Non-empirical nuclear energy functionals, pairing gaps and odd-even mass differences

First, we briefly outline some aspects of the starting project to design non-empirical energy functionals based on low-momentum vacuum interactions and many-body perturbation theory. Second, we present results obtained within an approximation of such a scheme where the pairing part of the energy density functional is constructed at first order in the nuclear plus Coulomb two-body interaction. We discuss in detail the physics of the odd-even mass staggering and the necessity to compute actual odd-even mass differences to analyze it meaningfully.