Determination of Parton Densities for QCD partons and Electroweak Bosons

TL;DR

This work provides a unified determination of parton densities for QCD partons and electroweak bosons by solving an extended DGLAP evolution with the Parton Branching method. The evolution treats QCD at next-to-leading order and electroweak sectors at leading order, generating both collinear and transverse momentum dependent densities that are fitted to HERA DIS data and validated against DIS cross sections. Three mass-treatment schemes for heavy bosons are explored, with MassCutScheme=1 chosen as default to yield smooth densities over a wide range of scales. The resulting PB-NLO-QCD+EW-2025 densities (Set1 and Set2) are provided in LHAPDF and TMDlib, enabling phenomenology that includes photon and heavy EW bosons, as well as validation against $d\sigma/dQ^2$ measurements. Overall, the study advances first-principles, data-driven determinations of comprehensive parton densities and their TMDs, with practical implications for high-energy collider predictions involving EW bosons.

Abstract

Parton densities are obtained from a solution of the extended DGLAP-type evolution equation that includes both QCD and electroweak contributions. The equations are solved using the Parton-Branching (PB) approach, and the evolution is performed at next-to-leading order for QCD partons and leading order for electroweak bosons. The initial QCD parton distributions are fitted to HERA deep inelastic scattering data, while photon and weak-boson densities are generated perturbatively and validated against $dσ/dQ^2$. The resulting collinear and transverse-momentum dependent (TMD) densities are provided in LHApdf and TMDlib formats for direct phenomenological use.

Figures (12)

• Figure 1: The collinear quark and gluon densities for Set1 at $\mu= 100$ GeV as a function of $x$. The EW set together with the one containing only QCD partons is shown. The lower panel shows the ratio between both.
• Figure 2: The collinear quark and gluon densities at $\mu= 100$ GeV as a function of $x$. Shown is PB-NLO-QCD+EW-2025 Set1 (upper row) and PB-NLO-QCD+EW-2025 Set2 (lower row). The uncertainty bands for experimental and model uncertainties are shown separately.
• Figure 3: The collinear photon density for PB-NLO-QCD+EW-2025 Set1 (upper row) and Set2 (lower row) at $\mu= 50$, 100 and 500 GeV as a function of $x$ including experimental and model uncertainties. For comparison the prediction from MSHT20 Cridge:2021pxm (total and inelastic) is shown.
• Figure 4: The collinear vector-boson densities for PB-NLO-QCD+EW-2025 Set1 at $\mu= 100$ GeV as a function of $x$ including experimental and model uncertainties.
• Figure 5: The collinear vector-boson density for PB-NLO-QCD+EW-2025 Set2 at $\mu= 100$ GeV as a function of $x$ including experimental and model uncertainties.