Ground state mass spectrum for scalar diquarks with Bethe-Salpeter equation
In this article, we study the structures of the pseudoscalar mesons $π$, $K$ and the scalar diquarks $U^a$, $D^a$, $S^a$ in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential. The $u$, $d$, $s$ quarks have small current masses, and the renormalization is very large, the mass poles in the timelike region are absent which implements confinement naturally. The Bethe-Salpeter wavefunctions of the pseudoscalar mesons $π$, $K$ and the scalar diquarks $U^a$, $D^a$, $S^a$ have the same type (Gaussian type) momentum dependence, center around zero momentum and extend to the energy scale about $q^2=1GeV^2$ which happen to be the energy scale for the chiral symmetry breaking, the strong interactions in the infrared region result in bound (or quasi-bound) states. The numerical results for the masses and decay constants of the $π$, $K$ mesons can reproduce the experimental values, the ground state masses of the scalar diquarks $U^a$, $D^a$, $S^a$ are consistent with the existing theoretical calculations. We suggest a new Lagrangian which may explain the uncertainty of the masses of the scalar diquarks .