Power-like decreasing solutions of the linearized Boltzmann equation for neutron thermalization and hard sphere interactions
In the neutronic and hard sphere cases, for non discrete eigenvalues we consider eigenfunctions of the linearized Boltzmann equation decreasing like powers of the velocity. The possible existence of such solutions would imply that there is no minimal relaxation rate to equilibrium. Here we show that they must be rejected because they violate the physical requirement of conservation of mass or energy.
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.