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 $\Lambda$, $⟨{\alpha }_s{G}^2⟩$ from independent sources. Agreement with experiment is found at the expected level $\sim 30\%$. Particularly interesting is a prediction for the hyperfine splitting, $M_{\mathrm{average}}(2^{3}P)-M(2^1{P}_1)=1.7\pm 0.9\mathrm{MeV}$, opposite in sign to the $c\bar{c}$ one ($\approx -0.9\mathrm{MeV}$), and where the nonzero value of $⟨{\alpha }_s{G}^2⟩$ plays a leading role.

Comments: 28 pages, preprint FTUAM 94-06