Singlet vs Nonsinglet Perturbative Renormalization factors of Fermion Bilinears
In this work we present the perturbative computation of the difference between the renormalization factors of flavor singlet and nonsinglet bilinear quark operators (scalar, pseudoscalar, vector, axial vector and tensor) on the lattice. Nonperturbative estimates of the renormalization factors for the singlet operators are notoriously difficult to obtain via numerical simulations, due to the presence of (fermion line) disconnected diagrams, which in principle require evaluation of the full fermion propagator. Then it is quite a challenge to obtain accurate results for the renormalization of the singlet operators directly. 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. 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. The corresponding calculation with Wilson/clover fermions had been previously performed by our group. The results have been published in Physical Review D (M. Constantinou, M. Hadjiantonis, H. Panagopoulos, G. Spanoudes, “Singlet versus Nonsinglet Perturbative Renormalization of Fermion Bilinears”, Phys. Rev. D94 (2016) 114513 [arXiv: 1610.06744]).
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Standard Model Parameters and Renormalization