Two-loop QED corrections to the Altarelli-Parisi splitting functions

Florian, Daniel de; Sborlini, Germán F. R.; Rodrigo, Germán

doi:10.1007/jhep10(2016)056

Cited by 48 publications

(62 citation statements)

References 47 publications

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“…We verified that the resulting αα s and α 2 P γx unpolarised splitting functions agree with recent computations [26,27]. From our results it is also possible to derive the αα s polarised splitting function, as well as the unpolarised splitting functions to one higher order.…”

Section: Discussionsupporting

confidence: 76%

“…(4.20) and (4.22), we find full agreement with formulae (3.9) and (3.21) of ref. [27]. It is remarkable that our expression for the photon PDF gives the DGLAP evolution kernel to one higher order in the couplings than was present in the input coefficient functions.…”

Section: Jhep12(2017)046mentioning

confidence: 99%

“…Here, we present this calculation in detail, including also the computation of the splitting kernels of order α 2 , which agree with ref. [27].…”

Section: Jhep12(2017)046mentioning

confidence: 99%

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The photon content of the proton

Manohar

Nason

Salam

et al. 2017

J. High Energ. Phys.

231

280

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The photon PDF of the proton is needed for precision comparisons of LHC cross sections with theoretical predictions. In a recent paper, we showed how the photon PDF could be determined in terms of the electromagnetic proton structure functions F 2 and F L measured in electron-proton scattering experiments, and gave an explicit formula for the PDF including all terms up to next-to-leading order. In this paper we give details of the derivation. We obtain the photon PDF using the factorisation theorem and applying it to suitable BSM hard scattering processes. We also obtain the same PDF in a processindependent manner using the usual definition of PDFs in terms of light-cone Fourier transforms of products of operators. We show how our method gives an exact representation for the photon PDF in terms of F 2 and F L , valid to all orders in QED and QCD, and including all non-perturbative corrections. This representation is then used to give an explicit formula for the photon PDF to one order higher than our previous result. We also generalise our results to obtain formulae for the polarised photon PDF, as well as the photon TMDPDF. Using our formula, we derive the P γi subset of DGLAP splitting functions to order αα s and α 2 , which agree with known results. We give a detailed explanation of the approach that we follow to determine a photon PDF and its uncertainty within the above framework.

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Section: Discussionsupporting

confidence: 76%

Section: Jhep12(2017)046mentioning

confidence: 99%

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The photon content of the proton

Manohar

Nason

Salam

et al. 2017

J. High Energ. Phys.

231

280

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“…Email addresses: alessandro.bacchetta@unipv.it (Alessandro Bacchetta), mgechevarria@pv.infn.it (Miguel G. Echevarria) In this context, it is necessary and timely to consider the QCD×QED contributions to TMD evolution. Similar corrections have been already taken into consideration for observables involving collinear PDFs [45][46][47][48][49][50][51]. Shortly before the completion of our work, similar improvements have been suggested also for the description of the transverse-momentum spectrum of Z bosons produced at hadron colliders by Cieri-Ferrera-Sborlini [52]: their results are intimately connected to ours, but we adopt a complementary approach, based on the TMD framework, which makes it easy, among other things, to generalize our results also to polarized TMDs and fragmentation functions.…”

Section: Motivationmentioning

confidence: 99%

QCD×QED evolution of TMDs

Bacchetta

Echevarría

2019

Physics Letters B

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We consider for the first time the QED corrections to the evolution of (un)polarized quark and gluon transverse-momentum-dependent distribution and fragmentation functions (TMDs in general). By extending their operator definition to QCD×QED, we provide the mixed new anomalous dimensions up to O(α s α) and the pure QED ones up to O(α 2 ). These new corrections are universal for all TMDs up to the flavor of the considered parton, i.e., the full flavor universality of TMD evolution found in pure QCD is broken in QCD×QED by the presence of the electric charge. In addition, we provide the leading-order QED corrections to the matching coefficients of the unpolarized quark TMD parton distribution function onto its integrated counterparts at O(α 0 s α).

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“…(A.10) and (A.11) the convention of Refs. [46, 47] is followed to indicate the power of and that each splitting function multiplies.The structure of the pure QCD splitting function matrix as well as the first term in , which represents the pure LO QED correction, were already discussed in Ref. [45].…”

Section: Appendix A: Implementation Of Nlo Qed Corrections In Apfelmentioning

confidence: 99%

The photon PDF from high-mass Drell–Yan data at the LHC

Giuli

2017

Eur. Phys. J. C

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Achieving the highest precision for theoretical predictions at the LHC requires the calculation of hard-scattering cross sections that include perturbative QCD corrections up to (N)NNLO and electroweak (EW) corrections up to NLO. Parton distribution functions (PDFs) need to be provided with matching accuracy, which in the case of QED effects involves introducing the photon parton distribution of the proton, . In this work a determination of the photon PDF from fits to recent ATLAS measurements of high-mass Drell–Yan dilepton production at TeV is presented. This analysis is based on the xFitter framework, and has required improvements both in the APFEL program, to account for NLO QED effects, and in the aMCfast interface to account for the photon-initiated contributions in the EW calculations within MadGraph5_aMC@NLO. The results are compared with other recent QED fits and determinations of the photon PDF, consistent results are found.

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Two-loop QED corrections to the Altarelli-Parisi splitting functions

Cited by 48 publications

References 47 publications

The photon content of the proton

The photon content of the proton

QCD×QED evolution of TMDs

The photon PDF from high-mass Drell–Yan data at the LHC

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