Abstract
By working in QED, we obtain the electron, positron, and photon Parton Distribution Functions (PDFs) of the unpolarised electron at the next-to-leading logarithmic accuracy. The PDFs account for all of the universal effects of initial-state collinear origin, and are key ingredients in the calculations of cross sections in the so-called structure- function approach. We present both numerical and analytical results, and show that they agree extremely well with each other. The analytical predictions are defined by means of an additive formula that matches a large-z solution that includes all orders in the QED coupling constant α, with a small- and intermediate-z solution that includes terms up to \( \mathcal{O} \)(α3).
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08 August 2022
An Erratum to this paper has been published: https://doi.org/10.1007/JHEP08(2022)108
References
S. Frixione, Initial conditions for electron and photon structure and fragmentation functions, JHEP 11 (2019) 158 [arXiv:1909.03886] [INSPIRE].
M. Cacciari, A. Deandrea, G. Montagna and O. Nicrosini, QED structure functions: A Systematic approach, Europhys. Lett. 17 (1992) 123 [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].
G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [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 [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].
W. Furmanski and R. Petronzio, Lepton-Hadron Processes Beyond Leading Order in Quantum Chromodynamics, Z. Phys. C 11 (1982) 293 [INSPIRE].
W. Beenakker et al., W W cross-sections and distributions, in CERN Workshop on LEP2 Physics, (followed by 2nd meeting, 15–16 June 1995 and 3rd meeting 2–3 November 1995) Geneva, Switzerland, 2–3 February 1995 pp. 79–139 (1996) [hep-ph/9602351] [INSPIRE].
V. Bertone, M. Cacciari, S. Catani, S. Frixione and G. Stagnitto, On the subtraction schemes for electron structure functions, in preparation.
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].
R. Frederix, S. Frixione, V. Hirschi, D. Pagani, H.-S. Shao and M. Zaro, The complete NLO corrections to dijet hadroproduction, JHEP 04 (2017) 076 [arXiv:1612.06548] [INSPIRE].
M. Bonvini, Resummation of soft and hard gluon radiation in perturbative QCD, Ph.D. Thesis, Genoa U. (2012) [arXiv:1212.0480] [INSPIRE].
NNPDF collaboration, Neural network determination of parton distributions: The Nonsinglet case, JHEP 03 (2007) 039 [hep-ph/0701127] [INSPIRE].
B. Mele and P. Nason, The Fragmentation function for heavy quarks in QCD, Nucl. Phys. B 361 (1991) 626 [Erratum ibid. B 921 (2017) 841] [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].
O. Nicrosini and L. Trentadue, Soft Photons and Second Order Radiative Corrections to e+ e− → Z0 , Phys. Lett. B 196 (1987) 551 [INSPIRE].
G. Altarelli, R.D. Ball and S. Forte, Small x Resummation with Quarks: Deep-Inelastic Scattering, Nucl. Phys. B 799 (2008) 199 [arXiv:0802.0032] [INSPIRE].
M. Ciafaloni, D. Colferai, G.P. Salam and A.M. Stasto, Renormalization group improved small x Green’s function, Phys. Rev. D 68 (2003) 114003 [hep-ph/0307188] [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].
W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math. 7 (1954) 649 [INSPIRE].
S. Blanes, F. Casas, J. Oteo and J. Ros, The Magnus expansion and some of its applications, Phys. Rept. 470 (2009) 151 [0810.5488].
G. Altarelli, Partons in Quantum Chromodynamics, Phys. Rept. 81 (1982) 1 [INSPIRE].
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Bertone, V., Cacciari, M., Frixione, S. et al. The partonic structure of the electron at the next-to-leading logarithmic accuracy in QED. J. High Energ. Phys. 2020, 135 (2020). https://doi.org/10.1007/JHEP03(2020)135
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DOI: https://doi.org/10.1007/JHEP03(2020)135