$M({\eta }_b)$ and ${\alpha }_s$ from Nonrelativistic Renormalization Group

Abstract

We sum up the next-to-leading logarithmic corrections to the heavy-quarkonium hyperfine splitting using the nonrelativistic renormalization group. On the basis of this result, we predict the mass of the ${\eta }_b$ meson to be $M({\eta }_b)=9419\pm 11(\mathrm{th}){}_{-8}^{+9}(\delta {\alpha }_s)MeV$. The experimental measurement of $M({\eta }_b)$ with a few MeV error would be sufficient to determine ${\alpha }_s(M_Z)$ with an accuracy of $\pm 0.003$. The use of the nonrelativistic renormalization group is mandatory to reproduce the experimental value of the hyperfine splitting in charmonium.

Eq. (1) corrected, numerical results slightly changed

References in corpus (4)

• Ultrasoft Renormalization in Non-Relativistic QCD
• Fine and Hyperfine Splittings of Charmonium and Bottomonium: An Improved Perturbative QCD Approach
• Heavy-quarkonium creation and annihilation with O(alpha_s^3 ln(alpha_s)) accuracy
• Quenched charmonium spectrum

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