EPS09 - a New Generation of NLO and LO Nuclear Parton Distribution Functions

Abstract: We present a next-to-leading order (NLO) global DGLAP analysis of nuclear parton distribution functions (nPDFs) and their uncertainties. Carrying out an NLO nPDF analysis for the first time with three different types of experimental input -- deep inelastic $\ell$+A scattering, Drell-Yan dilepton production in p+$A$ collisions, and inclusive pion production in d+Au and p+p collisions at RHIC -- we find that these data can well be described in a conventional collinear factorization framework. Although the pion production has not been traditionally included in the global analyses, we find that the shape of the nuclear modification factor $R_{\rm dAu}$ of the pion $p_T$-spectrum at midrapidity retains sensitivity to the gluon distributions, providing evidence for shadowing and EMC-effect in the nuclear gluons. We use the Hessian method to quantify the nPDF uncertainties which originate from the uncertainties in the data. In this method the sensitivity of $\chi^2$ to the variations of the fitting parameters is mapped out to orthogonal error sets which provide a user-friendly way to calculate how the nPDF uncertainties propagate to any factorizable nuclear cross-section. The obtained NLO and LO nPDFs and the corresponding error sets are collected in our new release called {\ttfamily EPS09}. These results should find applications in precision analyses of the signatures and properties of QCD matter at the LHC and RHIC.

• The paper provides a comprehensive NLO analysis integrating DIS, Drell-Yan, and inclusive pion data to constrain nuclear PDFs.
• It employs DGLAP evolution with nuclear modifications to free proton PDFs and uses the Hessian method for uncertainty quantification.
• The EPS09 set significantly improves precision in nuclear collision predictions, paving the way for advanced QCD research.

EPS09: A New Generation of NLO and LO Nuclear Parton Distribution Functions

The paper presents the EPS09 set of nuclear parton distribution functions (nPDFs) designed to enhance the precision of theoretical predictions in nuclear collisions. The research engages in a comprehensive next-to-leading order (NLO) analysis, building on the previous leading order (LO) frameworks, by integrating data from various high-energy experiments. Notably, the study makes use of deep inelastic scattering (DIS) data, Drell-Yan (DY) dilepton production, and for the first time, inclusive pion production data from RHIC, which adds new dimensions to comprehending the gluon distributions within nuclei.

Methodology and Analysis

The authors employ the DGLAP equations for the scale evolution of nPDFs, using a robust theoretical infrastructure. They introduce nuclear modifications to free proton PDFs, using the CTEQ6.1M set as the reference. Their approach adheres to the factorization framework, asserting its validity in capturing the dynamics of hard nuclear interactions.

Key extensions introduced in this paper include incorporating inclusive pion production in NLO nPDF analyses, which aids tremendously in constraining nuclear gluon densities. Furthermore, the paper offers a detailed account of using the Hessian method to quantify uncertainties in nPDFs, providing error sets for easy calculation of uncertainties propagating to various nuclear cross-sections.

Results

The paper provides comprehensive nPDFs and their uncertainty quantifications in the EPS09 release, which is poised to be an essential resource for investigating quantum chromodynamics (QCD) matter signatures at LHC and RHIC. The resulting nPDFs demonstrate substantial improvements in precision, witnessed through lower uncertainties at key kinematic regions compared to previous analyses.

The inclusion of new experimental data types notably impacts the understanding of gluon modifications, especially in the moderate to high-$x$ regions. The authors show that despite the noise present in experimental datasets, their methodology successfully navigates these challenges to produce reliable nPDF sets.

Implications and Future Directions

This research has far-reaching implications for theoretical and applied nuclear physics. The EPS09 nPDF sets allow for precise calculations in high-energy nuclear collisions — a critical need in the search for new physical phenomena. Additionally, they set the stage for further integration of experimental data, particularly from forthcoming LHC operations that could introduce new constraints enhancing the understanding of nuclear matter.

Future research could progress towards integrating the general-mass scheme in nPDF analyses or extend the sets to accommodate finer theoretical details within QCD. Also, addressing potential discrepancies arising from neutrino scattering off nuclei as compared to electromagnetic interactions could yield enriching insights into the universality of the nuclear modifications obtained.

In summary, by providing a comprehensive NLO global analysis, incorporating new datasets, and detailing uncertainties in the EPS09 nPDF sets, this paper significantly advances the tools available for nuclear physics research, providing a foundation for future explorations at the forefront of high-energy particle physics.