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Specialized minimal PDFs for optimized LHC calculations.

Stefano Carrazza1, Stefano Forte2, Zahari Kassabov3

  • 1TIF Lab, Dipartimento di Fisica, Università di Milano, Via Celoria 16, Milan, 20133 Italy ; Sezione di Milano, INFN, Via Celoria 16, Milan, 20133 Italy ; Theory Department, CERN, Geneva, 1211 Switzerland.

The European Physical Journal. C, Particles and Fields
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We introduce specialized minimal parton distribution function (PDF) sets (SM-PDFs) for precise uncertainty quantification in particle physics. These SM-PDFs efficiently represent process-specific uncertainties while preserving correlations and robustness.

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Area of Science:

  • High Energy Physics
  • Quantum Chromodynamics
  • Computational Physics

Background:

  • Parton distribution functions (PDFs) are crucial for interpreting particle collider data.
  • Quantifying PDF uncertainties accurately is essential for precise theoretical predictions.
  • Current methods can be computationally intensive and may not optimally represent process-specific uncertainties.

Purpose of the Study:

  • To develop a methodology for constructing specialized minimal PDF sets (SM-PDFs).
  • To ensure SM-PDFs accurately represent process-specific uncertainties and retain correlations.
  • To create a flexible framework for combining and expanding PDF sets.

Main Methods:

  • Construction of SM-PDFs by selecting a minimal set of error eigenvectors.
  • Ensuring robustness of SM-PDFs against variations in kinematic cuts.
  • Combining information from different input processes without loss of correlation.
  • Illustrating the method with SM-PDFs for Higgs, top-quark pair, and electroweak gauge boson production.

Main Results:

  • Demonstrated the construction of SM-PDFs tailored to specific physics processes.
  • Showed that a small number of Hessian eigenvectors (e.g., 11 for Higgs, 4 for top-quark pairs, 11 for W/Z bosons) are sufficient for accurate representation.
  • Confirmed that SM-PDF sets can be systematically enlarged, recovering the prior PDF set.

Conclusions:

  • The SM-PDF methodology provides an efficient and accurate way to handle PDF uncertainties for specific processes.
  • This approach simplifies uncertainty quantification in high-energy physics analyses.
  • SM-PDFs offer a flexible and extensible framework for future PDF determinations.