Study on the Mass Difference between pi and rho using a relativistic two-body model

초록

The mass of pion is relatively small compared to that of rho-meson when the case is compared to the mass differences between other meson pairs such as ηC and J/ψ or D_0 and D*_0. These two states are similar except for spin and therefore we can simply conjecture that this big difference between π- and ρ- masses is originated by the spin-dependent nature of two mesons. π and ρ are both two-quark systems which can be treated using the two-body Dirac equation (TBDE). This relativistic approach for two-body system has an advantage over the non-relativistic treatment in a sense that the spin-dependent nature is automatically coming out from the formalism. We employed Dirac’s relativistic constraint dynamics to describe two-quark system. Within this formalism, the 16-component Dirac equation is reduced to the 4-component 2nd-order differential equation and the radial part of this equation is simply Schrodinger-type equation with various terms calculated from the effective radial potential. The interaction terms in the equation are spin-orbit, spin-spin, tensor and a lot more spin-dependent terms as well as usual relativistic correction terms and Darwin terms.