Renormalon subtraction in OPE by dual space approach: nonlinear sigma model and QCD

It is becoming more important to subtract renormalons efficiently from perturbative calculations, in order to achieve high precision QCD calculations. We propose a new framework Dual Space Approach for renormalon separation, which enables subtraction of multiple renormalons simultaneously. Using a dual transform which suppresses infrared renormalons, we derive a one-parameter integral representation of a general observable. We investigate systematically how renormalons emerge and get canceled in the entire operator product expansion (OPE) of an observable, by applying the expansion-by-regions (EBR) method to this one-parameter integral expression. In particular we investigate in detail OPEs in a solvable model, the 2-dimensional O(N) nonlinear sigma model, by the dual space approach. A nontrivial mechanism of renormalon cancellation in this model can be understood from an integration identity on which the EBR method is founded. We demonstrate that the dual space approach can be useful by a simulation study imitating the QCD case. Application of this method to QCD calculations is also discussed.

Automated summary

Efficiently subtracting renormalons from perturbative calculations is increasingly important for achieving high precision QCD calculations. We propose a new framework, called the Dual Space Approach, for renormalon separation, which allows for simultaneous subtraction of multiple renormalons. By using a dual transform that suppresses infrared renormalons, we derive a one-parameter integral representation for a general observable. By applying the expansion-by-regions (EBR) method to this integral representation, we systematically investigate how renormalons emerge and cancel in the entire operator product expansion (OPE) of an observable. We also demonstrate the usefulness of the dual space approach through a simulation study emulating the QCD case, and discuss its potential application to QCD calculations.