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MiNNLO$_{\text{PS}}$: A new method to match NNLO QCD to parton showers

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read MiNNLOPS matches NNLO QCD to parton showers by adding one resummed third-order term.

desk verdict MiNNLOPS is a genuinely new and correct method for NNLO+PS matching; the central claim holds up, with minor presentation gaps around the completeness of the [D(pT)]^3 term. read the letter →

arxiv 1908.06987 v3 pith:V7KGYSZQ submitted 2019-08-19 hep-ph hep-ex

Pier Francesco Monni , Paolo Nason , Emanuele Re , Marius Wiesemann , Giulia Zanderighi This is my paper · ORCID
classification hep-phhep-ex
keywords NNLO+PSmatchingpartonshowertransverse-momentumresummationMiNLO'methodcolour-singletproductionHiggsDrell-YanprocessLHCphenomenology
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

The paper sets out a method, called MiNNLOPS, for attaching full next-to-next-to-leading-order (NNLO) QCD accuracy to parton-shower simulations of heavy colour-singlet production at the LHC. It builds on the MiNLO' procedure, which already makes a one-jet NLO calculation NLO-accurate for inclusive observables, and injects the missing NNLO information by connecting that procedure to transverse-momentum resummation. The key step is the addition of a single third-order term, $[D(p_T)]^{(3)}$, computed from resummation coefficients at event-generation time. The paper claims that the resulting master formula (4.34) is NNLO accurate for zero-jet observables, NLO accurate for one-jet observables, requires no merging scale, and preserves the leading-logarithmic structure of transverse-momentum-ordered showers. Proof-of-concept results for Higgs and Drell-Yan production reproduce fixed-order NNLO predictions within scale uncertainties at only about 50% more CPU time than MiNLO'.

What carries the argument

The central object is the MiNNLOPS master formula, eq. (4.34): $d\sigma/d\Phi_{FJ} = \exp[-\tilde{S}(p_T)]$ times an $\alpha_s$-expanded bracket containing the NLO one-jet cross section and the new $(\alpha_s/2\pi)^3 [D(p_T)]^{(3)} F^{\rm corr}(\Phi_{FJ})$ term, multiplied by the POWHEG radiation probability that generates the second emission and hands the remaining radiation to the shower. The load-bearing ingredient is $[D(p_T)]^{(3)}$, eq. (2.21), the third-order expansion of $D(p_T) = - (d\tilde{S}/dp_T) L(p_T) + dL/dp_T$, built from the resummation anomalous dimensions $A^{(1)}, A^{(2)}, A^{(3)}, B^{(1)}, \tilde{B}^{(2)}$, the hard-virtual coefficients $H^{(i)}$, the collinear coefficient functions $C^{(i)}$ and $G^{(i)}$, and the luminosity factors $L(p_T)$. Its role is to insert into MiNLO' all NNLO singular terms of the $p_T$ spectrum in the $p_T \to 0$ limit, so that after integration over $p_T$ the inclusive cross section is NNLO; $F^{\rm corr}(\Phi_{FJ})$ spreads those terms over the one-jet phase space in a way that matters only beyond the claimed accuracy.

What would settle it

Take the Drell-Yan implementation, remove $[D(p_T)]^{(3)}$, and compare the total cross section and rapidity distribution to the full MiNNLOPS result: if the shift is not a subleading $O(\alpha_s^3)$ effect, the singular reconstruction is incomplete. A sharper check is an order-by-order comparison of the expanded formula with a standard NNLO subtraction at fixed $\Phi_F$ and integrated over $p_T$, looking for any residual $1/p_T$ singularity beyond the claimed accuracy.

