Determination of Alpha_s(1 GeV) from the charmonium fine structure

TL;DR

This paper extracts the strong coupling constant at 1 GeV from charmonium spectrum analysis, accounting for relativistic effects, and finds a value supporting the freezing behavior of alpha_s at low energies.

Contribution

It provides a novel extraction of alpha_s at low energy using relativistic corrections in charmonium fine structure analysis.

Findings

Alpha_s(1 GeV) = 0.38 ± 0.03 (exp.) ± 0.04 (theor.)

Relativistic corrections increase spin matrix elements by up to 40%

Result supports the freezing of alpha_s at low energies.

Abstract

The strong coupling constant $\alpha_s(\mu)$ is extracted from the fits to charmonium spectrum and fine structure splittings. The relativistic kinematics is taken into account and relativistic corrections are shown to increase the matrix elements defining spin effects up to 40%. The value of $\alpha_s(\mu)$ at low-energy scale $\mu=1.0 \pm 0.2 GeV$ was found to be $\alpha_s(\mu) = 0.38 \pm 0.03 (exp.) + 0.04 (theor.)$ which is about 50% lower than standard perturbative two-loop approximation and is in good agreement with the freezing $\alpha_s$ behaviour.