Parton distribution functions and theory parameters: an NNPDF perspective

Abstract

Parton Distribution Functions (PDFs) are a key ingredient in theoretical predictions for Large Hadron Collider (LHC) observables and play a central role in the extraction of precision Standard Model (SM) and Beyond the SM (BSM) parameters from LHC data. Recent analyses demonstrate that the determination of fundamental SM parameters such as $α_s(m_Z)$, $m_W$, $m_t$, and $\sin^2θ_W$ is strongly influenced by the choice of input PDFs. In this contribution, we present the status and challenges of PDF determination from the NNPDF perspective, both in stand-alone fits and in joint extractions with (B)SM parameters. We place particular emphasis on results for $α_s(m_Z)$, $m_t$, and Wilson coefficients in the SM Effective Field Theory (SMEFT) framework.

Figures (6)

• Figure 1: Impact of aN$^3$LO QCD and QED corrections onto the gluon-gluon luminosity at $\sqrt{s}=13.6\,$ TeV (left) and the Higgs cross section in gluon fusion (right) shown as ratio against PDF4LHC21 PDF4LHCWorkingGroup:2022cjn (left) or the NNLO combination of Ref. Cridge:2024icl (right). On the right panel, the error bars correspond to MHOU combined with PDF uncertainties (outer) or only the latter (inner).
• Figure 2: The relative change in the total $\Delta \chi^2$ as given by Eq. \ref{['eq:delta_chi2']} for a selection of PDF sets considered in Chiefa:2025loi. The $\Delta \chi^2 = 0$ circumference is represented by the solid curve. From Ref. Chiefa:2025loi.
• Figure 3: The results of two multi-closure tests consisting of 100 pseudodata samples, performed using the TCM Ball:2021icz, to pseudodata generated at $\alpha_s(m_Z)=0.118$ (denoted by the dashed red line). Left: with positivity, right: without positivity (see text).
• Figure 4: Left panel: A comparison of $\alpha_s(m_Z)$ determinations by, from top to bottom, NNPDF4.0 Ball:2025xgq, NNPDF3.1 Ball:2018iqk, MSHT20 Cridge:2024exf, ABMP16tt Alekhin:2024bhs, ATLAS ATLAS:2023lhg, CMS CMS:2021yzl, ALPHA25 Brida:2025gii, and the PDG24 ParticleDataGroup:2024cfk Right panel: A comparison of gluon-gluon luminosities at $\sqrt{s} = 13,\text{TeV}$ from fits using fixed $\alpha_s(m_Z) = 0.119$ and those including a theory covariance matrix, constructed by varying $\alpha_s(m_Z)$ up and down by 0.002 around 0.119.
• Figure 5: 68 % C.L. intervals in the joint ($\alpha_s, m_t$) plane comparing the impact of including distributions differential in either the invariant mass $m_{t\bar{t}}$ of the top-pair, the top quark transverse momentum $p_T^t$ or its rapidity $y_t$ at NNLO QCD + MHOU accuracy. Note that these results are preliminary.