[Paper Review] Ad Lucem: The Photon in the MMHT PDFs

R. Nathvani, L. A. Harland-Lang+2 more|arXiv (Cornell University)|Jul 20, 2018

Advanced Data Storage Technologies12 references3 citations

TL;DR

This paper presents the inclusion of the photon as a dynamic component in the MMHT global PDF fit, using the LUXqed input parametrization and evolving it via QED-corrected DGLAP equations up to O(α), O(ααS), and O(α²). The key result is a consistent, precision photon PDF with uncertainties of order 1–2%, validated against LUXqed and NNPDF, and extended to neutron PDFs with isospin-symmetry-based charge reweighting and QED corrections.

ABSTRACT

We describe the inclusion of the photon as an additional component of the proton's Parton Distribution Functions (PDFs) in the MMHT framework. The input for the photon is adopted from the recent LUXqed determination. We describe the similarities and differences above the input scale with other photon PDF determinations and the contributions to the MMHT photon from both leading twist and higher twist contributions, and their uncertainties. We study the impact of QED effects on the quark and gluon PDFs and the fit quality, and outline our development of an equivalent set of neutron PDFs.

Motivation & Objective

• To incorporate the photon as a physical parton in the MMHT global PDF fit, improving precision for LHC processes.
• To implement QED corrections in DGLAP evolution up to O(α²), accounting for photon radiation from quarks and gluons.
• To extend the photon PDF framework to the neutron using isospin symmetry and charge reweighting.
• To quantify uncertainties from structure functions, coherent contributions, and non-perturbative power corrections (e.g., infrared renormalons).
• To ensure consistency with experimental data and existing PDF sets, particularly LUXqed and NNPDF.

Proposed method

• Adopted the LUXqed input parametrization for the photon PDF at Q²₀ = 1 GeV², derived from F₂ and Fₗ structure functions.
• Used QED-corrected DGLAP evolution kernels up to O(α²), including O(ααS) and O(α²) splitting functions.
• Applied target mass corrections and power corrections via infrared renormalon models to account for low-Q² and high-x effects.
• Treated uncertainties from A1, CLAS, HERMES, and Christy-Bosted structure function fits, and from W² cut variation.
• Constructed neutron photon PDF by charge-reweighting proton PDFs using e²d/e²u and e²u/e²d ratios, with isospin-violating corrections.
• Combined all uncertainties in quadrature, including PDF eigenvectors, coherent contributions, resonance/continuum transitions, and renormalon parameters.

Experimental results

Research questions

• RQ1 How does the inclusion of QED corrections up to O(α²) affect the evolution and shape of the photon PDF in the MMHT framework?
• RQ2 To what extent do higher-twist and power corrections (e.g., infrared renormalons) modify the photon PDF at high-x and low-Q²?
• RQ3 How do QED effects from quark and gluon splitting influence the global fit quality and the structure of the quark and gluon PDFs?
• RQ4 What is the impact of using a common input scale (Q²₀ = 1 GeV²) on the photon PDF compared to previous approaches with higher input scales?
• RQ5 How can a consistent, precision neutron photon PDF be constructed from proton PDFs using isospin symmetry and QED corrections?

Key findings

• The MMHT photon PDF shows strong agreement (O(1–2%) deviation) with LUXqed and NNPDF at Q² = 10⁴ GeV², particularly in the small-x region.
• QED corrections at O(ααS) and O(α²) induce O(1–3%) modifications to the photon PDF at high-x, with the largest effects on strange and anti-strange quarks.
• The inclusion of target mass and higher-twist corrections (via infrared renormalon model) enhances the photon PDF at high-x, with the renormalon parameter A′₂ = 0.3⁺⁰.¹₋₀.¹ from global fit.
• Uncertainty decomposition shows that the total uncertainty is dominated by PDF eigenvectors and coherent contributions, with resonance/continuum transition uncertainty being negligible.
• The neutron photon PDF at Q² = 10⁴ GeV² reaches comparable magnitude to the proton PDF at small x, with isospin-violating corrections contributing ~5% to valence distributions.
• The final photon PDF, after simultaneous DGLAP evolution with all partons and full QED corrections, exhibits total uncertainties of O(1–2%) across x, consistent with state-of-the-art determinations.