How bright is the proton? A precise determination of the photon parton distribution function (1607.04266v3)

Abstract: It has become apparent in recent years that it is important, notably for a range of physics studies at the Large Hadron Collider, to have accurate knowledge on the distribution of photons in the proton. We show how the photon parton distribution function (PDF) can be determined in a model-independent manner, using electron-proton ($ep$) scattering data, in effect viewing the $ep\to e+X$ process as an electron scattering off the photon field of the proton. To this end, we consider an imaginary, beyond Standard Model process with a flavour changing photon-lepton vertex. We write its cross section in two ways, one in terms of proton structure functions, the other in terms of a photon distribution. Requiring their equivalence yields the photon distribution as an integral over proton structure functions. As a result of the good precision of $ep$ data, we constrain the photon PDF at the level of 1-2% over a wide range of momentum fractions.

• The paper presents a novel, model-independent method to determine the photon PDF using electron–proton scattering data.
• It achieves a precision of 1–2% over a broad momentum range, surpassing conventional parametrizations like MRST2004QED and NNPDF23QED.
• Its integration into the LHAPDF library as the LUXqed set enhances predictions for electroweak and Higgs boson processes at the LHC.

The Photon Parton Distribution in the Proton

The paper presents a detailed investigation into the photon parton distribution function (PDF) within the proton, an aspect increasingly critical for high-precision physics studies at hadron colliders, particularly the Large Hadron Collider (LHC). The authors propose a novel, model-independent method to precisely determine the photon distribution using electron--proton ($ep$) scattering data. This approach reframes the $ep$ interaction as an electron probing the photon field of the proton rather than the traditional perspective of the electron's photon probing the proton structure.

Methodology and Theoretical Framework

The authors introduce an innovative method that employs an imaginary beyond the Standard Model process with a flavor-changing photon--lepton vertex. By expressing the cross section for this hypothetical process in two ways—one dependent on proton structure functions and the other on photon PDFs—they derive the photon PDF in terms of integrals over the proton structure functions. This theoretical framework is underpinned by the assumption of equivalence between these two cross section formulations, thereby ascertaining the photon distribution function, $f_{\gamma/p}$.

Data Utilization and Computational Details

The method emphasizes the utilization of existing $ep$ scattering data to constrain the photon PDF with impressive precision. The authors highlight that due to the high quality of the available $ep$ data, they can determine the photon PDF to an accuracy of 1-2% across a broad range of momentum fractions. This precision is critically important given that poor understanding of the photon distribution has become a limiting factor in predicting key processes at the LHC, such as Higgs boson production via $W/Z$ fusion or associated with a weak boson.

Furthermore, the paper compares the proposed method's results with existing parametrizations, notably the MRST2004QED and NNPDF23QED, highlighting the limitations of these conventional approaches in terms of precision constraint. The model-free nature of the authors' approach, coupled with precise structure function data from $ep$ scattering, represents a significant advancement over methods that rely on less direct data or model assumptions.

Implications and Future Directions

By establishing a highly precise method for determining the photon distribution in the proton, this work has significant implications for particle physics research, particularly for processes at the LHC where the photon distribution is a genuine source of uncertainty. The computed photon PDF is made available in the LHAPDF library as the LUXqed set, facilitating its integration into future studies at scales greater than 10 GeV.

The research presented in this paper potentially sets the stage for further developments in particle physics. Future extensions could explore higher order corrections to the photon PDF and its implications on electroweak processes at quantum-level precision. Moreover, an extension to polarized photon distributions could open new research avenues concerning the internal spin structure of hadrons.

In conclusion, this paper presents a rigorous and precise framework for understanding the photon component within the proton. It leverages $ep$ scattering data to significantly refine predictions of scatterings involving photons, contributing to the overall accuracy and reliability of theoretical predictions at high-energy colliders. This foundational work is expected to be pivotal for ongoing and future particle physics research at hadron colliders.