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 $$\alpha_{V}(r)$$ 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 (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.