Combined fixed-order and effective-theory approach to $b\bar{b}$ sum rules

Abstract

We combine the fixed-order evaluation of the $b\bar{b}$ sum rules with a non-relativistic effective-theory approach. The combined result for the $n$-th moment includes all terms suppressed with respect to the leading-order result by $\mathcal{O}({\alpha }_s^3)$ and $\mathcal{O}(({\alpha }_s\sqrt{n}{)}^l{\alpha }_s^2)$, counting ${\alpha }_s\sqrt{n}\sim 1$. When compared to experimental data, the moments thus obtained show a remarkable consistency and allow for an analysis in the whole range $1\le n\lesssim 16$.

Comments: 16 pages, 7 figures,