${\overline{\rm MS}}$ renormalization of $S$-wave quarkonium wavefunctions at the origin

TL;DR

This paper calculates S-wave quarkonium wavefunctions at the origin within the ar scheme, incorporating nonperturbative effects and providing improved, model-independent predictions for decay constants and electromagnetic decay rates that align better with experimental data.

Contribution

It introduces a method to compute ar-renormalized wavefunctions at the origin including nonperturbative effects, improving the accuracy of decay predictions for quarkonia.

Findings

Wavefunctions at the origin are ar-renormalized with correct scale dependence.

Predictions for decay constants and decay rates agree better with experiments.

Including wavefunction corrections improves perturbative QCD convergence.

Abstract

We compute $S$-wave quarkonium wavefunctions at the origin in the $\overline{\rm MS}$ scheme based on nonrelativistic effective field theories. We include the effects of nonperturbative long-distance behaviors of the potentials, while we determine the short-distance behaviors of the potentials in perturbative QCD. We obtain $\overline{\rm MS}$-renormalized quarkonium wavefunctions at the origin that have the correct scale dependences that are expected from perturbative QCD, so that the scale dependences cancel in physical quantities. Based on the calculation of the wavefunctions at the origin, we make model-independent predictions of decay constants and electromagnetic decay rates of $S$-wave charmonia and bottomonia, and compare them with measurements. We find that the poor convergence of perturbative QCD corrections are substantially improved when we include corrections to the wavefunctions at the origin in the calculation of decay constants and decay rates.