Renormalization Group Summation at High Orders and Implications to the Determination of Some Standard Model Parameters

Abstract

In perturbation theory, predictions from theories like Quantum Chromodynamics (QCD) are obtained by evaluating Feynman diagrams to high orders. Such calculations for re sults for various processes are already available in the literature, and their theoretical predictions depend on various parameters. With the availability of a large amount of data from experiments, it is possible to extract these parameters by comparing theoretical predictions with data. However, due to the finite order terms available from theory, any parameter determination depends on the perturbative scheme used and the choice of the renormalization scale. Once a renormalization scheme is fixed, the variation of the renor malization scale in a certain range can lead to large uncertainties, and optimizing pertur bative series with respect to such free parameters is necessary. We have achieved such op timization using the renormalization group summed perturbation theory (RGSPT), and the resulting perturbative series is significantly less sensitive to the renormalization scale dependence. It is a renormalization group (RG) improved version of the fixed order per turbation theory (FOPT), where the running RG-logarithms are summed to all orders using the RG equation. Once these running logarithms are summed, various operations such as analytic continuation, contour integrals, and Borel-Laplace transform are found to have enhanced convergence and scale variation improvement compared to a FOPT analysis. These operations are important in the precision determination of pQCD param eters using methods such as QCD sum rules.