The Photon Content of the Proton

Abstract

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 process-independent 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 formulæ for the polarised photon PDF, as well as the photon TMDPDF. Using our formula, we derive the $P_{\gamma i}$ subset of DGLAP splitting functions to order $\alpha {\alpha }_s$ and ${\alpha }^2$, 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.

arXiv comment75 pages, 25 figures, data files corresponding to the figures available at http://doi.org/10.5281/zenodo.837233, LUXqed17 PDF files available in LHAPDF, references added in v2

References in corpus (31)

• LHAPDF6: parton density access in the LHC precision era
• Parton distributions in the LHC era: MMHT 2014 PDFs
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• QCD factorization for B->PP and B->PV decays
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• The Spin Structure of the Nucleon
• Parton distributions incorporating QED contributions
• How bright is the proton? A precise determination of the photon parton distribution function
• Fully differential VBF Higgs production at NNLO
• A Higher Order Perturbative Parton Evolution Toolkit (HOPPET)
• Charm electroproduction viewed in the variable-flavour number scheme versus fixed-order perturbation theory
• Transverse momentum dependent (TMD) parton distribution functions: status and prospects
• Deep Inelastic Structure Functions at two Loops
• Heavy quark coefficient functions at asymptotic values $Q^2\gg m^2$
• Electroweak corrections to Higgs-strahlung off W/Z bosons at the Tevatron and the LHC with HAWK
• Vector-boson fusion Higgs production at N${}^3$LO in QCD
• NNLO evolution of deep-inelastic structure functions: the singlet case
• NNLO evolution of deep-inelastic structure functions: the non-singlet case
• Radiative corrections to the neutral-current Drell-Yan process in the Standard Model and its minimal supersymmetric extension
• The Theory of Deeply Inelastic Scattering
• Next-to-leading-order electroweak corrections to $pp\to W^{+}{W}^{-}\to$ 4 leptons at the LHC
• Precision Studies of Observables in pp->W->l nu and pp->gamma,Z->l+l- processes at the LHC
• Electroweak corrections to $pp\to {\mu }^{+}{\mu }^{-}{e}^{+}{e}^{-}+X$ at the LHC -- a Higgs background study
• QED corrections to the Altarelli-Parisi splitting functions
• The photon PDF in events with rapidity gaps
• NLO QCD and electroweak corrections to $Z+\gamma$ production with leptonic Z-boson decays
• The impact of the photon PDF and electroweak corrections on $t\bar{t}$ distributions
• Two-loop QED corrections to the Altarelli-Parisi splitting functions
• Manifestly Covariant Analysis of the QED Compton Process in $ep\to e\gamma p$ and $ep\to e\gamma X$
• Power corrections in the longitudinal and transverse structure functions of proton and deuteron
• $W^{+}{W}^{-}$ pair production in proton-proton collisions: small missing terms

Cited by in corpus (139)

