Experimental consistency in parton distribution fitting

The recently developed "Data Set Diagonalization" method (DSD) is applied to measure compatibility of the data sets that are used to determine parton distribution functions (PDFs). Discrepancies among the experiments are found to be somewhat larger than is predicted by propagating the published experimental errors according to Gaussian statistics. The results support a tolerance criterion of $\Delta\chi^2 \approx 10$ to estimate the 90% confidence range for PDF uncertainties. No basis is found in the data sets for the much larger $\Delta\chi^2$ values that are in current use; though it will be necessary to retain those larger values until improved methods can be developed to take account of systematic errors in applying the theory. The DSD method also measures how much influence each experiment has on the global fit, and identifies experiments that show significant tension with respect to the others. The method is used to explore the contribution from muon scattering experiments, which are found to exhibit the largest discrepancies in the current fit.Comment: 30 pages; 7 figure

Data set diagonalization in a global fit

The analysis of data sometimes requires fitting many free parameters in a theory to a large number of data points. Questions naturally arise about the compatibility of specific subsets of the data, such as those from a particular experiment or those based on a particular technique, with the rest of the data. Questions also arise about which theory parameters are determined by specific subsets of the data. I present a method to answer both of these kinds of questions. The method is illustrated by applications to recent work on measuring parton distribution functions.Comment: Published versio

Improving the Measurement of the Top Quark Mass

Two possible ways to improve the mass resolution for observing hadronic top quark decay $t \to bW \to 3 jets$ are studied: (1) using fixed cones in the rest frames of the $t$ and $W$ to define the decay jets, instead of the traditional cones in the rest frame of the detector; and (2) using the jet angles in the top rest frame to measure $m_t/m_W$. By Monte Carlo simulation, the second method is found to give a useful improvement in the mass resolution. It can be combined with the usual invariant mass method to get an even better mass measurement. The improved resolution can be used to make a more accurate determination of the top quark mass, and to improve the discrimination between $t \bar t$ events and background for studies of the production mechanism.Comment: Revised and expanded. New and better method introduced. Some conclusions changed. 17 pages, RevTeX, 4 uuencoded figure

Parton Distributions

I present an overview of some current topics in the measurement of Parton Distribution Functions.Comment: 13 pages, 9 figures. Plenary talk presented at the XIII International Workshop on Deep Inelastic Scattering (DIS 2005), Madison WI USA, April 27--May 1, 200

PDF uncertainties: A strong test of goodness of fit to multiple data sets

We present a new criterion for the goodness of global fits. It involves an exploration of the variation of \chi^2 for subsets of data.Comment: 4 pages, 1 figure. To appear in Proceedings of 9th International Workshop on Deep Inelastic Scattering and QCD (DIS 2001), Bologna, Italy, 27 Apr-1 May 200

Parametrization dependence and Delta Chi-squared in parton distribution fitting

Parton distributions functions (PDFs), which are essential to the interpretation of data from high energy colliders, are measured by representing them as functional forms containing many parameters. Those parameters are determined by fitting a wide variety of experimental data. The best-fit PDF set is obtained by minimizing the standard $\chi^2$ measure of fit quality. The uncertainty range is estimated in the Hessian method by regarding as acceptable, all fits for which $\chi^2$ lies within $\Delta\chi^2$ of its minimum. The appropriate value of $\Delta\chi^2$ for this purpose has been estimated by a variety of arguments to be approximately 50 - 100 for a 90% confidence limit. This paper resolves the long-standing paradox of why that empirical value is so much larger than the $\Delta\chi^2=2.7$ for 90% confidence that would be expected on the basis of standard Gaussian statistics.Comment: 6 pages, 1 figure. Revised version as published in PRD: includes a new Chebyshev Polynomial method for PDF fittin