Massless correlators of vector, scalar and tensor currents in position space at orders alpha_s^3 and alpha_s^4: explicit analytical results

Abstract

We present analytical results both in momentum and position space for the massless correlators of the vector and scalar currents to order alpha_s^4 as well as for the tensor currents to order alpha_s^3. The evolution equations for the correlators together with all relevant anomalous dimensions are discussed in detail. As an application we present explicit conversion formulas relating the MSbar-renormalized vector, scalar and tensor currents to their counterparts renormalized in the X-space renormalization scheme more appropriate for lattice calculations.

29 pages, 2 figures

References in corpus (29)

• Instantons in QCD
• The four-loop beta-function in Quantum Chromodynamics
• New features of FORM
• A General Method for Non-Perturbative Renormalization of Lattice Operators
• The 4-loop quark mass anomalous dimension and the invariant quark mass
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• Hadronic Z- and tau-Decays in Order alpha_s^4
• Quark Mass Anomalous Dimension to alpha_s**4
• The Multithreaded version of FORM
• Scalar Correlator at O(alpha_s^4), Higgs Decay into b-quarks and Bounds on the Light Quark Masses
• Correlator of the quark scalar currents and Γ_{tot}(H --> hadrons) at O(α_s^3) in pQCD
• QCD Corrections to the $e^{+}{e}^{-}$ Cross Section and the $Z$ Boson Decay Rate
• Explicit solutions of the multi-loop integral recurrence relations and its application
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• Explicit solutions of the 3--loop vacuum integral recurrence relations
• Reconstruction of heavy quark current correlators at O(α_s^3)
• Hints on the power corrections from current correlators in x-space
• Operator product expansion and quark condensate from Lattice QCD in coordinate space
• A practical criterion of irreducibility of multi--loop Feynman integrals
• Correlation Functions of Hadron Currents in the QCD Vacuum Calculated in Lattice QCD
• Short distance current correlators: Comparing lattice simulations to the instanton liquid
• Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals
• Five-loop anomalous dimension at critical wrapping order in N=4 SYM
• Non-perturbative renormalization of lattice operators in coordinate space
• Implications of the ALEPH tau-Lepton Decay Data for Perturbative and Non-Perturbative QCD
• Vacuum Saturation Hypothesis and QCD Sum Rules
• Three loop MSbar operator correlation functions for deep inelastic scattering in the chiral limit
• ParFORM: recent development
• Explicit solutions of the n--loop vacuum integral recurrence relations

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