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Extended reading notes

Core claim

The central claim is that eq. (4.34) is a valid master formula for NNLO+PS matching: a fully differential NNLO calculation is embedded in an event generator, with the NNLO corrections computed during event generation rather than imposed by reweighting. In the zero-jet phase space, meaning the Born kinematics of the colour singlet, the formula is NNLO accurate; in the one-jet phase space it is NLO accurate; the two multiplicities are combined without an unphysical merging scale; and for showers ordered in transverse momentum the leading-logarithmic accuracy of the shower is preserved. The argument works by writing the singular transverse-momentum spectrum of the colour singlet as a total derivative, $\exp[-\tilde{S}(p_T)] L(p_T)$, whose third-order expansion supplies exactly the singular terms at $O(\alpha_s^2)$ that MiNLO' is missing. Adding $[D(p_T)]^{(3)}$ to the MiNLO' formula and spreading it over the one-jet phase space with a correlation factor $F^{\rm corr}$ makes the $p_T$-integrated result NNLO while leaving jet observables at NLO. The paper validates this on Higgs production in gluon fusion and on on-shell $Z$ (Drell-Yan) production at 13 TeV, showing agreement with NNLO fixed-order results for inclusive and rapidity distributions and agreement with MiNLO' for jet distributions.

Load-bearing premise

The derivation rests on the assumption that the singular part of the transverse-momentum spectrum at $O(\alpha_s^2)$ is fully captured by the momentum-space resummation formula (4.2) built from inclusive correlated clusters, so that the single term $[D(p_T)]^{(3)}$ in eq. (2.21) supplies all NNLO singular corrections; the paper supports this by power counting and numerical validation, but does not prove it with an independent fixed-order calculation.

Editorial extensions

If this is right

  • Inclusive and Born-level observables for Higgs and Drell-Yan production, such as the rapidity of the boson and the lepton distributions, reach NNLO accuracy and agree with fixed-order NNLO within scale uncertainties.
  • One-jet observables, such as leading-jet rapidity, rapidity differences, and azimuthal angles, remain NLO accurate, and hard jet configurations are essentially unchanged relative to MiNLO'.
  • No unphysical merging scale separates the zero- and one-jet multiplicities, so the matched sample is a single smooth event sample.
  • The leading-logarithmic accuracy of transverse-momentum-ordered showers is preserved, because the method generates only the first two hardest emissions and lets the shower handle the rest.
  • The scheme is efficient enough for complex colour-singlet processes: the paper reports about 50% more CPU time than MiNLO' and no reweighting, making vector-boson pair production a direct next target.

Reading between the lines

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

  • If the master formula is as accurate as claimed, the same construction should transfer to top-quark pair production, where the heavy system is coloured; the paper identifies this as future work, and the needed input would be the corresponding transverse-momentum resummed spectrum.
  • A direct test of the method's power-counting assumption is to implement the next term, $[D(p_T)]^{(4)}$, and check that the inclusive cross section changes only by $O(\alpha_s^3)$ rather than by a leading shift; the paper does not make this claim.
  • The freedom in the spreading factor $F^{\rm corr}(\Phi_{FJ})$ means different choices should differ only beyond NNLO; comparing the uniform and collinear-splitting choices in forward-rapidity regions would quantify the size of those subleading effects.
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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

3 major / 5 minor

Summary. The paper presents MiNNLOPS, a method for matching NNLO QCD calculations to parton showers for colour-singlet production at hadron colliders. The method builds on the previously existing MiNLO' procedure and on transverse-momentum resummation in momentum space. The central object is the master formula, eq. (4.34), in which the MiNLO' formula is supplemented by a term [D(pT)]^(3) that supplies the missing O(alpha_s^2) singular and constant terms of the pT spectrum. The derivation is presented in Sections 2.3 and 4, with technical details in Appendices A-E. The authors claim that the resulting generator is NNLO accurate in the zero-jet phase space, NLO accurate in the one-jet phase space, has no merging scale, is substantially more efficient than reweighting-based NNLOPS, and preserves the leading-logarithmic accuracy of transverse-momentum-ordered showers. Proof-of-concept results for hadronic Higgs production and for the Drell-Yan process are validated against the independent fixed-order codes MATRIX, HNNLO, and DYNNLO. Overall, the manuscript is carefully written and the central construction is sound, but the completeness of the [D(pT)]^(3) term, and therefore the core NNLO accuracy claim, rests on an imported resummation result plus numerical validation that is not fully conclusive; this needs to be addressed before the claim is fully established.

