Parton Distributions at a 100 TeV Hadron Collider

TL;DR

At a 100 TeV hadron collider, accurate proton PDFs across extreme x and Q^2 regions are crucial for predictions. The paper surveys PDF uncertainties, kinematic coverage, and luminosity ratios between 100 TeV and 14 TeV, and discusses novel PDF-related phenomena such as a potential top-quark PDF, increased photon-initiated contributions, and the relevance of high-energy resummation. It shows that gluon-initiated channels gain greatly at high masses, that photon-initiated processes become non-negligible in Drell-Yan and diboson production, and that small-x resummation effects may be important for FCC physics. The results motivate improved photon PDFs, matched heavy-quark treatments, and resummation frameworks for precision predictions at 100 TeV.

Abstract

The determination of the parton distribution functions (PDFs) of the proton will be an essential input for the physics program of a future 100 TeV hadron collider. The unprecedented center-of-mass energy will require knowledge of PDFs in currently unexplored kinematical regions such as the ultra low-x region or the region of multi-TeV momentum transfers. In this contribution we briefly summarise the studies presented in the PDF section of the upcoming report on "Physics at a 100 TeV pp collider: Standard Model processes". First we map the PDF kinematical coverage in the $(x,Q^2)$ plane, quantify PDF uncertainties, and compute ratios of PDF luminosities between 100 TeV and 14 TeV. Then we show how the extreme kinematics of such collider lead to a number of remarkable PDF-related phenomena such as the top quark as a massless parton, an increased role of photon-initiated processes and the possible need of PDFs with high-energy resummation.

Figures (5)

• Figure 1: Kinematical coverage in the $(x,M_X)$ plane of a $\sqrt{s}=100$ TeV hadron collider (solid blue line), compared with the corresponding coverage of the LHC at $\sqrt{s}=14$ TeV (dot-dashed red line). The dotted lines indicate the lines of constant rapidity $y$ at the FCC. We also indicate the relevant $M_X$ regions for phenomenologically important processes, from low masses (Drell-Yan, low $p_T$ jets), electroweak scale processes (Higgs, $W,Z$, top), and possible new high-mass particles (squarks, $Z'$).
• Figure 2: The PDF uncertainties in the gluon-gluon luminosity at the FCC with $\sqrt{s}=100$ TeV computed with the PDF4LHC15_nnlo_mc set. Left plot: the rapidity-integrated luminosity $\mathcal{L}_{gg}(M_X)$. Right plot: the double-differential luminosity $\widetilde{\mathcal{L}}_{gg}(M_X,y)$.
• Figure 3: The ratio of PDF luminosities between $\sqrt{s_1}=100$ TeV and $\sqrt{s_2}=14$ TeV for different initial-state channels, computed with the PDF4LHC15 NNLO set. nameref-fig:lumirat fith LAB: fig:lumirat
• Figure 4: nameref-fig:epem-fcc1 fith LAB: fig:epem-fcc1 The invariant mass distribution of dileptons in $e^+e^-$ (Drell-Yan) production (left) and for $W^+W^-$ pairs (right) at a 100 TeV hadron collider, separating the contribution from each initial state.
• Figure 5: Left plot: the NNPDF2.3 NNLO $n_f=6$ PDF set at $Q=10$ TeV including the top quark PDF. Right plot: the gluon and quark single PDFs obtained from a preliminary DIS-only fit with NLO+NLLx DGLAP evolution, compared to a baseline fit with NLO evolution.