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

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.