Significance. If the central claim survives scrutiny, MiNNLOPS is a significant methodological advance: it replaces the multidimensional reweighting of earlier NNLOPS approaches with a direct, efficient calculation of NNLO corrections at event-generation time, and it avoids any merging scale between jet multiplicities. The paper provides explicit analytic expressions for all ingredients, including the [D(pT)]^(3) term in Appendix C and scale-dependence formulae in Appendix D, cross-checks the momentum-space derivation against the impact-parameter formulation in Appendix E, and offers a thorough numerical validation against independent fixed-order codes. The claimed CPU overhead of only 50% relative to MiNLO' makes the method suitable for processes such as vector-boson pair production. These are concrete strengths that make the paper a strong candidate for publication once the completeness issue discussed below is settled.

major comments (3)
  1. [Sections 2.3 and 4, eqs. (2.20), (4.34)] The central NNLO accuracy claim depends on the assertion that [D(pT)]^(3) of eq. (2.21), combined with the NLO FJ cross section, reconstructs all O(alpha_s^2) singular and constant terms of the pT spectrum. This completeness is imported from the two-cluster momentum-space resummation formula (4.2) of refs. [26,27], and the internal cross-check against the b-space formulation in Appendix E does not constitute an independent verification. The numerical validation is not conclusive: in Table 2 the Higgs total cross section is 7.9% below the NNLO central value, and because MiNNLOPS uses dynamical pT-dependent scales whereas the fixed-order result uses scales of order m_H, a missing or misassigned O(alpha_s^2) term at the few-percent level could be absorbed by the different scale treatment. I request a direct fixed-order consistency check, for example comparing the O(alpha_s^2) expansion of eq. (4.30) with the singular part of the pT spectrum from an independent computation, or a quantitative decomposition showing that no term of order alpha_s^2/pT is omitted.
  2. [Section 2.3, paragraph after eq. (2.20)] The paper states that the regular terms omitted from eq. (2.20) were 'explicitly verified' to give a subleading numerical effect, but no verification is shown. The power-counting argument in eq. (2.17) is plausible, yet the numerical check is asserted rather than documented. Since the master formula is presented as a derivation with a definite accuracy, the reader should be able to see the size of the omitted terms, at least in an appendix. This is a smaller instance of the completeness concern raised in the first major comment, but it should be addressed with an actual number or plot.
  3. [Section 3, eqs. (3.1), (3.8), (3.9)] The spreading of [D(pT)]^(3) over the FJ phase space via the factor F_corr and the large-pT cutoff modifications via the parameter p in eq. (3.8) are introduced as arbitrary choices whose consistency with NNLO accuracy is argued by power counting and by the property (3.2). The numerical flatness of the jet observables in Figs. 3 and 6 supports the chosen default, but the manuscript does not state precisely what conditions on F_corr and on the large-pT damping are sufficient to preserve the claimed accuracy for an arbitrary choice. I am not asking for an exhaustive proof, but a formal statement of these conditions would turn an ad-hoc assumption into a checked property and would strengthen the paper.
minor comments (5)
  1. [Section 5.1, setup] The text says 'with an on-shell top-quark mass' in the context of the infinitely heavy top-quark approximation; this wording is confusing and should be clarified to avoid implying that top-quark mass effects are included.
  2. [Section 5.1, eq. (3.8)] The damping parameter p is fixed to 6 with a comment that variations give 'very moderate effects', but no result is shown. A small table or plot documenting this stability would be useful.
  3. [Figures 2 and 4] The ratio insets for the rapidity distributions are flat in the central region, but the bins are large and statistical fluctuations are hard to assess; showing the statistical uncertainty of the ratios would improve the validation plots.
  4. [Appendix B] There is a typo 'prodcution' in the sentence introducing the Higgs hard-virtual coefficients; also, the phrase 'Drell-Y an' appears in the Section 5 heading and should be corrected.
  5. [Section 1, end of Introduction] The code is said to be made publicly available within POWHEG-BOX, but no URL or version identifier is given. The final version should include the actual release information.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the MiNNLOPS master formula is derived from an independent resummation formalism and validated against external fixed-order codes.

