Pith. sign in

REVIEW 7 minor 77 references

Challenges for Monte Carlo generators

T0 review · 0 major / 7 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Future lepton colliders will reach their permil-level physics goals only if Monte Carlo event generators overcome defined bottlenecks in beam spectra, QED resummation, NNLO electroweak corrections, and matching.

desk verdict A competent, well-cited review of MC generator challenges for future lepton colliders; no new results but a useful roadmap with a few minor overstatements. read the letter →

arxiv 2412.06580 v1 pith:VHVU5FT6 submitted 2024-12-09 hep-ph hep-ex

Jürgen Reuter This is my paper · ORCID
classification hep-phhep-ex
keywords MonteCarloeventgeneratorsleptoncollidersbeamstrahlungbeamspectraelectroweakcorrectionsQEDresummationpartonshowerstopthreshold
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

Future electron-positron and muon colliders aim at one-part-in-a-thousand cross-section precision and a top-mass measurement at the 30-50 MeV level. This paper argues that reaching those targets requires Monte Carlo event generators to overcome a specific list of bottlenecks: realistic beam spectra with beamstrahlung, polarized initial and final states, NNLO electroweak corrections, resummation of initial-state QED radiation, matching of fixed-order results to QED and electroweak showers, specialized threshold processes, BSM simulation, and computing performance. Much of the needed technology can be carried over from two decades of LHC generator development, but the QED-dominated environment of lepton colliders makes several problems genuinely new. The sympathetic reading is that these are the items the community must invest in before data taking starts, and the paper maps which tools already cover them and which do not.

What carries the argument

The central object is the Monte Carlo event generator itself, understood as a chain running from the accelerator beam spectrum, through hard matrix elements with fixed-order corrections, initial-state QED resummation, parton shower, matching, hadronization, and detector-facing event output. Within that chain, the load-bearing mechanisms are the two-dimensional histogrammed fit to accelerator beam spectra, the two resummation formalisms — YFS exponentiation for soft photons and collinear QED factorization for collinear logarithms — and the matching algorithms that attach these to NLO or NNLO matrix elements. The paper uses this chain to classify every challenge: each section names where in the chain current tooling stops being sufficient.

What would settle it

A concrete test: take a published lepton-collider luminometry Bhabha cross-section target of one part in ten thousand to one part in one hundred thousand and run the full generator chain (histogrammed beam spectrum, two-loop electroweak corrections, YFS resummation, QED shower); if the residual uncertainty between the best available code and an independent fixed-order calculation exceeds the target when data taking starts, the readiness assessment fails. Equivalently, a first high-statistics Z-pole or threshold run that disagrees with the state-of-the-art generator by more than the quoted permil uncertainty would falsify the claim that the listed roadmap suffices.

Watch

Extended reading notes

Core claim

The paper's central claim is that the precision physics programme of future lepton colliders is currently held back less by accelerator or detector questions than by the readiness of Monte Carlo event generators. It lists the decisive bottlenecks and anchors each in a concrete tooling gap: beam spectra need two-dimensional histogrammed fits rather than factorized smeared parameterizations; initial-state radiation needs a combination of YFS soft-photon exponentiation and collinear QED factorization that is not yet universally automated; NLO electroweak corrections are automated but NNLO electroweak corrections with two-loop multi-scale integrals remain years away; and matching QED and electroweak showers to fixed-order calculations is only partially solved. For special processes, luminometry requires complete two-loop plus leading three-loop electroweak corrections in dedicated Bhabha codes, while the top threshold needs an exclusive Monte Carlo at NLL matched to NLO NRQCD, with NNLL matched to NNLO as the desired target. If this assessment is right, generator development, not physics analysis, is on the critical path for the lepton-collider precision programme.

Load-bearing premise

The load-bearing premise is that the collider programme really needs one-part-in-a-thousand precision and that today's generator technology can be extended, above all by automating NNLO electroweak corrections, before data taking starts.

