Global analysis of nuclear PDFs - latest developments

TL;DR

This review surveys the current status of global, DGLAP-based analyses of nuclear PDFs (nPDFs), focusing on EPS09, nCTEQ, and DSSZ and their treatment of uncertainties. It highlights the progress in achieving good, factorization-consistent fits across DIS, DY, and hadron-production data, while emphasizing persistent gluon-sector uncertainties and tensions between neutrino and charged-lepton DIS data. A key advance is the introduction of spatial (impact-parameter) dependence, enabling centrality-differentiated cross-section predictions via EPS09s and EKS98s, and underscoring the need for simultaneous global fits of nPDFs with nuclear fragmentation functions and free-proton PDFs. The article also outlines future directions, including more diverse hard-process data and electron-ion collider measurements to sharpen gluon constraints and to integrate spatial dependence directly into global fits.

Abstract

In this review talk I discuss the latest developments in the DGLAP-based global analysis of nuclear parton distribution functions (nPDFs), focusing on the recent EPS09, nCTEQ and DSSZ global fits. I also briefly review the recent analysis for assigning a spatial dependence to the globally analysed nPDFs, resulting in the new sets EPS09s and EKS98s ("s" for spatial). With these, one can now compute nuclear hard-process cross sections and estimate their nPDF-originating uncertainties in different centrality classes for the first time consistently with the global nPDF fits.

Figures (4)

• Figure 1: (Color on-line) Left: The nuclear effects to bound-proton NLO PDFs in a lead nucleus as a function of $x$, at two different scales, according to the EPS09 global analysis. Comparison with the earlier NLO nPDFs is also shown. The error bands are computed from the 15+15 error sets obtained through a "90% confidence criterion". From Eskola:2009uj. Right: $Q^2$ evolution of the EPS09 nuclear effects at fixed values of $x$. From Eskola:2010jh.
• Figure 2: (Color on-line) The EPS09 fit to some of the $l$+$A$ DIS $\frac{1}{A}F_2^A(x,Q^2)/\frac{1}{2}F_2^{\rm d}(x,Q^2)$ data (upper left), p+$A$ DY $(\frac{1}{A}d\sigma^{{\rm p}A}/dx_2dQ^2)/(\frac{1}{2}d\sigma^{\rm pd}/dx_2dQ^2)$ data (upper right) sets used, as well as to the minimum-bias PHENIX nuclear modification factor data for $\pi^0$ production in d+Au collisions, $\frac{1}{2A}(d\sigma^{\rm dAu}/dp_Tdy)/(d\sigma^{\rm pp}/dp_Tdy)$, in mid-rapidity at RHIC Adler:2006wg (lower panel). The $\pi^0$ production is computed with the INCNLO code Aversa:1988vb and NLO KKP vacuum fragmentation functions (FFs) Kniehl:2000fe. From Eskola:2009uj.
• Figure 3: (Color on-line) Upper panels: The DSSZ and EPS09 nuclear effects to bound-proton PDFs (valence $u$ quarks, sea $u$ quarks, gluons) in a lead nucleus as a function of $x$ at the initial scales $Q_0^2=1.0$ GeV$^2$ for DSSZ (blue long dashed) and $1.69$ GeV$^2$ for EPS09 (green solid). The error bands are from EPS09. The DSSZ modifications at $Q^2=1.69$ GeV$^2$ are also shown (red short dashed); their complicated behaviour is caused by the negative gluon PDFs in MSTW and DSSZ at smallest $x$ and small $Q^2$. Lower panels: The same but for $Q^2=10$ GeV$^2$. Prepared by I. Helenius.
• Figure 4: (Color on-line) The minimum-bias nuclear modification ratio $R_{\rm dAu}^{\pi^0}$ as a function of $p_T$, see the text for details. Prepared by I. Helenius.