full rationale

The central derivation chain runs from the momentum-space resummation formula, eq. (4.2), imported with attribution to refs. [26,27], through eq. (4.30) to the master formula eq. (4.34). No step fits a parameter to the NNLO results that the paper claims to reproduce. The coefficients entering [D(pT)]^(3), namely A(i), B(i), H(i), and the collinear coefficient functions, are fixed by standard resummation input (appendices B and C, with references [58-64]); they are not adjusted to force agreement with the external benchmarks. The numerical validation in Table 2 and Figs. 2-4 is performed against genuinely external fixed-order codes (MATRIX, HNNLO, DYNNLO), so the NNLO-accuracy claim has independent support. The omitted regular terms in eq. (2.20) and the residual 7.9% difference for the Higgs total cross section are accuracy limitations, not evidence that the prediction reduces by construction to its input. Self-citations to earlier MiNLO/POWHEG and resummation papers are normal and do not smuggle in the target result as an unverified premise. The paper is therefore self-contained for the purpose of this pass.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central derivation adds no new physical entities or fitted constants. It relies on standard collinear factorization, on the momentum-space resummation framework of refs. [26,27] (same group), and on MiNLO'/POWHEG. The hand-chosen damping parameter p and the freezing scales affect only beyond-NNLO terms and are stability-tested in the paper.

free parameters (2)
  • Logarithm-damping parameter p = p = 6
    Introduced in eq. (3.8) to turn off resummation logarithms at pT >= Q. The authors state that variations of p lead to moderate effects within uncertainties, so it is not fitted to data but is a hand-chosen parameter affecting beyond-NNLO terms.
  • Freezing scale for mu_R and mu_F = 2.5 GeV for Higgs, 1.8 GeV for Drell-Yan
    Chosen in Section 5.1 as the lower bound for scale variation, determined by the PDF lower bound and Sudakov suppression. Table 1 shows stability under lowering the scale, so this is a choice rather than a fitted target.
assumptions (6)
  • domain assumption Hadronic cross sections factorize into parton densities and partonic hard-scattering cross sections (collinear factorization).
    Used throughout Sections 2 and 4 to write B, V, R, and luminosity factors L. This is the standard QCD assumption for LHC hard-scattering processes.
  • domain assumption The momentum-space transverse-momentum resummation of refs. [26,27] correctly describes the singular O(alpha_s^2) spectrum via inclusive correlated clusters.
    Starting point of Section 4, eq. (4.2). The new method inherits all resummation coefficients and the cluster decomposition from these references.
  • domain assumption The MiNLO'/POWHEG formulas, eqs. (2.1)-(2.2), provide NLO accuracy and unitarity and can be extended by an additive [D(pT)]^(3) term.
    Basis of Section 2. The derivation relies on the unitarity condition eq. (2.5) and on the known MiNLO' scale choices.
  • standard math Integrals of the form in eq. (2.17), with a 1/pT singularity, powers of alpha_s(pT), and logarithms of Q/pT, are suppressed by the Sudakov factor to the stated order after integration down to the infrared cutoff.
    Used in Section 2.3 to decide which terms are needed for NLO and NNLO accuracy. Established in ref. [7] and assumed here.
  • domain assumption Transverse-momentum-ordered parton showers are leading-logarithmic accurate for the pT spectrum, so that showering does not spoil the NNLO/LL structure.
    Invoked at the end of Section 4 and in footnote 9, citing refs. [27,34,35].
  • ad hoc to paper The arbitrary spreading of [D(pT)]^(3) over the FJ phase space via F_corr, and the large-pT cutoff modifications, do not alter NNLO accuracy.
    Assumed in Section 3 and eqs. (3.1)-(3.9) based on power counting. The effect is beyond the claimed accuracy and is only checked numerically in an indirect way.

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Cite this review

Pith. "Pith review of MiNNLO$_{\text{PS}}$: A new method to match NNLO QCD to parton showers." pith.science (2026). https://pith.science/paper/V7KGYSZQ

@misc{pith2026190806987,
  author       = {Pith},
  title        = {Pith review of: MiNNLO$_\textPS$: A new method to match NNLO QCD to parton showers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V7KGYSZQ}},
  note         = {Machine review of arXiv:1908.06987}
}
abstract

We present a novel method to combine QCD calculations at next-to-next-to-leading order (NNLO) with parton shower (PS) simulations, that can be applied to the production of heavy systems in hadronic collisions, such as colour singlets or a $t\bar{t}$ pair. The NNLO corrections are included by connecting the MiNLO$^\prime$ method with transverse-momentum resummation, and they are calculated at generation time without any additional reweighting, making the algorithm considerably efficient. Moreover, the combination of different jet multiplicities does not require any unphysical merging scale, and the matching preserves the structure of the leading logarithmic corrections of the Monte Carlo simulation for parton showers ordered in transverse momentum. We present proof-of-concept applications to hadronic Higgs production and the Drell-Yan process at the LHC.

