Singlet vs Nonsinglet Perturbative Renormalization factors of Staggered Fermion Bilinears

Abstract

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 (${\bar{\psi }}_{f_1}\Gamma {\psi }_{f_2},f_1\ne f_2$) bilinear quark operators (where $\Gamma =1,{\gamma }_5,{\gamma }_{\mu },{\gamma }_5{\gamma }_{\mu },{\gamma }_5{\sigma }_{\mu \nu }$) 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.

8 pages, 3 figures, 2 tables, Proceedings of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain

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• On the Feynman-Hellmann Theorem in Quantum Field Theory and the Calculation of Matrix Elements
• Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears
• A novel approach to nonperturbative renormalization of singlet and nonsinglet lattice operators
• Renormalization of Flavor Singlet and Nonsinglet Fermion Bilinear Operators
• Non-perturbative renormalization of flavor singlet quark bilinear operators in lattice QCD