Towards Ultimate Parton Distributions at the High-Luminosity LHC

TL;DR

The paper forecasts the ultimate precision of proton parton distribution functions (PDFs) achievable with the High-Luminosity LHC by generating HL-LHC pseudo-data for multiple PDF-sensitive processes and applying Hessian profiling to the PDF4LHC15 set. It shows that HL-LHC measurements can reduce PDF uncertainties by factors of approximately 2–4, with the strange quark and gluon sectors benefiting most, and Higgs boson transverse momentum in gluon fusion reaching few-percent level uncertainties. The study provides detailed, process-by-process and combined projections, including implications for SM and beyond-SM phenomenology, and releases public HL-LHC PDF grids. These results demonstrate a strong, robust case for continuing and expanding PDF-sensitive measurements at the HL-LHC to sharpen theory predictions and improve discovery reach.

Abstract

Since its start of data taking, the LHC has provided an impressive wealth of information on the quark and gluon structure of the proton. Indeed, modern global analyses of parton distribution functions (PDFs) include a wide range of LHC measurements of processes such as the production of jets, electroweak gauge bosons, and top quark pairs. In this work, we assess the ultimate constraining power of LHC data on the PDFs that can be expected from the complete dataset, in particular after the High-Luminosity (HL) phase, starting in around 2025. The huge statistics of the HL-LHC, delivering $\mathcal{L}=3$ ab$^{-1}$ to ATLAS and CMS and $\mathcal{L}=0.3$ ab$^{-1}$ to LHCb, will lead to an extension of the kinematic coverage of PDF-sensitive measurements as well as to an improvement in their statistical and systematic uncertainties. Here we generate HL-LHC pseudo-data for different projections of the experimental uncertainties, and then quantify the resulting constraints on the PDF4LHC15 set by means of the Hessian profiling method. We find that HL-LHC measurements can reduce PDF uncertainties by up to a factor of 2 to 4 in comparison to state-of-the-art fits, leading to few-percent uncertainties for important observables such as the Higgs boson transverse momentum distribution via gluon-fusion. Our results illustrate the significant improvement in the precision of PDF fits achievable from hadron collider data alone, and motivate the continuation of the ongoing successful program of PDF-sensitive measurements by the LHC collaborations.

Figures (20)

• Figure 2.1: Representative Feynman diagrams at the Born level of the six types of collider processes for which HL--LHC pseudo--data has been generated in this analysis: the production of top quark pairs, $W$ bosons in association with charm quarks, and the neutral and charged current Drell--Yan processes; the production of inclusive jets, $Z$ bosons at finite transverse momentum, and direct photons.
• Figure 2.2: The kinematical coverage in the $(x,Q^2)$ plane of the HL--LHC pseudo--data included in this analysis. For each data point, the values of $(x_1,Q^2)$ and $(x_2,Q^2)$ corresponding to each of the two colliding partons are determined approximatly from the corresponding leading--order kinematics. We assume $x_1=x_2$ if rapidities are not specified for the final states. The HL--LHC pseudo--data therefore spans a wide region in the kinematic plane, namely $6\times 10^{-5} \mathrel{\hbox{$\sim$} \hbox{$<$}} x \mathrel{\hbox{$\sim$} \hbox{$<$}} 0.7$ and $40~{\rm GeV} \mathrel{\hbox{$\sim$} \hbox{$<$}} Q \mathrel{\hbox{$\sim$} \hbox{$<$}} 7~{\rm TeV}$.
• Figure 2.3: Comparison between the baseline PDF4LHC15 set and the sets profiled with the LHC data, either with or without the correlations between the experimental systematic uncertainties accounted for. In the latter case, the $f_{\rm corr}$ factor is chosen to reproduce the results of the profiling when the correlations are included, see text. We show here the results of profiling with the top differential distributions at $\sqrt{s}=8$ TeV with $f_{\rm corr}= 0.25$ (left) and the $W+$charm rapidity distribution at $\sqrt{s}=13$ TeV with $f_{\rm corr}= 1$ (right plot). A tolerance factor of $T=1$ has been used for this specific comparison.
• Figure 3.1: The correlation coefficients $\rho$ between the PDFs and the HL--LHC pseudo--data. Left: the correlation between the anti--up quark and the high--mass Drell--Yan pseudo--data as a function of $x$ for $Q=100$ GeV. Right: the correlation between the anti--down quark and the inclusive $W,Z$ production process in the forward region. In each plot, the different curves correspond to each of the bins of the pseudo--data used in the fit.
• Figure 3.2: Comparison between the HL--LHC pseudo--data and the theoretical predictions for high--mass (left) and forward (right) Drell--Yan production. The theory calculations are shown both before (PDF4LHC15) and after profiling. Luminosity uncertainties are not shown in the experimental errors. In the bottom panel, we show the same results normalised to the central value of the original theory calculation. Note in the right plot the comparison are only made for forward $Z$ data though both $W$ and $Z$ data are included in the profiling.