  The big mass difference between the pion and rho meson possibly originates
from the spin-dependent nature of the interactions in the two states since
these two states are similar except for spin. Both pi and rho are
quark-antiquark systems which can be treated using the two-body Dirac equations
(TBDE) of constraint dynamics. This relativistic approach for two-body system
has the advantage over the non-relativistic treatment in the sense that the
spin-dependent nature is automatically coming out from the formalism. We
employed Dirac's relativistic constraint dynamics to describe quark-antiquark
systems. 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 a Schroedinger-type equation with various terms calculated
from the basic radial potential. We used a modified Richardson potential for
quark-antiquark systems which satisfies the conditions of confinement and
asymptotic freedom. We obtained the wave functions for these two mesons which
are not singular at short distances. We also found that the cancellation
between the Darwin and spin-spin interaction terms occurs in the pi mass but
not in the rho mass and this is the main source of the big difference in the
two meson masses.
