Duality between QCD Perturbative Series and Power Corrections

TL;DR

This paper explores the duality between perturbative series and power corrections in QCD, suggesting that long perturbative series can be dual to quadratic and possibly quartic power corrections, impacting theoretical understanding and phenomenology.

Contribution

It proposes that quadratic and possibly quartic power corrections are dual to perturbative series in QCD, challenging existing dogma and supported by phenomenological data.

Findings

Quadratic corrections are dual to long perturbative series.

Quartic corrections might also be dual to perturbative series.

No contradiction with phenomenology; improved agreement with data.

Abstract

We elaborate on the relation between perturbative and power-like corrections to short-distance sensitive QCD observables. We confront theoretical expectations with explicit perturbative calculations existing in literature. As is expected, the quadratic correction is dual to a long perturbative series and one should use one of them but not both. However, this might be true only for very long perturbative series, with number of terms needed in most cases exceeding the number of terms available. What has not been foreseen, the quartic corrections might also be dual to the perturbative series. If confirmed, this would imply a crucial modification of the dogma. We confront this quadratic correction against existing phenomenology (QCD (spectral) sum rules scales, determinations of light quark masses and of \alpha_s from \tau-decay). We find no contradiction and (to some extent) better agreement with the data and with recent lattice calculations.