Editorial extensions

If this is right

  • The precision reach of the proposed linear and circular electron-positron colliders is tied to NNLO electroweak automation; until two-loop multi-scale integrals and NNLO subtraction are available for generic four-fermion and six-fermion processes, permil-level cross sections cannot be certified.
  • Beam simulation must adopt two-dimensional histogrammed spectra including the electron-photon, photon-electron, and photon-photon components; simple factorized parameterizations are insufficient for radio-frequency, drive-beam, plasma, and photon colliders.
  • A universal matching formalism between fixed-order electroweak corrections and exclusive QED and electroweak showers is a stated prerequisite for permil precision on both inclusive and exclusive predictions.
  • The top-mass extraction at 30-50 MeV uncertainty depends on moving the top threshold from inclusive NNNLO NRQCD into an exclusive Monte Carlo, with NNLL matched to NNLO as the major remaining undertaking.
  • Performance is a first-class challenge: multi-fermion electroweak phase spaces at NLO require parallel adaptive sampling, GPU offloading, and machine-learning phase-space generators to keep simulation computationally affordable.

Reading between the lines

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

  • Beyond the paper: if the NNLO electroweak bottleneck really takes many years as stated, the first years of a lepton collider may have to run a staged precision programme, with only selected processes at permil accuracy and a central cross-section measurement waiting on generator maturity.
  • Beyond the paper: the unresolved competition between YFS and collinear-factorization resummation suggests a future hybrid generator that chooses method by process and kinematics; nothing in the current toolchain does this adaptively.
  • Beyond the paper: muon colliders extend the same challenges, and the paper's mention of full electroweak and Standard-Model collinear factorization implies they may need electroweak parton distributions and fragmentation functions as a baseline rather than a correction.
  • Beyond the paper: Tera-Z samples may make hadronization models the limiting systematic, so a data-driven or machine-learning-trained hadronization benchmarked against Z-pole data would be a testable extension of the paper's speculation.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 7 minor

Summary. The manuscript is a concise proceedings-style review, organized around the ECFA Higgs-Top-Electroweak Factory studies, of the status and challenges of Monte Carlo event generators for future lepton colliders. After an introduction listing the relevant multi-purpose generators (MG5_aMC@NLO, Sherpa, Whizard) and specialized tools (BabaYaga, BHLumi/BHWide, KKMC), it discusses beam-spectrum simulation, hard matrix elements and initial-state QED resummation, parton showers/matching/hadronization, special processes (two-fermion production, Bhabha scattering, photoproduction, WW and top thresholds), BSM simulation, and phase-space/performance issues. The central claim, stated in the abstract, is that these areas constitute a specific set of challenges that need to be solved before a future lepton collider starts data taking; the body supports this with an inventory of current capabilities and open problems rather than with new calculations.

Significance. If correct, the paper is a useful community roadmap: it identifies concrete bottlenecks (NNLO electroweak automation, combination of collinear and YFS QED resummation, realistic beam spectra including FCC-ee, EW showers, top-threshold exclusive MCs, and performance at Tera-Z) and connects them to ongoing developments. Its strengths are that it is well referenced, technically consistent with the current literature, and grounded in the ECFA/Snowmass process; it also credits the transfer of LHC-era NLO automation and parton-shower technology to lepton colliders. As a survey it contains no new derivations or machine-checkable claims, so its value lies in the accuracy and completeness of the inventory. The main risk is that the prioritization implicitly assumes current precision targets (permil-level cross sections, 30-50 MeV top mass) remain fixed; that assumption is external and does not make the list internally inconsistent.

minor comments (7)
  1. [Secs. 2 and 8] There is an internal inconsistency about CIRCE2: Sec. 2 states that 'spectra for CEPC, CLIC, and ILC are available, while the FCC-ee spectra will be made available soon', whereas Sec. 8 claims that the two-dimensional histogrammed fit 'allows to properly describe synchrotrons like CEPC and FCC-ee'. Please reconcile the two statements, for example by restricting the Sec. 8 claim to CEPC or by rephrasing it as a planned capability.
  2. [Sec. 4] The sentence on machine-learning hadronization ('might result in realistic hadronic event generation') is presented without a citation; please add a reference to concrete ML-hadronization studies or mark the sentence explicitly as the author's assessment.
  3. [Sec. 4] The 'speculations that samples of up to 200 ab-1 ... might necessitate the development of new formalisms' is attributed to no source; please either cite the discussion or state explicitly that this is the author's conjecture.
  4. [Sec. 3] The sentence 'NLO electroweak (EW) corrections dominate due to phyics processes dominate d by EW resonance production' is garbled and should be rewritten, for example as 'NLO electroweak corrections are particularly important for processes dominated by EW resonance production'.
  5. [Sec. 7] There is a typo in 'message-imaging protocal': MPI stands for Message Passing Interface, so 'message-passing protocol' (or simply 'MPI') is what is intended.
  6. [Sec. 1] The phrase 'we will discuss first discuss the simulation' contains a duplicated verb; remove one occurrence of 'discuss'.
  7. [Sec. 5] The term 'lumical' should be expanded or corrected (presumably 'luminosity calorimeter'), and 'CrystalBall' should be 'Crystal Ball'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity identified; the review's challenge list is supported by external literature, not derived from its own inputs.

