Isovector proton-neutron pairing and Wigner energy in Hartree-Fock mean field calculations
We propose a new approach for the treatment of isovector pairing in self-consistent mean field calculations which conserves exactly the isospin and the particle number in the pairing channel. The mean field is generated by a Skyrme-HF functional while the isovector pairing correlations are described in terms of quartets formed by two neutrons and two protons coupled to the total isospin T=0. In this framework we analyse the contribution of isovector pairing to the symmetry and Wigner energies. It is shown that the isovector pairing provides a good description of the Wigner energy, which is not the case for the mean field calculations in which the isovector pairing is treated by BCS-like models.
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.