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

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

1-(4-Methyl­phenyl­diazo­nium­yl)-2-naphtholate

In the title compound, C17H14N2O, the dihedral angle between the benzene ring and naphthalene ring system is 11.0 (3)°. The azo group adopts an anti configuration and an intra­molecular N—H⋯O hydrogen bond exists. Mol­ecules are packed by π–π inter­actions between adjacent mol­ecule (closest approach between centroids of benzene and naphthalene rings of 3.501 Å)