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Reference graph

Works this paper leans on

65 extracted references · 11 canonical work pages · cited by 10 Pith papers

  1. [1]

    Aad et al.,Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys

    ATLAScollaboration, G. Aad et al.,Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B716 (2012) 1–29, [1207.7214]

    arXiv 2012

  2. [2]

    Chatrchyan et al.,Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys

    CMS collaboration, S. Chatrchyan et al.,Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B716 (2012) 30–61, [1207.7235]

    arXiv 2012

  3. [3]

    Aaboud et al.,Measurement of the Drell-Yan triple-differential cross section inpp collisions at√s = 8 TeV, JHEP 12 (2017) 059, [1710.05167]

    ATLAScollaboration, M. Aaboud et al.,Measurement of the Drell-Yan triple-differential cross section inpp collisions at√s = 8 TeV, JHEP 12 (2017) 059, [1710.05167]

    arXiv 2017

  4. [4]

    CMS collaboration, A. M. Sirunyan et al.,Measurement of differential cross sections in the kinematic angular variableφ∗ for inclusive Z boson production in pp collisions at√s = 8 TeV, JHEP 03 (2018) 172, [1710.07955]

    work page Pith review arXiv 2018

  5. [5]

    Aaboud et al.,Measurement of theW-boson mass in pp collisions at√s = 7 TeV with the ATLAS detector, Eur

    ATLAScollaboration, M. Aaboud et al.,Measurement of theW-boson mass in pp collisions at√s = 7 TeV with the ATLAS detector, Eur. Phys. J.C78 (2018) 110, [1701.07240]

    arXiv 2018

  6. [6]

    Hamilton, P

    K. Hamilton, P. Nason and G. Zanderighi,MINLO: Multi-Scale Improved NLO, JHEP 10 (2012) 155, [1206.3572]

    arXiv 2012

  7. [7]

    Hamilton, P

    K. Hamilton, P. Nason, C. Oleari and G. Zanderighi,Merging H/W/Z + 0 and 1 jet at NLO with no merging scale: a path to parton shower + NNLO matching, JHEP 05 (2013) 082, [1212.4504]

    arXiv 2013

  8. [8]

    Extending the MINLO method

    R. Frederix and K. Hamilton,Extending the MINLO method, JHEP 05 (2016) 042, [1512.02663]

    work page Pith review arXiv 2016

Show all 65 references
  1. [9]

    Nason,A New method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040, [hep-ph/0409146]

    P. Nason,A New method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040, [hep-ph/0409146]

    2004 arXiv

  2. [10]

    Hamilton, P

    K. Hamilton, P. Richardson and J. Tully,A Positive-Weight Next-to-Leading Order Monte Carlo Simulation of Drell-Yan Vector Boson Production, JHEP 10 (2008) 015, [0806.0290]

    2008 arXiv

  3. [11]

    Bahr et al.,Herwig++ Physics and Manual, Eur

    M. Bahr et al.,Herwig++ Physics and Manual, Eur. Phys. J.C58 (2008) 639–707, [0803.0883]

    2008 arXiv

  4. [12]

    Hoeche, F

    S. Hoeche, F. Krauss, S. Schumann and F. Siegert,QCD matrix elements and truncated showers, JHEP 05 (2009) 053, [0903.1219]

    2009 arXiv

  5. [13]

    Hoche, F

    S. Hoche, F. Krauss, M. Schonherr and F. Siegert,NLO matrix elements and truncated showers, JHEP 08 (2011) 123, [1009.1127]

    2011 arXiv

  6. [14]

    Alioli, C

    S. Alioli, C. W. Bauer, C. Berggren, F. J. Tackmann, J. R. Walsh and S. Zuberi,Matching Fully Differential NNLO Calculations and Parton Showers, JHEP 06 (2014) 089, [1311.0286]

    2014 arXiv

  7. [15]

