Parton Distributions: Progress and Challenges

TL;DR

The article surveys progress and challenges in spin-averaged proton parton densities relevant to LHC physics, focusing on the QCD framework, higher-order evolution, and heavy-quark treatment. It details NNLO splitting functions, solution strategies for DGLAP equations, and factorization-scheme choices, along with recent global analyses and their impact on LHC observables like W/Z production. The work emphasizes benchmarking evolution codes, the role of HERA data for future precision, and the need for consistent, multi-PDF constraints to minimize theoretical uncertainties in hadronic cross sections.

Abstract

We briefly discuss recent research on the spin-averaged parton densities of the proton, focusing on some aspects relevant to hard processes at the LHC. Specifically, after recalling the basic framework and the need for higher-order calculations, we address the evolution equations governing the scale dependence of the parton distributions and their solution, schemes for initial conditions and the inclusion of heavy quarks, recent progress on fits to data, and future high-precision constraints from LHC measurements.

Figures (12)

• Figure 1: Kinematics of photon-exchange DIS in the QCD-improved parton model. Particle momenta are given in brackets.
• Figure 2: Perturbative expansion of the total cross section for Higgs production at the LHC. Shown are the dependence on the mass $M_H$ and the renormalization scale $\mu_{\rm r}$ (from Ref. Moch:2005ky).
• Figure 3: Minimal parton momenta $\xi_{-}$ probed at the LHC, compared with the DIS coverage of HERA and previous fixed-target experiments.
• Figure 4: The LO, NLO and NNLO approximations to the splitting-function moments $P_{\rm ns}^{\,+}(N)$ for four flavours at $\alpha_{\rm s} = 0.2\,$, and the resulting logarithmic scale derivatives for $xq_{\rm ns}^{\,+}\,=\, x^{\,0.5} (1-x)^3$, a schematic but characteristic model distribution (from Ref. Moch:2004pa).
• Figure 5: The exact $\alpha_{\rm s}^3$ contributions to the non-singlet splitting function and coefficient function for $F_2$, compared to approximations obtained from the small-$x$ logarithms (from Refs. Moch:2004paVermaseren:2005qc). The leading small-$x$ term of $P_{\rm ns +}^{(2)}$ was derived before in Ref. Blumlein:1995jp.