New parton distributions for collider physics (1007.2241v3)

Abstract: We extract new parton distribution functions (PDFs) of the proton by global analysis of hard scattering data in the general-mass framework of perturbative quantum chromodynamics. Our analysis includes new theoretical developments together with the most recent collider data from deep-inelastic scattering, vector boson production, and single-inclusive jet production. Due to the difficulty in fitting both the DO Run-II W lepton asymmetry data and some fixed-target DIS data, we present two families of PDFs, CT10 and CT10W, without and with these high-luminosity W lepton asymmetry data included in the global analysis. With both sets of PDFs, we study theoretical predictions and uncertainties for a diverse selection of processes at the Fermilab Tevatron and the CERN Large Hadron Collider.

• The paper introduces new proton PDF sets (CT10 and CT10W) with refined uncertainty management and flexible parameterizations to improve collider predictions.
• It integrates combined HERA-1 and high-luminosity DØ Run-II W lepton asymmetry data, reducing systematic errors and resolving dataset tensions.
• The enhanced PDFs yield more accurate cross-section predictions for key processes such as W, Z, and top-quark production at major colliders.

Insights on New Parton Distributions for Collider Physics

The paper presents a thorough investigation into the construction of new parton distribution functions (PDFs) of the proton, essential for accurate predictions at high-energy colliders such as the Fermilab Tevatron and CERN Large Hadron Collider (LHC). Key advancements in both the theoretical framework and data inclusion differentiate this paper from prior efforts, notably CTEQ6.6 and CT09 analyses. The work involves two main PDF sets, CT10 and CT10W, to account for disparities in high-luminosity D\O~ Run-II $W$ lepton asymmetry data.

Key Theoretical Advancements

The authors introduce significant refinements in the PDF determination process:

1. Systematic Treatment of Uncertainties: The normalization uncertainties are now managed akin to other systematic errors, simplifying algebraic solutions and offering improved uncertainty estimates by allowing normalization variations during the fitting process.
2. Enhanced Flexibility in PDF Parameterizations: More flexible parametrizations for certain parton flavors, namely $d$, $s$, and $g$, are adopted to minimize dependence on the initial parametrization, directly influencing the uncertainty estimation for quarks and gluons.
3. Uniform Weighting in $\chi^2$ Calculation: Using a consistent weight of 1 for all experiments in the CT10 fit ensures more uniform treatment across datasets, except for the CT10W set where specific weights on $W$ lepton asymmetry data are necessary to achieve fit concordance.

These methodological improvements address certain limitations in previous PDF analyses, emphasizing a systemic treatment of uncertainties, adaptable parameterizations, and consistent data weighting approaches.

Integration of New Collider Data Sets

The incorporation of recent high-precision experimental data marks a significant contribution of this paper. Particularly:

• Combined HERA-1 Data: The merged datasets from H1 and ZEUS experiments at HERA-1 replace individual datasets, providing reduced systematic uncertainties due to cross-calibration efforts. This integration has demonstrable effects on reducing PDF uncertainties, particularly at small $x$ values.
• D\O~ Run-II $W$ Lepton Asymmetry Data: Challenges arise in fitting this high-luminosity dataset, revealing tensions with other fitted measurements, particularly those from fixed-target DIS experiments. The paper addresses this by proposing two distinct PDF sets (CT10 and CT10W), allowing exploration of variations in $d/u$ ratios affecting collider predictions.

Impact on Theoretical Predictions and Collider Applications

The paper's PDF sets impact broad areas within the theoretical predictions for collider events:

• Precision in Cross Sections: Significant differences arise in cross-section calculations for processes such as $W$, $Z$, and top-quark production across the Tevatron and LHC when using CT10 or CT10W versus previous CTEQ6.6 sets. Notably, enhanced uncertainties in CT10 reflect increased parametrization flexibility.
• PDF Uncertainties in New Physics Scenarios: The CT10W PDFs reduce uncertainties in observables sensitive to large-$x$ $d/u$ ratios, indicating the importance of accurate asymmetry data in theoretical predictions.

Addressing Methodological and Data Tensions

A novel aspect of this work is the discussion on resolving tensions between different datasets and methodological advances in fitting parameters. By exploring $\chi^2$ and parameter distributions for each data set, and investigating potential saturation effects through the geometric scaling variable $A_{gs}$, the authors provide a robust analysis of the limitations and stability of NLO predictions against observed data.

Conclusion and Future Directions

This comprehensive paper offers critical insights into more accurate PDF determination through updated experimental data and enhanced theoretical treatment. While resolving tensions in extensive datasets remains challenging, the dual PDF sets CT10 and CT10W enable a more nuanced understanding of proton structures. Looking forward, refining these methodologies and further integrating upcoming collider data will continue to refine our understanding of proton dynamics at high energies, shaping future developments in collider physics.