Abstract
We illustrate how electron Parton Distribution Functions (PDFs) with next-to-leading collinear logarithmic accuracy must be employed in the context of perturbative predictions for high-energy e+e−-collision processes. In particular, we discuss how the renormalisation group equation evolution of such PDFs is affected by the presence of multiple fermion families and their respective mass thresholds, and by the dependences on the choices of the factorisation and renormalisation schemes. We study the impact of the uncertainties associated with the PDFs on physical cross sections, in order to arrive at realistic precision estimates for observables computed with collinear-factorisation formulae. We do so by presenting results for the production of a heavy neutral object as well as for \( t\overline{t} \) and W+W− pairs, including next-to-leading-order effects of electroweak origin.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
CEPC Study Group collaboration, CEPC Conceptual Design Report: Volume 2 - Physics & Detector, arXiv:1811.10545 [INSPIRE].
FCC collaboration, FCC-ee: The Lepton Collider : Future Circular Collider Conceptual Design Report Volume 2, Eur. Phys. J. ST 228 (2019) 261 [INSPIRE].
P. Bambade et al., The International Linear Collider: A Global Project, arXiv:1903.01629 [INSPIRE].
CLICdp, CLIC collaboration, The Compact Linear Collider (CLIC) - 2018 Summary Report, arXiv:1812.06018 [INSPIRE].
E.A. Kuraev and V.S. Fadin, On Radiative Corrections to e+e− Single Photon Annihilation at High-Energy, Sov. J. Nucl. Phys. 41 (1985) 466 [INSPIRE].
J.R. Ellis and R. Peccei, Physics at lep. 1., CERN-86-02-V-1 [INSPIRE].
D.R. Yennie, S.C. Frautschi and H. Suura, The infrared divergence phenomena and high-energy processes, Annals Phys. 13 (1961) 379 [INSPIRE].
S. Jadach, B.F.L. Ward and Z. Was, Coherent exclusive exponentiation for precision Monte Carlo calculations, Phys. Rev. D 63 (2001) 113009 [hep-ph/0006359] [INSPIRE].
H. Anlauf, H.D. Dahmen, P. Manakos, T. Mannel and T. Ohl, KRONOS: A Monte Carlo event generator for higher order electromagnetic radiative corrections to deep inelastic scattering at HERA, Comput. Phys. Commun. 70 (1992) 97 [INSPIRE].
J. Fujimoto, Y. Shimizu and T. Munehisa, Monte Carlo approach to radiative processes in e+e− annihilation, Prog. Theor. Phys. 90 (1993) 177 [INSPIRE].
T. Munehisa, J. Fujimoto, Y. Kurihara and Y. Shimizu, Improved QEDPS for radiative corrections in e+e− annihilation, Prog. Theor. Phys. 95 (1996) 375 [hep-ph/9603322] [INSPIRE].
C.M. Carloni Calame, C. Lunardini, G. Montagna, O. Nicrosini and F. Piccinini, Large angle Bhabha scattering and luminosity at flavor factories, Nucl. Phys. B 584 (2000) 459 [hep-ph/0003268] [INSPIRE].
V.N. Gribov and L.N. Lipatov, Deep inelastic e p scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [INSPIRE].
L.N. Lipatov, The parton model and perturbation theory, Sov. J. Nucl. Phys. 20 (1975) 94.
G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].
Y.L. Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e+e− Annihilation by Perturbation Theory in Quantum Chromodynamics, Sov. Phys. JETP 46 (1977) 641 [INSPIRE].
S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [INSPIRE].
P. Nason, A New method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [hep-ph/0409146] [INSPIRE].
M. Skrzypek and S. Jadach, Exact and approximate solutions for the electron nonsinglet structure function in QED, Z. Phys. C 49 (1991) 577 [INSPIRE].
M. Skrzypek, Leading logarithmic calculations of QED corrections at LEP, Acta Phys. Polon. B 23 (1992) 135 [INSPIRE].
M. Cacciari, A. Deandrea, G. Montagna and O. Nicrosini, QED structure functions: A Systematic approach, EPL 17 (1992) 123 [INSPIRE].
S. Frixione, Initial conditions for electron and photon structure and fragmentation functions, JHEP 11 (2019) 158 [arXiv:1909.03886] [INSPIRE].
V. Bertone, M. Cacciari, S. Frixione and G. Stagnitto, The partonic structure of the electron at the next-to-leading logarithmic accuracy in QED, JHEP 03 (2020) 135 [Erratum ibid. 08 (2022) 108] [arXiv:1911.12040] [INSPIRE].
S. Frixione, On factorisation schemes for the electron parton distribution functions in QED, JHEP 07 (2021) 180 [Erratum ibid. 12 (2012) 196] [arXiv:2105.06688] [INSPIRE].
J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].
