The PDF4LHC Working Group Interim Report

Abstract: This document is intended as a study of benchmark cross sections at the LHC (at 7 TeV) at NLO using modern parton distribution functions currently available from the 6 PDF fitting groups that have participated in this exercise. It also contains a succinct user guide to the computation of PDFs, uncertainties and correlations using available PDF sets. A companion note, also submitted to the archive, provides an interim summary of the current recommendations of the PDF4LHC working group for the use of parton distribution functions and of PDF uncertainties at the LHC, for cross section and cross section uncertainty calculations.

• The paper introduces standardized methodologies for determining PDFs and quantifying their uncertainties at 7 TeV LHC experiments.
• It compares analyses from six prominent PDF fitting groups to highlight key experimental and theoretical uncertainties, including αs impacts.
• The report establishes benchmark cross section predictions and offers recommendations to enhance the accuracy of future LHC analyses.

Overview of the PDF4LHC Working Group Interim Report

The Interim Report from the PDF4LHC Working Group provides a comprehensive examination of the methodologies, uncertainties, and recommendations concerning parton distribution functions (PDFs) in high-energy physics experiments at the Large Hadron Collider (LHC). The focus is on benchmark cross sections at a center-of-mass energy of 7 TeV, calculated at next-to-leading order (NLO), and on using modern PDFs produced by six prominent PDF fitting groups.

Key Elements of the Report

The document thoroughly explores the PDF determinations and the associated uncertainties that arise from varying datasets and methodologies across different groups. It emphasizes the need for a standardized user guide to the computation of PDFs and their uncertainties, enabling consistent use in cross section calculations at the LHC.

PDF Determinations and Uncertainties

The paper explores the distinct approaches to PDF determinations, addressing the experimental and theoretical uncertainties intrinsic to each:

• Experimental Uncertainties: These depend significantly on the choice of datasets, the type of uncertainty estimation methodology, and the parton parametrization form and size.
• Theoretical Uncertainties: Although several theoretical uncertainties exist, such as those related to the QCD coupling constant ($\alpha_s$) and heavy quark masses, the report primarily focuses on $\alpha_s$ uncertainty due to its significant impact on PDFs, particularly the gluon distribution.

The report outlines methods for computation of combined PDF and $\alpha_s$ uncertainties, highlighting how these can be accurately combined under the quadratic approximation framework used by different groups, though noting the necessity for alternative techniques in specific cases like the MSTW's dynamic tolerance.

Benchmark Results

A systematic comparison of benchmark predictions from several PDF sets shows reasonable agreement amongst groups such as CTEQ, MSTW, and NNPDF. However, variations exist, particularly concerning the predictions for Higgs production via gluon fusion, largely influenced by differences in $\alpha_s$ choices and PDF parameters.

Implications for Future Research

Understanding and minimizing uncertainties in PDFs is crucial for reliable cross section predictions at the LHC. The working group's interim report sets a foundation for future developments in PDF analysis, suggesting directions for more sophisticated treatments of theoretical uncertainties such as variable flavor number schemes and the incorporation of updated experimental data as new measurements become available at higher energy levels.

Conclusion

The PDF4LHC Working Group's Interim Report is a vital resource for clarifying the consensus on PDF use in LHC analyses, offering detailed insights into uncertainty quantification, while fostering collaboration between PDF providers and experimental physicists. Such efforts are indispensable in paving the way for more accurate predictions necessary for probing the Standard Model and beyond at the LHC.