Four-Loop Tadpoles: Applications in QCD

Abstract

Recent applications of single-scale four-loop tadpoles are briefly reviewed. An algorithm for the evaluation of current correlators based on differential equations is described and applied to obtain high moments of the vacuum polarization function at O(alphas^2) as a preparation of O(alphas^3) calculations.

5 pages, 1 figure, to appear in the proceedings of the 8th DESY Workshop on Elementary Particle Theory, Loops and Legs in Quantum Field Theory, April 23-28, 2006, Eisenach, Germany

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• The bottom-quark mass from non-relativistic sum rules at NNNLO
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• The Heavy Fermion Contributions to the Massive Three Loop Form Factors
• Precise Charm- and Bottom-Quark Masses: Theoretical and Experimental Uncertainties
• The MSR Mass and the $\mathcal{O}({\Lambda }_{\mathrm{QCD}})$ Renormalon Sum Rule
• QCD sum rule determination of the charm-quark mass
• Bottom-quark mass from finite energy QCD sum rules
• Resummation of Threshold, Low- and High-Energy Expansions for Heavy-Quark Correlators
• Analytic Reconstruction of heavy-quark two-point functions at O(α_s^3)
• The charm quark mass from non-relativistic sum rules
• Life of Π
• Charm-quark mass from weighted finite energy QCD sum rules
• Low- and High-Energy Expansion of Heavy-Quark Correlators at Next-To-Next-To-Leading Order
• Precise determination of ${\alpha }_s$ from relativistic quarkonium sum rules
• Small-momentum expansion of heavy-quark correlators in the large-${\beta }_0$ limit and ${\alpha }_s$ extractions
• Combined fixed-order and effective-theory approach to $b\bar{b}$ sum rules
• Renormalization Group Improvement and QCD Sum Rules