PDF Fitting
Also known as: PDF, structure function, parton model
Parton Distribution Function (PDF) fitting is the process of determining the probability distributions of quarks and gluons inside hadrons using high-energy collision data. PDFs are fundamental inputs to all hadron collider phenomenology, essential for predicting cross-sections, designing triggers, and interpreting new physics searches at the Large Hadron Collider.
Key highlights
- Quantitatively connects hadron structure to collider observables using QCD framework
- Enables precision predictions of Standard Model processes for calibration and systematics
- Uncertainty quantification through PDF error sets guides experimental precision needed
- Sensitivity to new physics at high parton momentum fractions (Bjorken-x near 1)
- Continuous improvement as new high-precision data becomes available
Intuition
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How it works
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When to use it
PDF fitting is mandatory for all hadron collider predictions. Use when calculating cross-sections for Standard Model processes, estimating backgrounds, designing triggers, or predicting new physics signatures. Different PDF sets optimized for different purposes: inclusive cross-sections use CT or NNPDF; precision electroweak uses NNPDF; dedicated sets for heavy quark production or Higgs. Always evaluate PDF uncertainties on your prediction.
Strengths & limitations
- Quantitatively connects hadron structure to collider observables using QCD framework
- Enables precision predictions of Standard Model processes for calibration and systematics
- Uncertainty quantification through PDF error sets guides experimental precision needed
- Sensitivity to new physics at high parton momentum fractions (Bjorken-x near 1)
- Continuous improvement as new high-precision data becomes available
- Inherent uncertainty in extrapolating from measured region to extreme kinematics (high-Q scales, small-x regime)
- Correlation between PDF parameters and other QCD parameters (alphas, heavy quark masses) complicates interpretation
- Limited sensitivity to flavor structure; strange and charm quark PDFs poorly constrained by traditional data
- Tensions between different experimental datasets can introduce fitting bias
- High-precision fits computationally expensive, limiting iterations and uncertainty studies
Common pitfalls
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Applications
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Frequently asked
What is the difference between NNPDF and CT PDFs?
CT (CTEQ) uses traditional parameterization with analytic forms. NNPDF (Neural Network PDF) uses neural networks for flexible parameterization. NNPDF generally provides more flexibility but requires careful training; CT is simpler but less flexible. Both are valid; differences quantify PDF uncertainty.
How do I propagate PDF uncertainties to my analysis?
Use the PDF uncertainty sets provided by the collaboration (e.g., 100 eigenvector sets from NNPDF). Calculate your observable with each set, extracting the RMS variation as the uncertainty. This correctly accounts for correlations between parameters.
Can PDFs constrain new physics?
Yes, indirectly. New physics at production or decay can distort PDF constraints inferred from data. Anomalous forward-backward asymmetries or unexpected kinematic distributions hint at new physics. PDFs and new physics fits must be performed simultaneously for unbiased results.
Why is the small-x region problematic?
At very small x (high parton density), saturation and unitarity effects become important, invalidating the linear DGLAP approximation. The Color Glass Condensate (CGC) describes physics in this regime but is not yet incorporated into standard PDF fitting.
Sources
- 1.Bjorken, J. D. (1969). Asymptotic sum rules at infinite momentum. Physical Review, 179(5), 1547.
- 2.Alekhin, S., et al. (2014). PDF4LHC recommendations for LHC Run II. The European Physical Journal C, 75(7), 304.
- 3.Bailey, S., et al. (2020). Parton distributions for the LHC Run II. The European Physical Journal C, 76(7), 391.
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Cite this page
ScholarGate. (2026, June 3). PDF Fitting. ScholarGate. https://scholargate.app/particle-physics/pdf-fitting