Renormalization group improved pQCD prediction for ${\rm Y}(1S)$ leptonic decay

Abstract

The complete next-to-next-to-next-to-leading order short-distance and bound-state QCD corrections to ${\rm Y}(1S)$ leptonic decay rate $\Gamma ({\rm Y}(1S)\to {\ell }^{+}{\ell }^{-})$ 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 $\Gamma ({\rm Y}(1S)\to {\ell }^{+}{\ell }^{-})$ 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 ${\rm Y}(1S)$ leptonic decay, i.e. ${\Gamma }_{{\rm Y}(1S)\to e^{+}{e}^{-}}{|}_{\mathrm{PMC}}=1.270_{-0.187}^{+0.137}$ 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.

11 pages, 4 figures. Numerical results and discussions improved, references updated, to be published in JHEP

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