    Höche, Y

    S. Höche, Y. Li and S. Prestel,Drell-Yan lepton pair production at NNLO QCD with parton showers, Phys. Rev. D91 (2015) 074015, [1405.3607]

    2015 arXiv

  8. [16]

    Hamilton, P

    K. Hamilton, P. Nason, E. Re and G. Zanderighi,NNLOPS simulation of Higgs boson production, JHEP 10 (2013) 222, [1309.0017]

    2013 arXiv

  9. [17]

    Höche, Y

    S. Höche, Y. Li and S. Prestel,Higgs-boson production through gluon fusion at NNLO QCD with parton showers, Phys. Rev. D90 (2014) 054011, [1407.3773]

    2014 arXiv

  10. [18]

    Karlberg, E

    A. Karlberg, E. Re and G. Zanderighi,NNLOPS accurate Drell-Yan production, JHEP 09 (2014) 134, [1407.2940]. – 42 –

    2014 arXiv

  11. [19]

    Alioli, C

    S. Alioli, C. W. Bauer, C. Berggren, F. J. Tackmann and J. R. Walsh,Drell-Yan production at NNLL’+NNLO matched to parton showers, Phys. Rev. D92 (2015) 094020, [1508.01475]

    2015 arXiv

  12. [20]

    Astill, W

    W. Astill, W. Bizon, E. Re and G. Zanderighi,NNLOPS accurate associated HW production, JHEP 06 (2016) 154, [1603.01620]

    2016 arXiv

  13. [21]

    Astill, W

    W. Astill, W. Bizoń, E. Re and G. Zanderighi,NNLOPS accurate associated HZ production with H→bb decay at NLO, JHEP 11 (2018) 157, [1804.08141]

    2018 arXiv

  14. [22]

    E. Re, M. Wiesemann and G. Zanderighi,NNLOPS accurate predictions forW +W− production, JHEP 12 (2018) 121, [1805.09857]

    2018 arXiv

  15. [23]

    Hamilton, T

    K. Hamilton, T. Melia, P. F. Monni, E. Re and G. Zanderighi,Merging WW and WW+jet with MINLO, JHEP 09 (2016) 057, [1606.07062]

    2016 arXiv

  16. [24]

    Grazzini, S

    M. Grazzini, S. Kallweit, S. Pozzorini, D. Rathlev and M. Wiesemann,W +W− production at the LHC: fiducial cross sections and distributions in NNLO QCD, JHEP 08 (2016) 140, [1605.02716]

    2016 arXiv

  17. [25]

    Grazzini, S

    M. Grazzini, S. Kallweit and M. Wiesemann,Fully differential NNLO computations with MATRIX, Eur. Phys. J.C78 (2018) 537, [1711.06631]

    2018 arXiv

  18. [26]

    P. F. Monni, E. Re and P. Torrielli,Higgs Transverse-Momentum Resummation in Direct Space, Phys. Rev. Lett.116 (2016) 242001, [1604.02191]

    2016 arXiv

  19. [27]

    Bizon, P

    W. Bizon, P. F. Monni, E. Re, L. Rottoli and P. Torrielli,Momentum-space resummation for transverse observables and the Higgsp⊥ at N3LL+NNLO, 1705.09127

    arXiv

  20. [28]

    Frixione, P

    S. Frixione, P. Nason and C. Oleari,Matching NLO QCD computations with Parton Shower simulations: the POWHEG method, JHEP 11 (2007) 070, [0709.2092]

    2007 arXiv

  21. [29]

    Alioli, P

    S. Alioli, P. Nason, C. Oleari and E. Re,A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP 06 (2010) 043, [1002.2581]

    2010 arXiv

  22. [30]

    Catani and M

    S. Catani and M. Grazzini,QCD transverse-momentum resummation in gluon fusion processes, Nucl. Phys. B845 (2011) 297–323, [1011.3918]

    2011 arXiv

  23. [31]

    J. G. M. Gatheral,Exponentiation of Eikonal Cross-sections in Nonabelian Gauge Theories, Phys. Lett. 133B (1983) 90–94

    1983

  24. [32]

