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Register a new userOperator product expansion on the lattice: analytic Wilson coefficients
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We present first results for Wilson coefficients of operators up to first order in the covariant derivatives for the case of Wilson fermions. They are derived from the off-shell Compton scattering amplitude $mathcal{W}_{mu u}(a,p,q)$ of massless quarks with momentum $p$. The Wilson coefficients are classified according to the transformation of the corresponding operators under the hypercubic group H(4). We give selected examples for a special choice of the momentum transfer $q$. All Wilson coefficients are given in closed analytic form and in an expansion in powers of $a$ up to first corrections.
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We investigate the Operator Product Expansion (OPE) on the lattice by directly measuring the product <Jmu Jnu> (where J is the vector current) and comparing it with the expectation values of bilinear operators. This will determine the Wilson coefficients in the OPE from lattice data, and so give an alternative to the conventional methods of renormalising lattice structure function calculations. It could also give us access to higher twist quantities such as the longitudinal structure function F_L = F_2 - 2 x F_1. We use overlap fermions because of their improved chiral properties, which reduces the number of possible operator mixing coefficients.
We have reported elsewhere in this conference on our continuing project to determine non-perturbative Wilson coefficients on the lattice, as a step towards a completely non-perturbative determination of the nucleon structure. In this talk we discuss how these Wilson coefficients can be used to extract Nachtmann moments of structure functions, using the case of off-shell Landau-gauge quarks as a first simple example. This work is done using overlap fermions, because their improved chiral properties reduce the difficulties due to operator mixing.
In this paper, we investigate operator product expansion for thermal correlation function of the two scalar currents. Due to breakdown of Lorentz invariance at finite temperature, more operators of the same dimension appear in the operator product expansion than at zero temperature. We calculated Wilson coefficients in the short distance expansion and obtain operator product expansion for thermal correlation function in terms of quark condensate, gluon condensate, quark energy density and gluon energy density.
Deep-inelastic scattering, in the laboratory and on the lattice, is most instructive for understanding how the nucleon is built from quarks and gluons. The long-term goal is to compute the associated structure functions from first principles. So far this has been limited to model calculations. In this Letter we propose a new method to compute the structure functions directly from the virtual, all-encompassing Compton amplitude, utilizing the operator product expansion. This overcomes issues of renormalization and operator mixing, which so far have hindered lattice calculations of power corrections and higher moments.
Nucleon structure functions can be observed in Deep Inelastic Scattering experiments, but it is an outstanding challenge to confront them with fully non-perturbative QCD results. For this purpose we investigate the product of electromagnetic currents (with large photon momenta) between quark states (of low momenta). By means of an Operator Product Expansion the structure function can be decomposed into matrix elements of local operators, and Wilson coefficients. For consistency both have to be computed non-perturbatively. Here we present precision results for a set of Wilson coefficients. They are evaluated from propagators for numerous quark momenta on the lattice, where the use of chiral fermions suppresses undesired operator mixing. This over-determines the Wilson coefficients, but reliable results can be extracted by means of a Singular Value Decomposition.
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