The Photon Content of the Proton (1708.01256v2)

Abstract: The photon PDF of the proton is needed for precision comparisons of LHC cross sections with theoretical predictions. In a 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 formul\ae\ 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.

• The paper derives an exact expression for the photon PDF from electromagnetic structure functions, enhancing prediction precision.
• It employs dual methodologies—factorisation theorem with BSM processes and light-cone Fourier transforms—to integrate QED and QCD effects.
• The refined photon PDF reduces uncertainties by a factor of forty compared to earlier models, enabling more accurate LHC phenomenology.

Analysis of "The Photon Content of the Proton"

"The Photon Content of the Proton" examines the parton distribution function (PDF) for photons within a proton, a critical component for precision theoretical predictions at the Large Hadron Collider (LHC). The paper by Manohar et al. provides a comprehensive approach for determining the photon PDF using two primary methodologies: the factorisation theorem in combination with beyond standard model (BSM) hard scattering processes and a process-independent method based on light-cone Fourier transforms of operator products.

Contribution and Detail

The paper meticulously derives an exact expression for the photon PDF in terms of measured electromagnetic structure functions ($F_2$, $F_L$) from electron-proton scattering experiments. This derivation considers all orders in both Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD) and includes non-perturbative corrections. The result offers an explicit expression for the photon PDF, extending the accuracy to one order higher than the team's preceding research, yielding reduced uncertainties in the photon PDF by about a factor of forty compared to prior determinations such as MRST2004qed and NNPDF23_qed.

Derivation and Methodology

The paper provides two core derivations: the photon PDF from the factorisation theorem applied to BSM photon probes, specifically by employing lepton-heavy lepton production and scalar production processes via photon fusion; and the detailed derivation through an operator approach, leveraging light-cone Fourier transforms. The methods uniquely define the photon PDF with precision comparable to unpolarised quark and gluon PDFs, crucial for precision measurements at the LHC.

Implications

The derived photon PDF has significant implications as the uncertainty tied to the photon PDF is becoming a limiting factor in precision LHC predictions, particularly in processes such as Higgs production through electroweak fusion and lepton-pair production. By offering an explicit formula that is exact and accounts for QED/QCD interactions, the research permits precise matching of experimental measurements with theoretical predictions.

Moreover, the work computes subsets of the DGLAP splitting functions related to photon distributions, providing results that align with known literature, establishing a foundation for further theoretical analyses and potential experimental investigations involving photon-initiated processes.

Future Prospects

This research positions the photon PDF ready for numerical evaluations using contemporary experimental inputs for the proton structure functions. The methodology laid out potentially generalises for photon PDFs in other hadronic contexts, promising avenues for future exploration within hadronic physics and extending into more precise lepton distributions in the proton, relevant as next-level precision demands arise.

In summary, "The Photon Content of the Proton" is an extensive derivation rich with theoretical advancements that refine the understanding and practical utility of photon distributions in protons, a critical piece for high-precision phenomenology at hadron colliders. As experimental setup capabilities continue to evolve, this paper's findings and methodologies are poised to be a foundational reference in particle physics.