    Frenkel and J

    J. Frenkel and J. C. Taylor,Nonabelian Eikonal Exponentiation, Nucl. Phys. B246 (1984) 231–245

    1984

  25. [33]

    Frixione, Z

    S. Frixione, Z. Kunszt and A. Signer,Three jet cross-sections to next-to-leading order, Nucl. Phys. B467 (1996) 399–442, [hep-ph/9512328]

    1996 arXiv

  26. [34]

    Parisi and R

    G. Parisi and R. Petronzio,Small Transverse Momentum Distributions in Hard Processes, Nucl. Phys. B154 (1979) 427–440

    1979

  27. [35]

    Dasgupta, F

    M. Dasgupta, F. A. Dreyer, K. Hamilton, P. F. Monni and G. P. Salam,Logarithmic accuracy of parton showers: a fixed-order study, JHEP 09 (2018) 033, [1805.09327]

    2018 arXiv

  28. [36]

    Butterworth et al.,PDF4LHC recommendations for LHC Run II, J

    J. Butterworth et al.,PDF4LHC recommendations for LHC Run II, J. Phys. G43 (2016) 023001, [1510.03865]

    2016 arXiv

  29. [37]

    NNPDF collaboration, R. D. Ball et al.,Parton distributions for the LHC Run II, JHEP 04 (2015) 040, [1410.8849]. – 43 –

    2015 arXiv

  30. [38]

    Alioli, P

    S. Alioli, P. Nason, C. Oleari and E. Re,Vector boson plus one jet production in POWHEG, JHEP 01 (2011) 095, [1009.5594]

    2011 arXiv

  31. [39]

    J. M. Campbell, R. K. Ellis, R. Frederix, P. Nason, C. Oleari and C. Williams,NLO Higgs Boson Production Plus One and Two Jets Using the POWHEG BOX, MadGraph4 and MCFM, JHEP 07 (2012) 092, [1202.5475]

    2012 arXiv

  32. [40]

    Buckley, J

    A. Buckley, J. Ferrando, S. Lloyd, K. Nordström, B. Page, M. Rüfenacht, M. Schönherr and G. Watt,LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J.C75 (2015) 132, [1412.7420]

    2015 arXiv

  33. [41]

    G. P. Salam and J. Rojo,A Higher Order Perturbative Parton Evolution Toolkit (HOPPET), Comput. Phys. Commun.180 (2009) 120–156, [0804.3755]

    2009 arXiv

  34. [42]

    Gehrmann and E

    T. Gehrmann and E. Remiddi,Numerical evaluation of harmonic polylogarithms, Comput. Phys. Commun. 141 (2001) 296–312, [hep-ph/0107173]

    2001 arXiv

  35. [43]

    R. V. Harlander and W. B. Kilgore,Next-to-next-to-leading order Higgs production at hadron colliders, Phys.Rev.Lett. 88 (2002) 201801, [hep-ph/0201206]

    2002 arXiv

  36. [44]

    Anastasiou and K

    C. Anastasiou and K. Melnikov,Higgs boson production at hadron colliders in NNLO QCD, Nucl.Phys. B646 (2002) 220–256, [hep-ph/0207004]

    2002 arXiv

  37. [45]

    Ravindran, J

    V. Ravindran, J. Smith and W. L. van Neerven,NNLO corrections to the total cross-section for Higgs boson production in hadron hadron collisions, Nucl.Phys. B665 (2003) 325–366, [hep-ph/0302135]

    2003 arXiv

  38. [46]

    Ravindran, J

    V. Ravindran, J. Smith and W. Van Neerven,Next-to-leading order QCD corrections to differential distributions of Higgs boson production in hadron-hadron collisions, Nucl. Phys. B634 (2002) 247–290, [hep-ph/0201114]

    2002 arXiv

  39. [47]

    Hamberg, W

    R. Hamberg, W. L. van Neerven and T. Matsuura,A complete calculation of the orderα2 s correction to the Drell-YanK factor, Nucl. Phys. B359 (1991) 343–405

    1991

  40. [48]

    W. L. van Neerven and E. B. Zijlstra,The O(α2 s) corrected Drell-YanK factor in the DIS and MS scheme, Nucl. Phys. B382 (1992) 11–62

    1992

  41. [49]

