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Register a new userRenormalization of non-singlet quark operator matrix elements for off-forward hard scattering
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We calculate non-singlet quark operator matrix elements of deep-inelastic scattering in the chiral limit including operators with total derivatives. This extends previous calculations with zero-momentum transfer through the operator vertex which provides the well-known anomalous dimensions for the evolution of parton distributions, as well as calculations in off-forward kinematics utilizing conformal symmetry. Non-vanishing momentum-flow through the operator vertex leads to mixing with total derivative operators under renormalization. In the limit of a large number of quark flavors $n_f$ and for low moments in full QCD, we determine the anomalous dimension matrix to fifth order in the perturbative expansion in the strong coupling $alpha_s$ in the $overline{mbox{MS}}$-scheme. We exploit consistency relations for the anomalous dimension matrix which follow from the renormalization structure of the operators, combined with a direct calculation of the relevant diagrams up to fourth order.
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We calculate the unpolarized and polarized three--loop anomalous dimensions and splitting functions $P_{rm NS}^+, P_{rm NS}^-$ and $P_{rm NS}^{rm s}$ in QCD in the $overline{sf MS}$ scheme by using the traditional method of space--like off shell massless operator matrix elements. This is a gauge--dependent framework. For the first time we also calculate the three--loop anomalous dimensions $P_{rm NS}^{rm pm tr}$ for transversity directly. We compare our results to the literature.
If physics beyond the Standard Model enters well above the electroweak scale, its low-energy effects are described by Standard Model Effective Field Theory. Already at dimension six many operators involve the antisymmetric quark tensor $bar q sigma^{mu u} q$, whose matrix elements are difficult to constrain from experiment, Ward identities, or low-energy theorems, in contrast to the corresponding vector and axial-vector or even scalar and pseudoscalar currents. However, with normalizations determined from lattice QCD, analyticity and unitarity often allow one to predict the momentum dependence in a large kinematic range. Starting from recent results in the meson sector, we extend this method to the nucleon case and, in combination with pole dominance, provide a comprehensive assessment of the current status of the nucleon form factors of the quark tensor.
The heavy quark effects in deep--inelastic scattering in the asymptotic regime $Q^2 gg m^2$ can be described by heavy flavor operator matrix elements. Complete analytic expressions for these objects are currently known to ${sf NLO}$. We present first results for fixed moments at ${sf NNLO}$. This involves a recalculation of fixed moments of the corresponding ${sf NNLO}$ anomalous dimensions, which we thereby confirm.
Recent developments in lattice QCD calculation of flavor singlet nucleon matrix elements are reviewed. Substantial sea quark contributions are found in the $pi$-$N sigma$ term and the quark spin content of the nucleon such that the total magnitude including valence contributions is in reasonable agreement with experiments. Some problems with flavor non-singlet nucleon matrix elements are pointed out. Recent work on lattice QCD calculation of hadron scattering length is also discussed.
We construct the two loop Greens functions for a quark bilinear operator inserted at non-zero momentum in a quark 2-point function for the most general off-shell configuration. In particular we consider the quark mass operator, vector and tensor currents as well as the second moment of the flavour non-singlet Wilson operator.
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