full rationale

This paper is a survey/roadmap, not a derivation: it lists Monte Carlo challenges for future lepton colliders and supports each item with citations to the literature. There are no fitted parameters renamed as predictions, no equations that reduce to their own inputs, and no central claim whose force depends on a self-citation chain. The author's self-citations (Whizard, O'Mega, NLO EW results, top-threshold tools, parallelization) are used as examples of ongoing work, which is normal in a review and not load-bearing: the claim that beam spectra, polarization, EW higher orders, QED resummation, matching/showers, BSM simulation, and performance are challenges stands independently of whether the author's own tools are the best solutions. The only concrete issue is an internal inconsistency between Sec. 2 (FCC-ee spectra 'will be made available soon' in CIRCE2/Whizard) and Sec. 8 ('properly describe synchrotrons like CEPC and FCC-ee'), but that is a peripheral overstatement about a specific tool, not circular reasoning. The ECFA study orientation and the many external citations also make the review's content externally grounded. Therefore no circular step is exhibited, and the honest finding is score 0.

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

This is a review paper; it introduces no free parameters, no invented entities, and no new axioms beyond the standard perturbative QFT framework assumed by all cited tools.

assumptions (2)
  • domain assumption Perturbative QCD and electroweak factorization are valid at energies of future lepton colliders.
    The review assumes these frameworks throughout; they underlie all cited MC generators.
  • domain assumption Standard Model and its effective field theories are the correct framework for simulating signals and backgrounds.
    The review's BSM discussion relies on SMEFT and Lagrangian-level tools; it does not question the SM as baseline.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Challenges for Monte Carlo generators." pith.science (2026). https://pith.science/paper/VHVU5FT6

@misc{pith2026241206580,
  author       = {Pith},
  title        = {Pith review of: Challenges for Monte Carlo generators},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VHVU5FT6}},
  note         = {Machine review of arXiv:2412.06580}
}
read the original abstract

This contribution lists challenges of Monte Carlo event generators for future lepton, especially linear colliders. A lot of the recent development benefits from the achievements at the Large Hadron Collider (LHC), but several aspects are unique for lepton colliders like beam simulation, polarization, electroweak higher order corrections and resummed QED corrections. We will describe the status of multi-purpose event generators and specialized codes and outline the challenges for these tools until such a collider starts data taking.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

77 extracted references · 7 canonical work pages

  1. [1]

    Alwall, R

    J. Alwall, R. Frederix, S. Frixione, V . Hirschi, F. Malto ni, O. Mattelaer, H.S. Shao, T. Stelzer, P . Torrielli, M. Zaro, The automated computatio n of tree-level and next-to- leading order di fferential cross sections, and their matching to parton showe r simula- tions, JHEP 07, 079 (2014), 1405.0301. 10.1007/JHEP07(2014)079

    arXiv 2014

  2. [2]

    Gleisberg, S

    T. Gleisberg, S. Hoeche, F. Krauss, A. Schalicke, S. Schu mann, J.C. Winter, SHERP A

    work page

  3. [3]

    10.1088/1126-6708/2004/02/056

    alpha: A Proof of concept version, JHEP 02, 056 (2004), hep-ph/0311263. 10.1088/1126-6708/2004/02/056

    arXiv 2004

  4. [4]

    Bothmann et al

    E. Bothmann et al. (Sherpa), Event Generation with Sherp a 2.2, SciPost Phys. 7, 034 (2019), 1905.09127. 10.21468/SciPostPhys.7.3.034

    arXiv 2019

  5. [5]

    Kilian, T

    W . Kilian, T. Ohl, J. Reuter, WHIZARD: Simulating Multi- Particle Pro- cesses at LHC and ILC, Eur. Phys. J. C 71, 1742 (2011), 0708.4233. 10.1140/epjc/s10052-011-1742-y

    arXiv 2011

  6. [6]

    Moretti, T

    M. Moretti, T. Ohl, J. Reuter, O’Mega: An Optimizing matr ix element generator, pp. 1981–2009 (2001), hep-ph/0102195

    arXiv 2001

  7. [7]

