Implications of Hadron Collider Observables on Parton Distribution Function Uncertainties

TL;DR

This paper addresses the lack of quantified uncertainties in parton distribution functions (PDFs) and their impact on hadron-collider interpretations. It introduces a Bayesian inference framework that propagates PDF uncertainties to new observables via Monte Carlo sampling, tests the compatibility of new data with the existing fit using a confidence level, and updates the PDF distributions without redoing full fits. The authors demonstrate the method on two Tevatron datasets (one-jet inclusive cross section and W lepton charge asymmetry), showing that compatible data can tighten PDF uncertainties and shift key parameters, such as $\alpha_S(M_Z)$ and the gluon high-$x$ exponent $β$. The approach is modular and flexible, accommodating experimental and theoretical uncertainties and enabling inclusion or exclusion of data sets as needed, which is crucial for robust SM tests and future LHC analyses.

Abstract

Standard parton distribution function sets do not have rigorously quantified uncertainties. In recent years it has become apparent that these uncertainties play an important role in the interpretation of hadron collider data. In this paper, using the framework of statistical inference, we illustrate a technique that can be used to efficiently propagate the uncertainties to new observables, assess the compatibility of new data with an initial fit, and, in case the compatibility is good, include the new data in the fit.

Figures (2)

• Figure 1: (a) Single inclusive jet cross section as a function of the jet transverse energy. The results are divided by the average prediction calculated with the initial PDF's. The data points are the CDF run 1$^a$ results. The dotted lines represent the initial one-sigma PDF uncertainties. The solid lines are the theory predictions calculated with the new PDF's. The inner (outer) error bars on the data points are the diagonal entries of the experimental (total) covariance matrix. The dashed line is the prediction obtained with the MRSD0 PDF set. (b) The one-sigma correlation contour between the strong coupling constant $\alpha_S(M_Z)$ and the $\beta$-parameter in the gluon PDF ($\simeq x^\alpha(1-x)^\beta$ at the initial factorization scale) calculated for both the initial and new PDF's.
• Figure 2: (a) The lepton charge asymmetry as a function of the lepton pseudo-rapidity. The results are normalized to the theory prediction using the average value of the initial PDF's. The data are the CDF run 1$^b$ preliminary results. The error bars, dotted and solid lines have the same definition as in Fig. 1. (b) The ratio $R(y_W)$ normalized as in (a) as a function of the $W$-boson rapidity. The dotted and solid lines are defined as in Fig. 1.