Massless Propagators, $R(s)$ and Multiloop QCD

Abstract

This is a short review of recent developments in calculation of higher order corrections to various two-point correlators and related quantities in (massless) QCD.

Material presented at the final Workshop of Sonderforschungsbereich Transregio 9 "Advances in Computational Physics" of Deutsche Forschungsgemeinschaft (DFG), 15-19 Sep 2014, Durbach, Germany, to appear in the proceedings, 16 pages, 5 figures, 1 table

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• Five-loop quark mass and field anomalous dimensions for a general gauge group
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• Complete renormalization of QCD at five loops
• Five-loop contributions to low-N non-singlet anomalous dimensions in QCD
• Six loop analytical calculation of the field anomalous dimension and the critical exponent $\eta$ in $O(n)$-symmetric ${\phi }^4$ model
• The Complete $O({\alpha }_s^2)$ Non-Singlet Heavy Flavor Corrections to the Structure Functions $g_{1,2}^{ep}(x,Q^2)$, $F_{1,2,L}^{ep}(x,Q^2)$, $F_{1,2,3}^{\nu (\bar{\nu })}(x,Q^2)$ and the Associated Sum Rules
• Decoupling of heavy quarks at four loops and effective Higgs-fermion coupling
• Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of $SU(N_c)$ conformal anomaly and studies of the conformal symmetry limit
• First Forcer results on deep-inelastic scattering and related quantities
• Generalized threshold resummation in inclusive DIS and semi-inclusive electron-positron annihilation
• Forcer: a FORM program for 4-loop massless propagators
• Gottfried sum rule in QCD NS analysis of DIS fixed target data