The Spin-Spin Dynamics of Glueballs

The masses of pure gauge glueballs are calculated with the use of relativistic string Hamiltonian without fitting parameters. The string tension $\sigma_f=0.184$~GeV$^2$ in fundamental representation is fixed, using the Necco-Sommer lattice data, and to calculate the vector coupling $\alpha_{\rm V}(r)$ the value of $\Lambda_{\overline{MS}}^0=238$~MeV ($N_f=0$) is taken. The spin-spin potential, defined via the vacuum correlation function, is shown to produce a screening effect and decrease a hyperfine splittings between tensor and scalar glueballs. The masses of first and second $0^{++}$, $2^{++}$ excitations are predicted. For the ground states the masses $M(0^{++})=1508$~MeV, $M(2^{++})=2292$~MeV (in case A), in agreement with those of $f_0(1500),~f_2(2300)$ are obtained, and the first excitation mass $M(0^{++})=2613$~MeV is predicted. In case B $M(0^{++})=1.669$~MeV, $M(2^{++})=2212$~MeV are obtained.