Influence of relativistic and nonperturbative effects on the charmonium spin structure

It has been shown that relativistic corrections to the matrix elements that determine the spin structure of charmonium 1P states are between 20 and 40 %. Therefore, the coupling constant alpha(s)(mu = m(c)) (in the MS renormal ization scheme) as extracted from a comparison of experimental and theoreti cal results proves to be less in the relativistic case than in the case of a nonrelativistic treatment [alpha(s)(m(c)) similar or equal to 0.32 +/- 0. 01 versus alpha(s)(m(c)) similar or equal to 0.36]. The values of m, sigma, and alpha(s)(m(c)) at which the fine-structure parameters agree with their experimental values to a precision higher than 10% have been determined, i dentical values of alpha(s)(m(c)) being used for L . S, tensor, and S S int eractions. It has been shown that the spin-spin shift of the P-1(1) level w ith respect to M-cog(P-3(J)) involves both a perturbative and a nonperturba tive contribution (Delta(SS)(P) similar or equal to -1.35 +/- 0.10 MeV and Delta(SS)(NP) similar or equal to 1.0 MeV, respectively), the latter being dependent on the magnitude of the gluon condensate and the vacuum correlati on length.