Abstract
We compute the two-loop QED corrections to the Altarelli-Parisi (AP) splitting functions by using a deconstructive algorithmic Abelianization of the well-known NLO QCD corrections. We present explicit results for the full set of splitting kernels in a basis that includes the leptonic distribution functions that, starting from this order in the QED coupling, couple to the partonic densities. Finally, we perform a phenomenological analysis of the impact of these corrections in the splitting functions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Moch, J.A.M. Vermaseren and A. Vogt, Next-to-next-to leading order QCD corrections to the photon’s parton structure, Nucl. Phys. B 621 (2002) 413 [hep-ph/0110331] [INSPIRE].
S. Moch, J.A.M. Vermaseren and A. Vogt, The three loop splitting functions in QCD: the nonsinglet case, Nucl. Phys. B 688 (2004) 101 [hep-ph/0403192] [INSPIRE].
A. Vogt, S. Moch and J.A.M. Vermaseren, The three-loop splitting functions in QCD: the singlet case, Nucl. Phys. B 691 (2004) 129 [hep-ph/0404111] [INSPIRE].
A. Vogt, S. Moch and J. Vermaseren, Photon-parton splitting functions at the next-to-next-to-leading order of QCD, Acta Phys. Polon. B 37 (2006) 683 [hep-ph/0511112] [INSPIRE].
S. Alekhin, J. Blumlein and S. Moch, The ABM parton distributions tuned to LHC data, Phys. Rev. D 89 (2014) 054028 [arXiv:1310.3059] [INSPIRE].
S. Dulat et al., New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev. D 93 (2016) 033006 [arXiv:1506.07443] [INSPIRE].
P. Jimenez-Delgado and E. Reya, Delineating parton distributions and the strong coupling, Phys. Rev. D 89 (2014) 074049 [arXiv:1403.1852] [INSPIRE].
ZEUS and H1 collaborations, H. Abramowicz et al., Combination of measurements of inclusive deep inelastic e ± p scattering cross sections and QCD analysis of HERA data, Eur. Phys. J. C 75 (2015) 580 [arXiv:1506.06042] [INSPIRE].
L.A. Harland-Lang, A.D. Martin, P. Motylinski and R.S. Thorne, Parton distributions in the LHC era: MMHT 2014 PDFs, Eur. Phys. J. C 75 (2015) 204 [arXiv:1412.3989] [INSPIRE].
NNPDF collaboration, R.D. Ball et al., Parton distributions for the LHC run II, JHEP 04 (2015) 040 [arXiv:1410.8849] [INSPIRE].
A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne, Parton distributions incorporating QED contributions, Eur. Phys. J. C 39 (2005) 155 [hep-ph/0411040] [INSPIRE].
NNPDF collaboration, R.D. Ball et al., Parton distributions with QED corrections, Nucl. Phys. B 877 (2013) 290 [arXiv:1308.0598] [INSPIRE].
V. Bertone, S. Carrazza and J. Rojo, APFEL: a PDF evolution library with QED corrections, Comput. Phys. Commun. 185 (2014) 1647 [arXiv:1310.1394] [INSPIRE].
C. Schmidt, J. Pumplin, D. Stump and C.-P. Yuan, CT14QED parton distribution functions from isolated photon production in deep inelastic scattering, Phys. Rev. D 93 (2016) 114015 [arXiv:1509.02905] [INSPIRE].
R. Sadykov, Impact of QED radiative corrections on parton distribution functions, arXiv:1401.1133 [INSPIRE].
S. Carrazza, Parton distribution functions with QED corrections, arXiv:1509.00209 [INSPIRE].
V. Bertone, S. Carrazza, D. Pagani and M. Zaro, On the impact of lepton PDFs, JHEP 11 (2015) 194 [arXiv:1508.07002] [INSPIRE].
D. de Florian, G.F.R. Sborlini and G. Rodrigo, QED corrections to the Altarelli-Parisi splitting functions, Eur. Phys. J. C 76 (2016) 282 [arXiv:1512.00612] [INSPIRE].
M. Gluck and E. Reya, Boundary conditions for the photon structure function in the leading and subleading order, Phys. Rev. D 28 (1983) 2749 [INSPIRE].
M. Gluck, E. Reya and A. Vogt, Parton structure of the photon beyond the leading order, Phys. Rev. D 45 (1992) 3986 [INSPIRE].
M. Fontannaz and E. Pilon, Reexamination of the photon structure function beyond the leading logarithm, Phys. Rev. D 45 (1992) 382 [INSPIRE].
G.F.R. Sborlini, D. de Florian and G. Rodrigo, Double collinear splitting amplitudes at next-to-leading order, JHEP 01 (2014) 018 [arXiv:1310.6841] [INSPIRE].
G.F.R. Sborlini, NLO QCD corrections to triple collinear splitting functions, arXiv:1410.1680 [INSPIRE].
G.F.R. Sborlini, D. de Florian and G. Rodrigo, Triple collinear splitting functions at NLO for scattering processes with photons, JHEP 10 (2014) 161 [arXiv:1408.4821] [INSPIRE].
G.F.R. Sborlini, D. de Florian and G. Rodrigo, Polarized triple-collinear splitting functions at NLO for processes with photons, JHEP 03 (2015) 021 [arXiv:1409.6137] [INSPIRE].
G. Altarelli and G. Parisi, Asymptotic freedom in parton language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].
G. Curci, W. Furmanski and R. Petronzio, Evolution of parton densities beyond leading order: the nonsinglet case, Nucl. Phys. B 175 (1980) 27 [INSPIRE].
W. Furmanski and R. Petronzio, Singlet parton densities beyond leading order, Phys. Lett. B 97 (1980) 437 [INSPIRE].
R.K. Ellis and W. Vogelsang, The evolution of parton distributions beyond leading order: the singlet case, hep-ph/9602356 [INSPIRE].
M. Roth and S. Weinzierl, QED corrections to the evolution of parton distributions, Phys. Lett. B 590 (2004) 190 [hep-ph/0403200] [INSPIRE].
J. Blumlein, The theory of deeply inelastic scattering, Prog. Part. Nucl. Phys. 69 (2013) 28 [arXiv:1208.6087] [INSPIRE].
A.L. Kataev, Higher order O(α 2) and O(αα s ) corrections to σ tot(e + e − → hadrons) and Z boson decay rate, Phys. Lett. B 287 (1992) 209 [INSPIRE].
J. Blümlein and S. Kurth, Harmonic sums and Mellin transforms up to two loop order, Phys. Rev. D 60 (1999) 014018 [hep-ph/9810241] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1606.02887
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
de Florian, D., Sborlini, G.F.R. & Rodrigo, G. Two-loop QED corrections to the Altarelli-Parisi splitting functions. J. High Energ. Phys. 2016, 56 (2016). https://doi.org/10.1007/JHEP10(2016)056
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2016)056