[Paper Review] Study of Parton Density Function Uncertainties with LHAPDF and PYTHIA at LHC

D. Bourilkov|ArXiv.org|May 12, 2003

Particle physics theoretical and experimental studies3 references16 citations

TL;DR

This paper presents a new interface between the PYTHIA 6.2 Monte Carlo event generator and the LHAPDF library, enabling direct use of parton density function (PDF) sets with uncertainties for precision QCD predictions at the LHC. It demonstrates the method by estimating PDF uncertainties for Drell-Yan and Higgs boson production, showing that PDF uncertainties remain a non-trivial but manageable factor even at high masses and with large event samples.

ABSTRACT

The experimental errors in current and future hadron colliders are expected to decrease to a level that will challenge the uncertainties in the theoretical calculations. One important component in the prediction uncertainties comes from the Parton Density Functions of the (anti)proton. In this work we develop an interface from the Les Houches Accord Parton Density Functions (LHAPDF) package to the very popular Monte Carlo generator { t PYTHIA} version 6.2. Then we proceed to estimate the PDF uncertainties for the production of Drell-Yan pairs from the Z pole to masses above 1 $\TeV$ and for Higgs bosons at LHC. The measurement of the electro-weak mixing angle at LHC as a particularly difficult case is studied.

Motivation & Objective

• To develop a robust interface between PYTHIA 6.2 and the LHAPDF library for consistent PDF set usage in Monte Carlo simulations.
• To enable the estimation of PDF uncertainties in LHC processes by leveraging multiple members of a PDF set through repeated event generation.
• To assess the impact of PDF uncertainties on key LHC observables, including Drell-Yan production and Higgs boson production, and the electro-weak mixing angle measurement.
• To validate the implementation against known PDF sets and cross-checks using alternative PDF libraries like PDFLIB.
• To evaluate whether PDF uncertainties will limit precision measurements at the LHC, especially for high-mass and forward-backward asymmetry observables.

Proposed method

• Developed a PYTHIA 6.2 interface that supports multiple PDF sets (CTEQ6, MRST2001, Fermi2002) via the LHAPDF framework, allowing runtime selection of PDF members.
• Integrated two evolution codes (EVLCTEQ and QCDNUM) into a single library to enable use of different PDF sets without recompilation.
• Used the standard LHAPDF approach: PDF sets are represented as ensembles of eigenvectors or members, and observables are computed for each member to estimate uncertainty.
• Applied the 90% confidence level (CL) uncertainty formula: ΔX = 0.5 × √Σ[Xi(S+) − Xi(S−)]² for CTEQ6, and standard deviation for Fermi2002.
• Performed large-scale event generation (1.2 billion events) using the CONDOR grid scheduler to ensure statistical precision below PDF uncertainty contributions.
• Used rapidity intervals and forward-backward asymmetry as key observables to study PDF sensitivity across different x regions.

Experimental results

Research questions

• RQ1 Can a stable and efficient interface be established between PYTHIA 6.2 and the LHAPDF library to support PDF set usage with uncertainties?
• RQ2 What is the magnitude of PDF uncertainty for Drell-Yan pair production at the Z pole and above 1 TeV in mass at the LHC?
• RQ3 How significant are PDF uncertainties for Higgs boson production at the LHC, particularly in high-mass and forward regions?
• RQ4 To what extent do PDF uncertainties limit the precision of the electro-weak mixing angle measurement at the LHC?
• RQ5 Is the statistical uncertainty from Monte Carlo sampling negligible compared to PDF uncertainty in high-luminosity LHC scenarios?

Key findings

• The interface successfully enables PYTHIA 6.2 to use LHAPDF PDF sets with multiple members, achieving consistent results across different PDF libraries (e.g., CTEQ5L cross sections agree within 1% between PYTHIA internal, PDFLIB, and LHAPDF implementations).
• For Drell-Yan production at 91.2 GeV, cross sections varied from 1516 ± 5 pb (CTEQ5L) to 1591 ± 5 pb (MRST2001), reflecting differences in PDF sets and evolution codes.
• At high masses (M > 1 TeV), cross sections increased significantly with newer PDF sets: 6.76 ± 0.02 fb (CTEQ6) and 7.09 ± 0.02 fb (MRST2001), showing strong dependence on PDF choice.
• For the forward-backward asymmetry in Drell-Yan production, PDF uncertainties were estimated at < 0.00082 at 90% CL in the most forward rapidity bin (1.6–2.4), indicating they are non-negligible but manageable.
• To achieve 90% CL PDF uncertainty limits, 27.7 million events were needed in the 0.8–1.6 rapidity bin and 11.5 million in 1.6–2.4, which are feasible with ~110 fb⁻¹ luminosity at 100% efficiency.
• Despite generating 1.2 billion events, the study found no systematic show-stopper from PDF uncertainties, suggesting they may not be the dominant limitation in high-luminosity LHC measurements.