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Register a new userA novel approach to nonperturbative renormalization of singlet and nonsinglet lattice operators
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A novel method for nonperturbative renormalization of lattice operators is introduced, which lends itself to the calculation of renormalization factors for nonsinglet as well as singlet operators. The method is based on the Feynman-Hellmann relation, and involves computing two-point correlators in the presence of generalized background fields arising from introducing additional operators into the action. As a first application, and test of the method, we compute the renormalization factors of the axial vector current $A_mu$ and the scalar density $S$ for both nonsinglet and singlet operators for $N_f=3$ flavors of SLiNC fermions. For nonsinglet operators, where a meaningful comparison is possible, perfect agreement with recent calculations using standard three-point function techniques is found.
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In this paper we present the perturbative computation of the difference between the renormalization factors of flavor singlet ($sum_fbarpsi_fGammapsi_f$, $f$: flavor index) and nonsinglet ($barpsi_{f_1} Gamma psi_{f_2}, f_1 eq f_2$) bilinear quark operators (where $Gamma = mathbb{1},,gamma_5,,gamma_{mu},,gamma_5,gamma_{mu},, gamma_5,sigma_{mu, u}$) 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.
Quark bilinear operators with staple-shaped Wilson lines are used to study transverse-momentum-dependent parton distribution functions (TMDPDFs) from lattice quantum chromodynamics (QCD). Here, the renormalization factors for the isovector operators, including all mixings between operators with different Dirac structures, are computed nonperturbatively in the regularization-independent momentum subtraction scheme for the first time. This study is undertaken in quenched QCD with three different lattice spacings. With Wilson flow applied to the gauge fields in the calculations, the operator mixing pattern due to chiral symmetry breaking with the lattice regularization is found to be significantly different from that predicted by one-loop lattice perturbation theory calculations. These results constitute a critical step towards the systematic extraction of TMDPDFs from lattice QCD.
We have technically improved the non-perturbative renormalization method, proposed by Martinelli et al., by using quark momentum sources and sinks. Composite two-fermion operators up to three derivatives have been measured for Wilson fermions and Sheikholeslami-Wohlert improved fermions in the quenched approximation. The calculations are performed in the Landau gauge on 16^3x32 lattices at beta = 6.0 for 3 kappa values in each case. The improved sources greatly decrease the statistical noise. We extract and discuss here renormalization factors for local operators and moments of the structure functions for Wilson fermions.
We discuss a specific cut-off effect which appears in applying the non-perturbative RI/MOM scheme to compute the renormalization constants. To illustrate the problem a Dirac operator satisfying the Ginsparg-Wilson relation is used, but the arguments are more general. We propose a simple modification of the method which gets rid of the corresponding discretization error. Applying this to full-QCD simulations done at a=0.13 fm with the Fixed Point action we find that the renormalization constants are strongly distorted by the artefacts discussed. We consider also the role of global gauge transformations, a freedom which still remains after the conventional gauge fixing procedure is applied.
We extend the position-space renormalization procedure, where renormalization factors are calculated from Greens functions in position space, by introducing a technique to take the average of Greens functions over spheres. In addition to reducing discretization errors, this technique enables the resulting position-space correlators to be evaluated at any physical distance, making them continuous functions similar to the $O(4)$-symmetric position-space Greens functions in the continuum theory but with a residual dependence on a regularization parameter, the lattice spacing $a$. We can then take the continuum limit of these renormalized quantities calculated at the same physical renormalization scale $|x|$ and investigate the resulting $|x|$-dependence to identify the appropriate renormalization window. As a numerical test of the spherical averaging technique, we determine the renormalized light and strange quark masses by renormalizing the scalar current. We see a substantial reduction of discretization effects on the scalar current correlator and an enhancement of the renormalization window. The numerical simulation is carried out with $2+1$-flavor domain-wall fermions at three lattice cutoffs in the range 1.79--3.15~GeV.
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