Renormalization group improved pQCD prediction for $\Upsilon(1S)$ leptonic decay

TL;DR

This paper improves the theoretical prediction of the $
S$ leptonic decay rate using renormalization group techniques and the principle of maximum conformality, resulting in a more accurate, scheme-independent prediction that aligns with experimental data.

Contribution

It applies the principle of maximum conformality to RG-improved pQCD calculations, reducing scheme and scale ambiguities in predicting $
S$ leptonic decay rates.

Findings

The RG-improved prediction agrees with experimental measurements.

Application of PMC reduces renormalization scheme and scale uncertainties.

Achieves a more convergent and scheme-independent pQCD series.

Abstract

The complete next-to-next-to-next-to-leading order short-distance and bound-state QCD corrections to $\Upsilon(1S)$ leptonic decay rate $\Gamma(\Upsilon(1S)\to \ell^+\ell^-)$ has been finished by Beneke {\it et al.} \cite{Beneke:2014qea}. Based on those improvements, we present a renormalization group (RG) improved pQCD prediction for $\Gamma(\Upsilon(1S)\to \ell^+\ell^-)$ by applying the principle of maximum conformality (PMC). The PMC is based on RG-invariance and is designed to solve the pQCD renormalization scheme and scale ambiguities. After applying the PMC, all known-type of $\beta$-terms at all orders, which are controlled by the RG-equation, are resummed to determine optimal renormalization scale for its strong running coupling at each order. We then achieve a more convergent pQCD series, a scheme- independent and more accurate pQCD prediction for $\Upsilon(1S)$ leptonic decay, i.e. $\Gamma_{\Upsilon(1S) \to e^+ e^-}|_{\rm PMC} = 1.270^{+0.137}_{-0.187}$ keV, where the uncertainty is the squared average of the mentioned pQCD errors. This RG-improved pQCD prediction agrees with the experimental measurement within errors.