    Anastasiou, L

    C. Anastasiou, L. J. Dixon, K. Melnikov and F. Petriello,Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD, Phys. Rev. Lett.91 (2003) 182002, [hep-ph/0306192]

    2003 arXiv

  42. [50]

    Melnikov and F

    K. Melnikov and F. Petriello,Electroweak gauge boson production at hadron colliders through O(α2 s), Phys. Rev. D74 (2006) 114017, [hep-ph/0609070]

    2006 arXiv

  43. [51]

    Anastasiou, L

    C. Anastasiou, L. J. Dixon, K. Melnikov and F. Petriello,High precision QCD at hadron colliders: Electroweak gauge boson rapidity distributions at NNLO, Phys. Rev. D69 (2004) 094008, [hep-ph/0312266]

    2004 arXiv

  44. [52]

    Grazzini,NNLO predictions for the Higgs boson signal in the H —> WW —> lnu lnu and H —> ZZ —> 4l decay channels, JHEP 02 (2008) 043, [0801.3232]

    M. Grazzini,NNLO predictions for the Higgs boson signal in the H —> WW —> lnu lnu and H —> ZZ —> 4l decay channels, JHEP 02 (2008) 043, [0801.3232]

    2008 arXiv

  45. [53]

    Catani, L

    S. Catani, L. Cieri, G. Ferrera, D. de Florian and M. Grazzini,Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett.103 (2009) 082001, [0903.2120]

    2009 arXiv

  46. [54]

    Sjöstrand, S

    T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O. Rasmussen and P. Z. Skands,An Introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159–177, [1410.3012]. – 44 –

    2015 arXiv

  47. [55]

    A. Banfi, P. F. Monni, G. P. Salam and G. Zanderighi,Higgs and Z-boson production with a jet veto, Phys. Rev. Lett.109 (2012) 202001, [1206.4998]

    2012 arXiv

  48. [56]

    Cacciari, G

    M. Cacciari, G. P. Salam and G. Soyez,The anti-kt jet clustering algorithm, JHEP 04 (2008) 063, [0802.1189]

    2008 arXiv

  49. [57]

    Nason and G

    P. Nason and G. Ridolfi,A Positive-weight next-to-leading-order Monte Carlo for Z pair hadroproduction, JHEP 08 (2006) 077, [hep-ph/0606275]

    2006 arXiv

  50. [58]

    de Florian and M

    D. de Florian and M. Grazzini,The Structure of large logarithmic corrections at small transverse momentum in hadronic collisions, Nucl. Phys. B616 (2001) 247–285, [hep-ph/0108273]

    2001 arXiv

  51. [59]

    Becher and M

    T. Becher and M. Neubert,Drell-Yan Production at SmallqT, Transverse Parton Distributions and the Collinear Anomaly, Eur. Phys. J.C71 (2011) 1665, [1007.4005]

    2011 arXiv

  52. [60]

    C. T. H. Davies and W. J. Stirling,Nonleading Corrections to the Drell-Yan Cross-Section at Small Transverse Momentum, Nucl. Phys. B244 (1984) 337–348

    1984

  53. [61]

    Catani and M

    S. Catani and M. Grazzini,Higgs Boson Production at Hadron Colliders: Hard-Collinear Coefficients at the NNLO, Eur. Phys. J.C72 (2012) 2013, [1106.4652]

    2012 arXiv

  54. [62]

    Gehrmann, T

    T. Gehrmann, T. Luebbert and L. L. Yang,Calculation of the transverse parton distribution functions at next-to-next-to-leading order, JHEP 06 (2014) 155, [1403.6451]

    2014 arXiv

  55. [63]

    M. G. Echevarria, I. Scimemi and A. Vladimirov,Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order, JHEP 09 (2016) 004, [1604.07869]

    2016 arXiv

  56. [64]

    Catani, L

    S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini,Vector boson production at hadron colliders: hard-collinear coefficients at the NNLO, Eur. Phys. J.C72 (2012) 2195, [1209.0158]

    2012 arXiv

  57. [65]

    Bozzi, S

    G. Bozzi, S. Catani, D. de Florian and M. Grazzini,Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC, Nucl. Phys. B737 (2006) 73–120, [hep-ph/0508068]. – 45 –

    2006 arXiv

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