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

    M. Bahr et al., Herwig ++ Physics and Manual, Eur. Phys. J. C 58, 639 (2008), 0803.0883. 10.1140/epjc/s10052-008-0798-9

    arXiv 2008

  8. [8]

    Bellm et al., Herwig 7.0 /Herwig++ 3.0 release note, Eur

    J. Bellm et al., Herwig 7.0 /Herwig++ 3.0 release note, Eur. Phys. J. C 76, 196 (2016), 1512.01178. 10.1140/epjc/s10052-016-4018-8

    arXiv 2016

Show all 77 references
  1. [9]

    Sjostrand, S

    T. Sjostrand, S. Mrenna, P .Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05, 026 (2006), hep-ph/0603175. 10.1088/1126-6708/2006/05/026

    2006 arXiv

  2. [10]

    Sjöstrand, S

    T. Sjöstrand, S. Ask, J.R. Christiansen, R. Corke, N. Des ai, P . Ilten, S. Mrenna, S. Pres- tel, C.O. Rasmussen, P .Z. Skands, An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191, 159 (2015), 1410.3012. 10.1016/j.cpc.2015.01.024

    2015 arXiv

  3. [11]

    Bierlich et al., A comprehensive guide to the physics and usage of PYTHIA 8.3 (2022), 2203.11601

    C. Bierlich et al., A comprehensive guide to the physics and usage of PYTHIA 8.3 (2022), 2203.11601. 10.21468/SciPostPhysCodeb.8

    2022 arXiv

  4. [12]

    Carloni Calame, G

    C.M. Carloni Calame, G. Montagna, O. Nicrosini, F. Picc inini, The BABA Y AGA event generator, Nucl. Phys. B Proc. Suppl. 131, 48 (2004), hep-ph/0312014. 10.1016/j.nuclphysbps.2004.02.008

    2004 arXiv

  5. [13]

    Jadach, W

    S. Jadach, W . Placzek, E. Richter-Was, B.F.L. Ward, Z. W as, Upgrade of the Monte Carlo program BHLUMI for Bhabha scattering at low angles to v ersion 4.04, Comput. Phys. Commun. 102, 229 (1997). 10.1016/S0010-4655(96)00156-7

    1997 doi

  6. [14]

    Jadach, W

    S. Jadach, W . Placzek, B.F.L. Ward, BHWIDE 1.00: O(alph a) YFS exponentiated Monte Carlo for Bhabha scattering at wide angles for LEP-1 / SLC and LEP-2, Phys. Lett. B 390, 298 (1997), hep-ph/9608412. 10.1016/S0370-2693(96)01382-2

    1997 arXiv

  7. [15]

    Jadach, B.F.L

    S. Jadach, B.F.L. Ward, Z. W ˛ as, S.A. Y ost, A. Siodmok, M ulti-photon Monte Carlo event generator KKMCee for lepton and quark pair production in lepton colliders, Com- put. Phys. Commun. 283, 108556 (2023), 2204.11949. 10.1016/j.cpc.2022.108556

    2023 arXiv

  8. [16]

    Campbell et al., Event generators for high-energy physics experiments, SciPost Phys

    J.M. Campbell et al., Event generators for high-energy physics experiments, SciPost Phys. 16, 130 (2024), 2203.11110. 10.21468/SciPostPhys.16.5.130

    2024 arXiv

  9. [17]

    Berggren (LCC), Generating the full SM at linear coll iders, PoS ICHEP2020, 903 (2021), 2105.04049

    M. Berggren (LCC), Generating the full SM at linear coll iders, PoS ICHEP2020, 903 (2021), 2105.04049. 10.22323/1.390.0903

    2021 arXiv

  10. [18]

    Abdallah et al

    W . Abdallah et al. (CEPC Study Group), CEPC Technical De sign Report: Accelerator, Radiat. Detect. Technol. Methods 8, 1 (2024), 2312.14363. 10.1007/s41605-024-00463-y

    2024

  11. [19]

    The International Linear Collider Technical Design Re port - V olume 2: Physics (2013), 1306.6352

    2013 arXiv

  12. [20]

    Abramowicz et al., The International Linear Collide r Technical Design Report - V ol- ume 4: Detectors (2013), 1306.6329

    H. Abramowicz et al., The International Linear Collide r Technical Design Report - V ol- ume 4: Detectors (2013), 1306.6329

    2013 arXiv

  13. [21]

