Heavy Quarkonium Spectrum at $\mathcal{O}({\alpha }_s^5{m}_q)$ and Bottom/Top Quark Mass Determination

Abstract

We present the next-to-next-to-next-to-leading $\mathcal{O}({\alpha }_s^5{m}_q)$ result for the ground state energy of a heavy quarkonium system. On the basis of this result we determine the bottom quark mass from ${\rm Y}(1S)$ resonance and provide an explicit formula relating the top quark mass to the resonance energy in $t\bar{t}$ threshold production.

Comments: 16 pages, result based on upsilon expansion revised, version to appear in Phys. Lett. B