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Register a new userOne-loop renormalization of staple-shaped operators in continuum and lattice regularizations
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In this paper we present one-loop results for the renormalization of nonlocal quark bilinear operators, containing a staple-shaped Wilson line, in both continuum and lattice regularizations. The continuum calculations were performed in dimensional regularization, and the lattice calculations for the Wilson/clover fermion action and for a variety of Symanzik-improved gauge actions. We extract the strength of the one-loop linear and logarithmic divergences (including cusp divergences), which appear in such nonlocal operators; we identify the mixing pairs which occur among some of these operators on the lattice, and we calculate the corresponding mixing coefficients. We also provide the appropriate RI-like scheme, which disentangles this mixing nonperturbatively from lattice simulation data, as well as the one-loop expressions of the conversion factors, which turn the lattice data to the MS-bar scheme. Our results can be immediately used for improving recent nonperturbative investigations of transverse momentum-dependent distribution functions (TMDs) on the lattice. Finally, extending our perturbative study to general Wilson-line lattice operators with n cusps, we present results for their renormalization factors, including identification of mixing and determination of the corresponding mixing coefficients, based on our results for the staple operators.
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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 study 4-dimensional SQCD with gauge group SU(Nc) and Nf flavors of chiral supermultiplets on the lattice. We perform extensive calculations of matrix elements and renormalization factors of composite operators in Perturbation Theory. In particular, we compute the renormalization factors of quark and squark bilinears, as well as their mixing at the quantum level with gluino and gluon bilinear operators. From these results we construct correctly renormalized composite operators, which are free of mixing effects and may be employed in non-perturbative studies of Supersymmetry. All our calculations have been performed with massive matter fields, in order to regulate the infrared singularities which are inherent in renormalizing squark bilinears. Furthermore, the quark and squark propagators are computed in momentum space with nonzero masses. This work is a feasibility study for lattice computations relevant to a number of observables, such as spectra and distribution functions of hadrons, but in the context of supersymmetric QCD, as a forerunner to lattice investigations of SUSY extensions of the Standard Model.
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.
In this paper, we present one- and two-loop results for the renormalization of the gluon and quark gauge-invariant operators which appear in the definition of the QCD energy-momentum tensor, in dimensional regularization. To this end, we consider a variety of Greens functions with different incoming momenta. We identify the set of twist-2 symmetric traceless and flavor singlet operators which mix among themselves and we calculate the corresponding mixing coefficients for the nondiagonal components. We also provide results for some appropriate regularization-independent (RI)-like schemes, which address this mixing, and we discuss their application to nonperturbative studies via lattice simulations. Finally, we extract the one- and two-loop expressions of the conversion factors between the proposed RI and the MSbar schemes. From our results regarding the MSbar-renormalized Greens functions, one can easily derive conversion factors relating numerous variants of RI-like schemes to MSbar. To make our results easily accessible, we also provide them as Supplemental Material, in the form of a Mathematica input file and, also, an equivalent text file.
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