R. Frederix, S. Frixione, V. Hirschi, D. Pagani, H.S. Shao and M. Zaro, The automation of next-to-leading order electroweak calculations, JHEP 07 (2018) 185 [Erratum ibid. 11 (2021) 085] [arXiv:1804.10017] [INSPIRE].
S. Frixione, O. Mattelaer, M. Zaro and X. Zhao, Lepton collisions in MadGraph5_aMC@NLO, arXiv:2108.10261 [INSPIRE].
S. Dittmaier and M. Krämer, Electroweak radiative corrections to W boson production at hadron colliders, Phys. Rev. D 65 (2002) 073007 [hep-ph/0109062] [INSPIRE].
A. Denner, Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortsch. Phys. 41 (1993) 307 [arXiv:0709.1075] [INSPIRE].
D. de Florian, G.F.R. Sborlini and G. Rodrigo, Two-loop QED corrections to the Altarelli-Parisi splitting functions, JHEP 10 (2016) 056 [arXiv:1606.02887] [INSPIRE].
S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys. B 467 (1996) 399 [hep-ph/9512328] [INSPIRE].
S. Frixione, A General approach to jet cross-sections in QCD, Nucl. Phys. B 507 (1997) 295 [hep-ph/9706545] [INSPIRE].
R. Frederix, S. Frixione, F. Maltoni and T. Stelzer, Automation of next-to-leading order computations in QCD: The FKS subtraction, JHEP 10 (2009) 003 [arXiv:0908.4272] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
G. Degrassi and A. Vicini, Two loop renormalization of the electric charge in the standard model, Phys. Rev. D 69 (2004) 073007 [hep-ph/0307122] [INSPIRE].
J.C. Collins, F. Wilczek and A. Zee, Low-Energy Manifestations of Heavy Particles: Application to the Neutral Current, Phys. Rev. D 18 (1978) 242 [INSPIRE].
V. Bertone, S. Carrazza, D. Pagani and M. Zaro, On the Impact of Lepton PDFs, JHEP 11 (2015) 194 [arXiv:1508.07002] [INSPIRE].
V. Bertone, S. Carrazza and E.R. Nocera, Reference results for time-like evolution up to \( \mathcal{O} \)(\( {\alpha}_s^3 \)), JHEP 03 (2015) 046 [arXiv:1501.00494] [INSPIRE].
M. Bonvini, Resummation of soft and hard gluon radiation in perturbative QCD, PhD thesis, Genoa University (2012), arXiv:1212.0480 [INSPIRE].
W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math. 7 (1954) 649.
NNPDF collaboration, L. Del Debbio, S. Forte, J.I. Latorre, A. Piccione and J. Rojo, Neural network determination of parton distributions: The Nonsinglet case, JHEP 03 (2007) 039 [hep-ph/0701127] [INSPIRE].
S. Frixione et al., Initial state QED radiation aspects for future e+e− colliders, in 2022 Snowmass Summer Study, (2022), arXiv:2203.12557 [INSPIRE].
A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].
C.W. Bauer, N. Ferland and B.R. Webber, Standard Model Parton Distributions at Very High Energies, JHEP 08 (2017) 036 [arXiv:1703.08562] [INSPIRE].
B. Fornal, A.V. Manohar and W.J. Waalewijn, Electroweak Gauge Boson Parton Distribution Functions, JHEP 05 (2018) 106 [arXiv:1803.06347] [INSPIRE].
C.W. Bauer and B.R. Webber, Polarization Effects in Standard Model Parton Distributions at Very High Energies, JHEP 03 (2019) 013 [arXiv:1808.08831] [INSPIRE].
O. Nicrosini and L. Trentadue, Soft Photons and Second Order Radiative Corrections to e+e− → Z0, Phys. Lett. B 196 (1987) 551 [INSPIRE].
C.F. von Weizsacker, Radiation emitted in collisions of very fast electrons, Z. Phys. 88 (1934) 612 [INSPIRE].
E.J. Williams, Nature of the high-energy particles of penetrating radiation and status of ionization and radiation formulae, Phys. Rev. 45 (1934) 729 [INSPIRE].
W. Beenakker et al., WW cross-sections and distributions, in CERN Workshop on LEP2 Physics (followed by 2nd meeting, 15-16 Jun 1995 and 3rd meeting 2-3 Nov 1995), 2, 1996. hep-ph/9602351 [INSPIRE].
R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, R. Pittau and P. Torrielli, Four-lepton production at hadron colliders: aMC@NLO predictions with theoretical uncertainties, JHEP 02 (2012) 099 [arXiv:1110.4738] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2207.03265
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Bertone, V., Cacciari, M., Frixione, S. et al. Improving methods and predictions at high-energy e+e− colliders within collinear factorisation. J. High Energ. Phys. 2022, 89 (2022). https://doi.org/10.1007/JHEP10(2022)089
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2022)089