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

TL;DR

This paper develops a combined fixed-order and effective-theory method for calculating $b\bar{b}$ sum rules, achieving high precision and consistency with experimental data across a broad range of moments.

Contribution

It introduces a novel combined approach that incorporates higher-order corrections, improving the accuracy of $b\bar{b}$ sum rule calculations compared to previous methods.

Findings

Results show excellent agreement with experimental data.

The method is effective for moments with $1\le n\lesssim 16$.

Higher-order corrections enhance the precision of sum rule evaluations.

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 ${\cal O}(\alpha_s^3)$ and ${\cal O}((\alpha_s \sqrt{n})^l \alpha_s^2)$, 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 $1\le n\lesssim 16$.