    Abada et al

    A. Abada et al. (FCC), FCC-ee: The Lepton Collider: Futu re Circular Col- lider Conceptual Design Report V olume 2, Eur. Phys. J. ST 228, 261 (2019). 10.1140/epjst/e2019-900045-4

    2019 doi

  14. [22]

    10.5170/CERN-2012-007

    A Multi-TeV Linear Collider Based on CLIC Technology: C LIC Conceptual Design Report (2012). 10.5170/CERN-2012-007

    2012 doi

  15. [23]

    10.5170/CERN-2012-003

    Physics and Detectors at CLIC: CLIC Conceptual Design R eport (2012), 1202.5940. 10.5170/CERN-2012-003

    2012 arXiv

  16. [24]

    Accettura et al., Towards a muon collider, Eur

    C. Accettura et al., Towards a muon collider, Eur. Phys. J. C 83, 864 (2023), [Erratum: Eur.Phys.J.C 84, 36 (2024)], 2303.08533. 10.1140/epjc/s10052-023-11889-x

    2023 arXiv

  17. [25]

    Ohl, CIRCE version 1.0: Beam spectra for simulating l inear collider physics, Comput

    T. Ohl, CIRCE version 1.0: Beam spectra for simulating l inear collider physics, Comput. Phys. Commun. 101, 269 (1997), hep-ph/9607454. 10.1016/S0010-4655(96)00167-1

    1997 arXiv

  18. [26]

    Frixione, O

    S. Frixione, O. Mattelaer, M. Zaro, X. Zhao, Lepton coll isions in Mad- Graph5_aMC@NLO (2021), 2108.10261

    2021 arXiv

  19. [27]

    Ohl, Functional Directed Acyclical Graphs for Scatt ering Amplitudes in Perturbation Theory (2023), 2306.02414

    T. Ohl, Functional Directed Acyclical Graphs for Scatt ering Amplitudes in Perturbation Theory (2023), 2306.02414

    2023 arXiv

  20. [28]

    Ballestrero et al., Precise predictions for same-si gn W-boson scattering at the LHC, Eur

    A. Ballestrero et al., Precise predictions for same-si gn W-boson scattering at the LHC, Eur. Phys. J. C 78, 671 (2018), 1803.07943. 10.1140/epjc/s10052-018-6136-y

    2018 arXiv

  21. [29]

    Rothe, Ph.D

    V . Rothe, Ph.D. thesis, Hamburg U., Universität Hambur g, Hamburg U., Hamburg (2021)

    2021

  22. [30]

    Bredt, Ph.D

    P .M. Bredt, Ph.D. thesis, Hamburg U., Hamburg (2022), 2212.04393

    2022 arXiv

  23. [31]

    Stienemeier, Ph.D

    P . Stienemeier, Ph.D. thesis, Hamburg U., Hamburg (202 2)

  24. [32]

    Kilian, J

    W . Kilian, J. Reuter, T. Robens, NLO Event Generation fo r Chargino Pro- duction at the ILC, Eur. Phys. J. C 48, 389 (2006), hep-ph/0607127. 10.1140/epjc/s10052-006-0048-y

    2006 arXiv

  25. [33]

    Robens, J

    T. Robens, J. Kalinowski, K. Rolbiecki, W . Kilian, J. Re uter, (N)LO Simulation of Chargino Production and Decay, Acta Phys. Polon. B 39, 1705 (2008), 0803.4161

    2008 arXiv

  26. [34]

    Bredt, W

    P .M. Bredt, W . Kilian, J. Reuter, P . Stienemeier, NLO el ectroweak corrections to multi-boson processes at a muon collider, JHEP 12, 138 (2022), 2208.09438. 10.1007/JHEP12(2022)138

    2022 arXiv

  27. [35]

    Cullen et al

    G. Cullen et al. (GoSam), G OSAM-2.0: a tool for automated one-loop calculations within the Standard Model and beyond, Eur. Phys. J. C 74, 3001 (2014), 1404.7096. 10.1140/epjc/s10052-014-3001-5

    2014 arXiv

  28. [36]

    Cascioli, P

    F. Cascioli, P . Maierhofer, S. Pozzorini, Scattering A mplitudes with Open Loops, Phys. Rev. Lett. 108, 111601 (2012), 1111.5206. 10.1103/PhysRevLett.108.111601

    2012 arXiv

  29. [37]

    Buccioni, J.N

    F. Buccioni, J.N. Lang, J.M. Lindert, P . Maierhöfer, S. Pozzorini, H. Zhang, M.F. Zoller (OpenLoops 2), OpenLoops 2, Eur. Phys. J. C 79, 866 (2019), 1907.13071. 10.1140/epjc/s10052-019-7306-2

