J

    G. Billis, J. K. L. Michel, and F. J. Tackmann, JHEP 02, 170 (2025), arXiv:2411.16004 [hep-ph]

    2025 arXiv

  52. [60]

    A. J. Larkoski, D. Neill, and J. Thaler, JHEP 04, 017 (2014), arXiv:1401.2158 [hep-ph]

    2014 arXiv

  53. [61]

    I. W. Stewart, F. J. Tackmann, J. Thaler, C. K. Ver- milion, and T. F. Wilkason, JHEP 11, 072 (2015), arXiv:1508.01516 [hep-ph]

    2015 arXiv

  54. [62]

    Bertolini, D

    D. Bertolini, D. Kolodrubetz, D. Neill, P. Pietrulewicz, I. W. Stewart, F. J. Tackmann, and W. J. Waalewijn, JHEP 07, 099 (2017), arXiv:1704.08262 [hep-ph]

    2017 arXiv

  55. [63]

    Thaler and K

    J. Thaler and K. Van Tilburg, JHEP 03, 015 (2011), arXiv:1011.2268 [hep-ph]

    2011 arXiv

  56. [64]

    Thaler and K

    J. Thaler and K. Van Tilburg, JHEP 02, 093 (2012), arXiv:1108.2701 [hep-ph]

    2012 arXiv

  57. [65]

    Banfi, G

    A. Banfi, G. P. Salam, and G. Zanderighi, JHEP 08, 062 (2004), arXiv:hep-ph/0407287

    2004 arXiv

  58. [66]

    Becher and M

    T. Becher and M. Neubert, JHEP 07, 108 (2012), arXiv:1205.3806 [hep-ph]. 16

    2012 arXiv

  59. [67]

    Becher, M

    T. Becher, M. Neubert, and L. Rothen, JHEP 10, 125 (2013), arXiv:1307.0025 [hep-ph]

    2013 arXiv

  60. [68]

    Gavardi, Next-to-next-to-leading order predictions for diboson production in hadronic scattering combined with parton showers , Ph.D

    A. Gavardi, Next-to-next-to-leading order predictions for diboson production in hadronic scattering combined with parton showers , Ph.D. thesis, Universit` a degli Studi di Milano-Bicocca, Italy, Milan Bicocca U. (2023)

    2023

  61. [69]

    Bailey, T

    S. Bailey, T. Cridge, L. A. Harland-Lang, A. D. Mar- tin, and R. S. Thorne, Eur. Phys. J. C 81, 341 (2021), arXiv:2012.04684 [hep-ph]

    2021 arXiv

  62. [70]

    R. L. Workman et al. (Particle Data Group), PTEP 2022, 083C01 (2022)

    2022

  63. [71]

    R. V. Harlander, S. Liebler, and H. Mantler, Comput. Phys. Commun. 184, 1605 (2013), arXiv:1212.3249 [hep- ph]

    2013 arXiv

  64. [72]

    Alioli, G

    S. Alioli, G. Billis, A. Broggio, and G. Stagnitto, (2025), arXiv:2504.11357 [hep-ph]

    2025 arXiv

  65. [73]

    Boughezal, J

    R. Boughezal, J. M. Campbell, R. K. Ellis, C. Focke, W. Giele, X. Liu, F. Petriello, and C. Williams, Eur. Phys. J. C 77, 7 (2017), arXiv:1605.08011 [hep-ph]

    2017 arXiv

  66. [74]

    Mondini and C

    R. Mondini and C. Williams, JHEP 05, 045 (2021), arXiv:2102.05487 [hep-ph]

    2021 arXiv

  67. [75]

    Dulat, T.-J

    S. Dulat, T.-J. Hou, J. Gao, M. Guzzi, J. Hus- ton, P. Nadolsky, J. Pumplin, C. Schmidt, D. Stump, and C. P. Yuan, Phys. Rev. D 93, 033006 (2016), arXiv:1506.07443 [hep-ph]

    2016 arXiv

  68. [76]

    Sj¨ ostrand, S

    T. Sj¨ ostrand, S. Mrenna, and P. Z. Skands, Comput. Phys. Commun. 178, 852 (2008), arXiv:0710.3820 [hep- ph]

    2008 arXiv

  69. [77]

    Chekhovsky et al

    V. Chekhovsky et al. (CMS), (2024), arXiv:2412.13872 [hep-ex]

    2024 arXiv

  70. [78]

    Alioli, G

    S. Alioli, G. Bell, G. Billis, A. Broggio, B. Dehnadi, M. A. Lim, G. Marinelli, R. Nagar, D. Napoletano, and R. Rahn, Phys. Rev. D 109, 094009 (2024), arXiv:2312.06496 [hep-ph]

    2024 arXiv

  71. [79]

    G. Bell, R. Rahn, and J. Talbert, JHEP 07, 101 (2019), arXiv:1812.08690 [hep-ph]

    2019 arXiv

  72. [80]

    G. Bell, R. Rahn, and J. Talbert, JHEP 09, 015 (2020), arXiv:2004.08396 [hep-ph]

    2020 arXiv

  73. [81]

    G. Bell, B. Dehnadi, T. Mohrmann, and R. Rahn, (2023), arXiv:2312.11626 [hep-ph]

    2023 arXiv

  74. [82]

    F. J. Tackmann, (2024), arXiv:2411.18606 [hep-ph]

    2024 arXiv

  75. [83]

    M. A. Lim and R. Poncelet, (2024), arXiv:2412.14910 [hep-ph]

    2024

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.