Heavy Quarkonium Physics beyond the Next-to-Next-to-Leading Order of NRQCD

The theoretical study of the nonrelativistic heavy quark-antiquark system [1] and its application to bottomonium [2] and toponium [3] physics is of special interest because it relies entirely on the first principles of QCD. The system in principle allows for a perturbative treatment with the nonperturbative effects being well under control and with no crucial model dependence. This makes the heavy quarkonium to be an ideal place to determine the fundamental QCD parameters such as the heavy quark mass mq and the strong coupling constant αs. Recently an essential progress has been made in the theoretical investigation of the nonrelativistic heavy quark dynamics based on the effective theory approach [4]. The analytical results for the main parameters of the nonrelativistic heavy quarkantiquark system are now available up to nextto-next-to-leading order (NNLO) in the strong coupling constant and the heavy quark velocity β [5–21]. The NNLO corrections have turned out to be so sizeable that it appears to be indispensable also to gain control over the next-to-nextto-next-to-leading order (NLO) both in regard of phenomenological applications and in order to understand the structure and the peculiarities of the nonrelativistic expansion. In this talk we review the first steps in this direction and consider