    2019 arXiv

  30. [38]

    Actis, A

    S. Actis, A. Denner, L. Hofer, J.N. Lang, A. Scharf, S. Uc cirati, RECOLA: REcur- sive Computation of One-Loop Amplitudes, Comput. Phys. Com mun. 214, 140 (2017), 1605.01090. 10.1016/j.cpc.2017.01.004

    2017 arXiv

  31. [39]

    Binoth et al., A Proposal for a Standard Interface bet ween Monte Carlo Tools and One-Loop Programs, Comput

    T. Binoth et al., A Proposal for a Standard Interface bet ween Monte Carlo Tools and One-Loop Programs, Comput. Phys. Commun. 181, 1612 (2010), 1001.1307. 10.1016/j.cpc.2010.05.016

    2010 arXiv

  32. [40]

    Alioli et al., Update of the Binoth Les Houches Accord for a standard interface be- tween Monte Carlo tools and one-loop programs, Comput

    S. Alioli et al., Update of the Binoth Les Houches Accord for a standard interface be- tween Monte Carlo tools and one-loop programs, Comput. Phys . Commun. 185, 560 (2014), 1308.3462. 10.1016/j.cpc.2013.10.020

    2014 arXiv

  33. [41]

    Catani, M.H

    S. Catani, M.H. Seymour, A General algorithm for calcul ating jet cross-sections in NLO QCD, Nucl. Phys. B 485, 291 (1997), [Erratum: Nucl.Phys.B 510, 503–504 (1998)], hep-ph/9605323. 10.1016/S0550-3213(96)00589-5

    1997 arXiv

  34. [42]

    Frixione, Z

    S. Frixione, Z. Kunszt, A. Signer, Three jet cross-sect ions to next-to-leading order, Nucl. Phys. B 467, 399 (1996), hep-ph/9512328. 10.1016/0550-3213(96)00110-1

    1996 arXiv

  35. [43]

    Frixione, A General approach to jet cross-sections i n QCD, Nucl

    S. Frixione, A General approach to jet cross-sections i n QCD, Nucl. Phys. B 507, 295 (1997), hep-ph/9706545. 10.1016/S0550-3213(97)00574-9

    1997 arXiv

  36. [44]

    Gribov, L.N

    V .N. Gribov, L.N. Lipatov, Deep inelastic e p scatterin g in perturbation theory, Sov. J. Nucl. Phys. 15, 438 (1972)

    1972

  37. [45]

    Kuraev, V .S

    E.A. Kuraev, V .S. Fadin, On Radiative Corrections to e + e- Single Photon Annihilation at High-Energy, Sov. J. Nucl. Phys. 41, 466 (1985)

    1985

  38. [46]

    Skrzypek, S

    M. Skrzypek, S. Jadach, Exact and approximate solution s for the electron nonsinglet structure function in QED, Z. Phys. C 49, 577 (1991). 10.1007/BF01483573

    1991 doi

  39. [47]

    Cacciari, A

    M. Cacciari, A. Deandrea, G. Montagna, O. Nicrosini, QE D structure functions: A Systematic approach, EPL 17, 123 (1992). 10.1209/0295-5075/17/2/007

    1992 doi

  40. [48]

    Frixione, Initial conditions for electron and photo n structure and fragmentation func- tions, JHEP 11, 158 (2019), 1909.03886

    S. Frixione, Initial conditions for electron and photo n structure and fragmentation func- tions, JHEP 11, 158 (2019), 1909.03886. 10.1007/JHEP11(2019)158

    2019 arXiv

  41. [49]

    Bertone, M

    V . Bertone, M. Cacciari, S. Frixione, G. Stagnitto, The partonic structure of the electron at the next-to-leading logarithmic accuracy in QED, JHEP 03, 135 (2020), [Erratum: JHEP 08, 108 (2022)], 1911.12040. 10.1007/JHEP03(2020)135

    2020 arXiv

  42. [50]

    Bertone, M

    V . Bertone, M. Cacciari, S. Frixione, G. Stagnitto, M. Z aro, X. Zhao, Improving meth- ods and predictions at high-energy e +e−colliders within collinear factorisation, JHEP 10, 089 (2022), 2207.03265. 10.1007/JHEP10(2022)089

    2022 arXiv

  43. [51]

