The R-evolution of QCD matrix elements

TL;DR

This paper explores the R-evolution method in QCD to sum large logarithms, control renormalon ambiguities, and develop a new sum rule for testing these ambiguities using known perturbative data.

Contribution

It introduces a novel R-evolution approach that sums large logarithms and recovers the asymptotic form of singularities in QCD perturbation series.

Findings

R-evolution sums large logarithms across different R scales

A convergent sum rule for renormalon singularities is derived

The method provides a new test for renormalon ambiguities without large-beta_0 approximation

Abstract

Perturbation series in QCD are generally asymptotic and suffer from so-called infrared renormalon ambiguities. In the context of the standard operator product expansion in MS-bar these ambiguities are compensated by matrix elements of higher dimension operators, but the procedure can be difficult to control due to large numerical cancellations. Explicit subtractions for matrix elements and coefficients, depending on a subtraction scale R, can avoid this problem. The appropriate choice for R in the Wilson coefficients can widely vary for different processes. In this talk we discuss renormalization group evolution with the scale R, and show that it sums large logarithms in the difference of processes with widely different R's. We also show that the solution of the R-evolution equations can be used to recover the all order asymptotic form of the singularities in the Borel transform of the perturbative series. For the normalization of these singularities we obtain a quickly converging sum rule that only needs the known perturbative coefficients as an input. This sum rule can be used as a novel test for renormalon ambiguities without replying on the large-beta_0 approximation.