Novel analysis for the energy-energy correlation in electron-positron annihilation in the perturbative domain

TL;DR

This paper introduces a novel analysis method for the energy-energy correlation in electron-positron annihilation using the Principle of Maximum Conformality, improving theoretical predictions in QCD.

Contribution

It applies PMC to eliminate renormalization ambiguities and dynamically determine scales, enhancing agreement with experimental data in the perturbative domain.

Findings

PMC scales vary with the EEC angular distribution.

PMC predictions align well with experimental data.

Reabsorbing all β-terms alters the behavior of perturbative coefficients.

Abstract

The energy-energy correlation (EEC) in electron-positron annihilation plays a crucial role in precision tests of quantum chromodynamics (QCD) and measurements of the QCD coupling constant. In this paper, we provide a novel analysis for the EEC by using the Principle of Maximum Conformality (PMC), a systematic method for eliminating renormalization scheme-and-scale ambiguities. The PMC scales are determined by resumming the non-conformal $\beta$-terms that govern the behavior of the QCD running coupling via the renormalization group equation, and reflect the virtuality of the propagating gluons in QCD. It is noteworthy that the resulting PMC scale varies dynamically with the EEC's angular distribution, reflecting the expected scale's physical behavior. Moreover, due to the reabsorption of all $\beta$-terms, including also those related to the divergent renormalon terms such as $n!\beta^n_0\alpha^n_s$, in the pQCD series, the behavior of the QCD perturbative coefficient using PMC, differs entirely from that of the conventional coefficient. Consequently, the PMC predicted EEC distribution agrees well with the experimental data in the perturbative domain.