Abstract
In this paper we present the perturbative computation of the difference between the renormalization factors of flavor singlet ([see formula in PDF], f : flavor index) and nonsinglet ([see formula in PDF]) bilinear quark operators (where Γ = 𝟙, γ5, γ µ, γ5 γ µ, γ5 σµv 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 [1].
Highlights
Renormalization of flavor singlet operators is essential for the study of a number of hadronic properties, including topological features and the spin structure of hadrons; for example, the knowledge of the axial singlet renormalization factor is required to compute the light quarks’ contribution to the spin of the nucleon [2]
In recent years there has been some progress in the numerical study of flavor singlet operators; for some of them, a nonperturbative estimate of their renormalization has been obtained using the Feynman-Hellmann relation, for both improved Wilson and staggered fermion actions [3,4,5]
Given that the renormalization factors of the nonsinglet operators can be calculated nonperturbatively with quite good precision, we can give an estimate of the renormalization factors for the singlet operators through the perturbative evaluation of the difference between singlet and nonsinglet cases; this difference first shows up at two loops
Summary
Renormalization of flavor singlet operators is essential for the study of a number of hadronic properties, including topological features and the spin structure of hadrons; for example, the knowledge of the axial singlet renormalization factor is required to compute the light quarks’ contribution to the spin of the nucleon [2]. Matrix elements of such operators are notoriously difficult to study via numerical simulations, due to the presence of fermion-line-disconnected diagrams, which in principle require evaluation of the full fermion propagator. Application of stout improvement on staggered fermions far has been explored, by our group, only to one-loop computations [10]; a two-loop computation had never been investigated before
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