    Y ennie, S.C

    D.R. Y ennie, S.C. Frautschi, H. Suura, The infrared div ergence phenomena and high- energy processes, Annals Phys. 13, 379 (1961). 10.1016/0003-4916(61)90151-8

    1961 doi

  44. [52]

    Jadach, B.F.L

    S. Jadach, B.F.L. Ward, Z. Was, Coherent exclusive expo nentiation for precision Monte Carlo calculations, Phys. Rev. D 63, 113009 (2001), hep-ph/0006359. 10.1103/Phys- RevD.63.113009

    2001 arXiv

  45. [53]

    Krauss, A

    F. Krauss, A. Price, M. Schönherr, YFS Resummation for F uture Lepton-Lepton Col- liders in SHERP A, SciPost Phys. 13, 026 (2022), 2203.10948. 10.21468/SciPost- Phys.13.2.026

    2022 arXiv

  46. [54]

    Heinemeyer, S

    S. Heinemeyer, S. Jadach, J. Reuter, Theory requiremen ts for SM Higgs and EW precision physics at the FCC-ee, Eur. Phys. J. Plus 136, 911 (2021), 2106.11802. 10.1140/epjp/s13360-021-01875-1

    2021 arXiv

  47. [55]

    Frixione et al., Initial state QED radiation aspects for future e+e−colliders, in Snow- mass 2021 (2022), 2203.12557

    S. Frixione et al., Initial state QED radiation aspects for future e+e−colliders, in Snow- mass 2021 (2022), 2203.12557

    2022 arXiv

  48. [56]

    Dasgupta, F.A

    M. Dasgupta, F.A. Dreyer, K. Hamilton, P .F. Monni, G.P . Salam, G. Soyez, Parton showers beyond leading logarithmic accuracy, Phys. Rev. Le tt. 125, 052002 (2020), 2002.11114. 10.1103/PhysRevLett.125.052002

    2020 arXiv

  49. [57]

    Herren, S

    F. Herren, S. Höche, F. Krauss, D. Reichelt, M. Schoenhe rr, A new ap- proach to color-coherent parton evolution, JHEP 10, 091 (2023), 2208.06057. 10.1007/JHEP10(2023)091

    2023 arXiv

  50. [58]

    Nagy, D.E

    Z. Nagy, D.E. Soper, Summations of large logarithms by p arton showers, Phys. Rev. D 104, 054049 (2021), 2011.04773. 10.1103/PhysRevD.104.054049

    2021 arXiv

  51. [59]

    Forshaw, J

    J.R. Forshaw, J. Holguin, S. Plätzer, Building a consis tent parton shower, JHEP 09, 014 (2020), 2003.06400. 10.1007/JHEP09(2020)014

    2020 arXiv

  52. [60]

    Knobbe, F

    M. Knobbe, F. Krauss, D. Reichelt, S. Schumann, Measuri ng hadronic Higgs boson branching ratios at future lepton colliders, Eur. Phys. J. C 84, 83 (2024), 2306.03682. 10.1140/epjc/s10052-024-12430-4

    2024 arXiv

  53. [61]

    Kilian, J

    W . Kilian, J. Reuter, S. Schmidt, D. Wiesler, An Analyti c Initial-State Parton Shower, JHEP 04, 013 (2012), 1112.1039. 10.1007/JHEP04(2012)013

    2012 arXiv

  54. [62]

    Frixione, P

    S. Frixione, P . Nason, C. Oleari, Matching NLO QCD compu tations with Parton Shower simulations: the POWHEG method, JHEP 11, 070 (2007), 0709.2092. 10.1088/1126-6708/2007/11/070

    2007 arXiv

  55. [63]

    Kalinowski, W

    J. Kalinowski, W . Kotlarski, P . Sopicki, A.F. Zarnecki , Simulating hard pho- ton production with WHIZARD, Eur. Phys. J. C 80, 634 (2020), 2004.14486. 10.1140/epjc/s10052-020-8149-6

    2020 arXiv

  56. [64]

    Bach, B.C

    F. Bach, B.C. Nejad, A. Hoang, W . Kilian, J. Reuter, M. St ahlhofen, T. Teubner, C. Weiss, Fully-di fferential Top-Pair Production at a Lepton Collider: From Thr esh- old to Continuum, JHEP 03, 184 (2018), 1712.02220. 10.1007/JHEP03(2018)184

    2018 arXiv

  57. [65]