• New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC
• Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs
• Parton distributions and lattice QCD calculations: a community white paper
• Illuminating the photon content of the proton within a global PDF analysis
• The PDF4LHC21 combination of global PDF fits for the LHC Run III
• Electroweak Radiative Corrections for Collider Physics
• Large NLO corrections in $t\bar{t}{W}^{\pm }$ and $t\bar{t}t\bar{t}$ hadroproduction from supposedly subleading EW contributions
• Top-quark pair hadroproduction in association with a heavy boson at NLO+NNLL including EW corrections
• Snowmass 2021 whitepaper: Proton structure at the precision frontier
• Hadron structure in high-energy collisions
• Heavy Neutrinos with Dynamic Jet Vetoes: Multilepton Searches at $\sqrt{s}=14,27,$ and $100$ TeV
• Measurements of top-quark pair differential and double-differential cross-sections in the $\ell$+jets channel with $pp$ collisions at $\sqrt{s}=13$ TeV using the ATLAS detector
• Associated top quark pair production with a heavy boson: differential cross sections at NLO+NNLL accuracy
• Lepton-quark collisions at the Large Hadron Collider
• QCD$\oplus$QED NNLO corrections to Drell Yan production
• An automated subtraction of NLO EW infrared divergences
• Lepton Pair Production Through Two Photon Process in Heavy Ion Collisions
• Quark and Gluon Contents of a Lepton at High Energies
• Multi-jet merged top-pair production including electroweak corrections
• A new approach to modelling elastic and inelastic photon-initiated production at the LHC: SuperChic 4
• Towards Ultimate Parton Distributions at the High-Luminosity LHC
• Doubly Charged Higgs Boson Production at Hadron Colliders
• Complete predictions for high-energy neutrino propagation in matter
• Non-standard neutrino interactions and low energy experiments
• Combining QED and QCD transverse-momentum resummation for Z boson production at hadron colliders
• Neutrino-nucleus cross sections for W-boson and trident production
• Monopole production via photon fusion and Drell-Yan processes: MADGRAPH implementation and perturbativity via velocity-dependent coupling and magnetic moment as novel features
• The top-quark charge asymmetry at the LHC and Tevatron through NNLO QCD and NLO EW
• PineAPPL: combining EW and QCD corrections for fast evaluation of LHC processes
• Ad Lucem: QED Parton Distribution Functions in the MMHT Framework
• Mixed QCD$\otimes$QED corrections to on-shell $Z$ boson production at the LHC
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• QED Parton Distribution Functions in the MSHT20 Fit
• QCD and electroweak corrections to WZ scattering at the LHC
• Mixed QCD-electroweak corrections to W-boson production in hadron collisions
• Low- and high-energy phenomenology of a doubly charged scalar
• LePDF: Standard Model PDFs for High-Energy Lepton Colliders
• Electroweak Logarithms in Inclusive Cross Sections
• Probing the Weinberg Operator at Colliders
• Nucleon Gluon Distribution Function from 2+1+1-Flavor Lattice QCD
• $(g-2)$ anomalies and neutrino mass
• Vector-Boson Scattering at the LHC: unravelling the Electroweak sector
• Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics
• Electroweak Gauge Boson Parton Distribution Functions
• Majorana Neutrinos in Same-Sign $W^{\pm }{W}^{\pm }$ Scattering at the LHC: Breaking the TeV Barrier
• Axion-like Particle Searches at DarkQuest
• Testing momentum dependence of the nonperturbative hadron structure in a global QCD analysis
• The photon PDF within the CT18 global analysis
• Precise predictions for multi-$\mathrm{TeV}$ and $\mathrm{PeV}$ energy neutrino scattering rates
• Leptons in the Proton
• $ZZ$ production at nNNLO+PS with MiNNLO${}_{\text{PS}}$
• Safe Jet Vetoes
• Fiducial polarization observables in hadronic WZ production: A next-to-leading order QCD+EW study
• Next-to-leading order electroweak corrections to off-shell WWW production at the LHC
• One-loop electroweak Sudakov logarithms: a revisitation and automation
• RIP $Hb\bar{b}$: How other Higgs production modes conspire to kill a rare signal at the LHC
• Polarization Effects in Standard Model Parton Distributions at Very High Energies
• Search for heavy neutral leptons in final states with electrons, muons, and hadronically decaying tau leptons in proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Search for new physics in final states with a single photon and missing transverse momentum in proton-proton collisions at $\sqrt{s}=$ 13 TeV
• Discovery prospects for long-lived multiply charged particles at the LHC
• Detecting long-lived multi-charged particles in neutrino mass models with MoEDAL
• Measurement of the mass dependence of the transverse momentum of lepton pairs in Drell-Yan production in proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Full NLO corrections to 3-jet production and R32 at the LHC
• Search for magnetic monopoles and stable particles with high electric charges in $\sqrt{s}=$13 TeV $pp$ collisions with the ATLAS detector
• Estimating the impact of mixed QCD-electroweak corrections on the $W$-mass determination at the LHC
• Exploiting the WH/ZH symmetry in the search for New Physics
• Type-III see-saw: Search for triplet fermions in final states with multiple leptons and fat-jets at 13 TeV LHC
• Flavorful leptoquarks at the LHC and beyond: Spin 1
• Combining initial-state resummation with fixed-order calculations of electroweak corrections
• $W^{\pm }Z$ production at NNLO QCD and NLO EW matched to parton showers with MiNNLO${}_{\mathrm{PS}}$
• A fast and accurate method for perturbative resummation of transverse momentum-dependent observables
• Physics with Leptons and Photons at the LHC
• NLO electroweak corrections to doubly-polarized $W^{+}{W}^{-}$ production at the LHC
