Renormalization group improved pQCD prediction for Υ(1S) leptonic decay

Abstract

Abstract The complete next-to-next-to-next-to-leading order short-distance and bound-state QCD corrections to Υ(1S) leptonic decay rate Γ(Υ(1S) → ℓ+ℓ−) has been finished by Beneke et al. [8]. Based on those improvements, we present a renormalization group (RG) improved pQCD prediction for Γ(Υ(1S) → ℓ+ℓ−) 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 β-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 Υ(1S) leptonic decay, i.e. $$ \varGamma {\left.{}_{Y(1S)\to {\mathrm{e}}^{+}{\mathrm{e}}^{-}}\right|}_{\mathrm{PMC}}=1.27{0}_{-0.187}^{+0.137} $$ Γ Υ 1 S → e + e − P M C = 1.27 0 − 0.187 + 0.137 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.