Two fermion relativistic bound states

We consider the relativistic quantum mechanics of a two interacting fermions system. We first present a covariant formulation of the kinematics of the problem and give a short outline of the classical results. We then quantize the system with a general interaction potential and deduce the explicit equations in a spherical basis. The case of the Coulomb interaction is studied in detail by numerical methods, solving the eigenvalue problem for J=0, J=1, J=2 and determining the spectral curves for a varying ratio of the mass of the interacting particles. Details of the computations, together with a perturbative approach in the mass ratio and an extended description of the ground states of the Para- and Orthopositronium are given in Appendix.Comment: 26 pages, 6 figure

Unified covariant treatment of hyperfine splitting for heavy and light mesons

This paper aims at proving the fundamental role of a relativistic formulation for quarkonia models. We present a completely covariant description of a two-quark system interacting by the Cornell potential with a Breit term describing the hyperfine splitting. Using an appropriate procedure to calculate the Breit correction, we find heavy meson masses in excellent agreement with experimental data. Moreover, also when applied to light quarks and even taking average values of the running coupling constant, we prove that covariance properties and hyperfine splitting are sufficient to explain the light mesons spectrum and to give a very good agreement with the data.Comment: 4 page

Relativistic two-body calculation of bbˉb\bar{b}-mesons radiative decays

This paper is a prosecution of a previous work where we presented a unified two-fermion covariant scheme which produced very precise results for the masses of light and heavy mesons. We extend the analysis to some radiative decays of mesons $\Upsilon,\,\chi_{b2}\,,h_b\,,\chi_{b1}\,,\chi_{b0}\,,\eta_b\,$ and we calculate their branching ratios and their widths. For most of them we can make a comparison with experimental data finding a good agreement.For the decays for which data are not available we compare ours with other recent theoretical previsions.Comment: 7 pages, 1 figur