    Chokoufé Nejad, W

    B. Chokoufé Nejad, W . Kilian, J.M. Lindert, S. Pozzorin i, J. Reuter, C. Weiss, NLO QCD predictions for o ff-shell tt and ttH production and decay at a linear collider, JHEP 12, 075 (2016), 1609.03390. 10.1007/JHEP12(2016)075

    2016 arXiv

  58. [66]

    Staub, SARAH 4 : A tool for (not only SUSY) model builde rs, Comput

    F. Staub, SARAH 4 : A tool for (not only SUSY) model builde rs, Comput. Phys. Com- mun. 185, 1773 (2014), 1309.7223. 10.1016/j.cpc.2014.02.018

    2014 arXiv

  59. [67]

    Semenov, LanHEP: A Package for the automatic generat ion of Feynman rules in field theory

    A. Semenov, LanHEP: A Package for the automatic generat ion of Feynman rules in field theory. V ersion 3.0, Comput. Phys. Commun. 180, 431 (2009), 0805.0555. 10.1016/j.cpc.2008.10.012

    2009 arXiv

  60. [68]

    Alloul, N.D

    A. Alloul, N.D. Christensen, C. Degrande, C. Duhr, B. Fu ks, FeynRules 2.0 - A com- plete toolbox for tree-level phenomenology, Comput. Phys.Commun. 185, 2250 (2014), 1310.1921. 10.1016/j.cpc.2014.04.012

    2014 arXiv

  61. [69]

    Christensen, C

    N.D. Christensen, C. Duhr, B. Fuks, J. Reuter, C. Speckn er, Introducing an interface between WHIZARD and FeynRules, Eur. Phys. J. C 72, 1990 (2012), 1010.3251. 10.1140/epjc/s10052-012-1990-5

    2012 arXiv

  62. [70]

    Degrande, C

    C. Degrande, C. Duhr, B. Fuks, D. Grellscheid, O. Mattel aer, T. Reiter, UFO - The Universal FeynRules Output, Comput. Phys. Commun. 183, 1201 (2012), 1108.2040. 10.1016/j.cpc.2012.01.022

    2012 arXiv

  63. [71]

    Darmé et al., UFO 2.0: the ‘Universal Feynman Output’ format, Eur

    L. Darmé et al., UFO 2.0: the ‘Universal Feynman Output’ format, Eur. Phys. J. C 83, 631 (2023), 2304.09883. 10.1140/epjc/s10052-023-11780-9

    2023 arXiv

  64. [72]

    Ohl, Birdtracks of exotic SU(N) color structures, JH EP 06, 203 (2024), 2403.04685

    T. Ohl, Birdtracks of exotic SU(N) color structures, JH EP 06, 203 (2024), 2403.04685. 10.1007/JHEP06(2024)203

    2024 arXiv

  65. [73]

    Kilian, T

    W . Kilian, T. Ohl, J. Reuter, C. Speckner, QCD in the Color-Flow Representation, JHEP 10, 022 (2012), 1206.3700. 10.1007/JHEP10(2012)022

    2012 arXiv

  66. [74]

    Brass, W

    S. Brass, W . Kilian, J. Reuter, Parallel Adaptive Monte Carlo Integration with the Event Generator WHIZARD, Eur. Phys. J. C 79, 344 (2019), 1811.09711. 10.1140/epjc/s10052-019-6840-2

    2019 arXiv

  67. [75]

    Hagiwara, J

    K. Hagiwara, J. Kanzaki, Q. Li, N. Okamura, T. Stelzer, F ast computation of Mad- Graph amplitudes on graphics processing unit (GPU), Eur. Ph ys. J. C 73, 2608 (2013), 1305.0708. 10.1140/epjc/s10052-013-2608-2

    2013 arXiv

  68. [76]

    V alassi, S

    A. V alassi, S. Roiser, O. Mattelaer, S. Hageboeck, Desi gn and engineering of a simpli- fied workflow execution for the MG5aMC event generator on GPUs and vector CPUs, EPJ Web Conf. 251, 03045 (2021), 2106.12631. 10.1051/epjconf/202125103045

    2021 arXiv

  69. [77]

    Bothmann, W

    E. Bothmann, W . Giele, S. Hoeche, J. Isaacson, M. Knobbe , Many-gluon tree ampli- tudes on modern GPUs: A case study for novel event generators , SciPost Phys. Codeb. 2022, 3 (2022), 2106.06507. 10.21468/SciPostPhysCodeb.3

    2022 arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.