• Precise predictions for single-top production: the impact of EW corrections and QCD shower on the t-channel signature
• Angular coefficients in W+j production at the LHC with high precision
• Yadism: Yet Another Deep-Inelastic Scattering Module
• Quark and gluon two-loop beam functions for leading-jet $p_T$ and slicing at NNLO
• Next-to-leading-order QCD and electroweak corrections to triple-W production with leptonic decays at the LHC
• The Proton in High Definition: Revisiting Photon-Initiated Production in High Energy Collisions
• Combining QED and QCD transverse-momentum resummation for W and Z boson production at hadron colliders
• Combining QED and Approximate N${}^3$LO QCD Corrections in a Global PDF Fit: MSHT20qed_an3lo PDFs
• Complete NLO corrections to top-quark pair production with isolated photons
• $pp$ scattering at the LHC with the lepton pair production and one proton tagging
• Search for exotic leptons in final states with two or three leptons and fat-jets at 13 TeV LHC
• Electroweak corrections to the angular coefficients in finite-$p_T$ $Z$-boson production and dilepton decay
• Production of $t\bar{t}$ pairs via $\gamma \gamma$ fusion with photon transverse momenta and proton dissociation
• Modelling $W^{+}{W}^{-}$ production with rapidity gaps at the LHC
• Nonperturbatively Renormalized Nucleon Gluon Momentum Fraction in the Continuum Limit of $N_f=2+1+1$ Lattice QCD
• Doubly Charged Higgs Boson Production at Hadron Colliders II: A Zee-Babu Case Study
• Bounds and Prospects for Stable Multiply Charged Particles at the LHC
• The $pp\to W(\to l\nu )+\gamma$ process at next-to-next-to-leading order
• Like-Sign W-Boson Scattering at the LHC -- Approximations and Full Next-to-Leading-Order Predictions
• Backward timelike Compton scattering to decipher the photon content of the nucleon
• Production of $W^{+}{W}^{-}$ pairs via ${\gamma }^{\ast }{\gamma }^{\ast }\to W^{+}{W}^{-}$ subprocess with photon transverse momenta
• The dark side of the proton
• Resummation schemes for high-electric-charge objects leading to improved experimental mass limits
• Measurement of the Drell-Yan forward-backward asymmetry at high dilepton masses in proton-proton collisions at $\sqrt{s}=$ 13 TeV
• Exclusive and diffractive ${\mu }^{+}{\mu }^{-}$ production in $pp$ collisions at the LHC
• On electroweak corrections to neutral current Drell-Yan with the POWHEG BOX
• Reconstructing partonic kinematics at colliders with Machine Learning
• $WW\gamma$ production at hadron colliders with NLO QCD+EW corrections and parton shower effects
• Hints of a new leptophilic Higgs sector?
• Asymmetric heavy-quark hadroproduction at LHCb: Predictions and applications
• Hunting for QCD Instantons at the LHC in Events with Large Rapidity Gaps
• Detecting a μτ-philic Z' boson via photon initiated processes at the LHC
• Evidence for the charge asymmetry in $pp\to t\bar{t}$ production at $\sqrt{s}=13$ TeV with the ATLAS detector
• Leptophilic $Z^{\prime }$ bosons at the FCC-ee: discovery opportunities
• Exclusive doubly charged Higgs boson pair production in $pp$ collisions at the LHC
• Probing the polarized photon content of the proton in $ep$ collisions at the EIC
• The Genuine Type-V Seesaw Model: Phenomenological Introduction
• Automated next-to-leading order QCD and electroweak predictions of photon-photon processes in ultraperipheral collisions
• KKMChh: matching CEEX photonic ISR to a QED-corrected parton shower
• Non-exclusive particle production by $\gamma \gamma$ interactions in $pp$ collisions at the LHC
• QED corrections to parton distributions and Altarelli-Parisi splitting functions in the polarized case
• Third-Family Lepton-Quark Fusion
• Probing the photonic content of the proton using photon-induced dilepton production in $p+\text{Pb}$ collisions at the LHC
• Constraining fragmentation functions through hadron-photon production at higher-orders
• Diffractive and photon-induced production of top quark
• QCD, from its inception to its stubbornly unsolved problems
• Search for $t$-channel scalar and vector leptoquark exchange in the high-mass dimuon and dielectron spectra in proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Search for scalar leptoquarks produced via $\tau$-lepton-quark scattering in pp collisions at $\sqrt{s}$ = 13 TeV
• Semiexclusive dilepton production in proton-proton collisions with one forward proton measurement at the LHC
• The polarized photon distribution function
• Electroweak corrections to Higgs boson production via W W fusion at the future LHeC
• Production of $e^{+}{e}^{-}$ in proton-lead collision: photon-photon fusion
• State-of-the-art cross sections for ttH: NNLO predictions matched with NNLL resummation and EW corrections
• Photo-production of Higgs Boson at the LHeC
• Electroweak $t\bar{t}$ hadroproduction in the presence of heavy $Z^{\prime }$ and $W^{\prime }$ bosons at NLO QCD in POWHEG
• New Developments in KKMChh: Quark-Level Exponentiated Radiative Corrections and Semi-analytical Results
• Monte Carlo Event Generators for Future Lepton Colliders
• Complete NLO corrections to off-shell $\mathbf{t}\bar{\mathbf{t}}$ production in the $\mathbf{\ell }+\mathbf{j}$ decay channel
• Weak interaction corrections to muon pair production via the photon fusion at the LHC
• Illuminating the charged leptons in the proton
• Weak bosons as partons below 10 TeV partonic center-of-momentum
• Parton distribution functions and strong coupling constant: MSHT
• Photon and Leptons induced processes at the LHC
• Semiexclusive production of vector mesons in proton-proton collisions with electromagnetic dissociation
• Overview of IR-Improvement in Precision LHC/FCC Physics
• Phenomenological extraction of fragmentation functions in a $p\bar{p}$ environment