Phenomenological impact of the resummation of logs of alpha in heavy quarkonium

Abstract

Here we would like to review recent progress on the resummation on logarithms of $\alpha_s$ in heavy quarkonium. We will mainly focus on the phenomenological relevance of these achievements. Determinations of the $\eta_b(1S)$ mass, $B_c(1S)$ hyperfine splitting, inclusive electromagnetic decays and implications for $t$-$\bar t$ production near threshold.