Rigourous QCD Evaluation of Spectrum and Other Properties of Heavy Quarkonium Systems; II Bottomium with n=2, l=0,1

Abstract

We calculate the Lamb, fine and hyperfine shifts in $b\bar b$ with $n=2$, $l=0,1$. Radiative corrections as well as leading nonperturbative corrections (known to be due to the gluon condensate) are taken into account. The calculation is parameter-free, as we take $\Lambda$, ${\langle \alpha_s G^2 \rangle}$ from independent sources. Agreement with experiment is found at the expected level $\sim 30\%$. Particularly interesting is a prediction for the hyperfine splitting, $M_{\rm average}(2^3P)-M(2^1P_1) = 1.7 \pm 0.9\, {\rm MeV}$, opposite in sign to the $c\bar c$ one ($\approx -0.9\, {\rm MeV}$), and where the nonzero value of ${\langle \alpha_s G^2 \rangle}$ plays a leading role.