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$M(η_b)$ and $α_s$ from Nonrelativistic Renormalization Group

B. A. Kniehl·A. A. Penin·A. Pineda·V. A. Smirnov·M. Steinhauser
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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 $η_b$ meson to be $M(η_b)=9419 \pm 11 {(\rm th)} {}^{+9}_{-8} (δα_s) MeV$. The experimental measurement of $M(η_b)$ with a few MeV error would be sufficient to determine $α_s(M_Z)$ 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.

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B. A. Kniehl, A. A. Penin, A. Pineda, V. A. Smirnov, M. Steinhauser. 2009-10-15. $M(η_b)$ and $α_s$ from Nonrelativistic Renormalization Group. https://doi.org/10.1103/physrevlett.92.242001

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