Singlet vs Nonsinglet Perturbative Renormalization factors of Staggered Fermion Bilinears

In this paper we present the perturbative computation of the difference between the renormalization factors of flavor singlet ($\sum_f\bar\psi_f\Gamma\psi_f$, $f$: flavor index) and nonsinglet ($\bar\psi_{f_1} \Gamma \psi_{f_2}, f_1 \neq f_2$) bilinear quark operators (where $\Gamma = \mathbb{1},\,\gamma_5,\,\gamma_{\mu},\,\gamma_5\,\gamma_{\mu},\, \gamma_5\,\sigma_{\mu\,\nu}$) on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, using Symanzik improved gluons and staggered fermions with twice stout-smeared links. The stout smearing procedure is also applied to the definition of bilinear operators. A significant part of this work is the development of a method for treating some new peculiar divergent integrals stemming from the staggered formalism. Our results can be combined with precise simulation results for the renormalization factors of the nonsinglet operators, in order to obtain an estimate of the renormalization factors for the singlet operators. The results have been published in Physical Review D.Comment: 8 pages, 3 figures, 2 tables, Proceedings of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

Analytic regularity for a singularly perturbed fourth order reaction-diffusion boundary value problem

We consider a fourth order, reaction-diffusion type, singularly perturbed boundary value problem, and the regularity of its solution. Specifically, we provide estimates for arbitrary order derivatves, which are explicit in the singular perturbation parameter as well as the differentiation order. Such estimates are needed for the numerical analysis of high order methods, e.g.hp Finite Element Method (FEM).Comment: arXiv admin note: text overlap with arXiv:1901.0939