Some further considerations in particle‐size broadening
The diffraction profile and its moments are obtained for particle-size broadening, the expressions being `exact' in the kinematic approximation for crystals of simple shapes (parallelepiped, tetrahedron, octahedron, sphere). A further term in the variance-range curve is obtained, depending on Mitra's parameter 34, for which the name `rotundity parameter' is proposed. The effect of a distribution of particle sizes is discussed; the Scherrer constant and the taper parameter are affected in a way already known, and M is unaffected.
We describe preliminary results from an effort to quantify the uncertainties in parton distribution functions and the resulting uncertainties in predicted physical quantities. The production cross section of the $W$ boson is given as a first example. Constraints due to the full data sets of the CTEQ global analysis are used in this study. Two complementary approaches, based on the Hessian and the Lagrange multiplier method respectively, are outlined. We discuss issues on obtaining meaningful uncertainty estimates that include the effect of correlated experimental systematic uncertainties and illustrate them with detailed calculations using one set of precision DIS data.