Ground State Mass Spectrum for Scalar Diquarks withBethe–Salpeter Equation

Abstract

In this article, we study the structures of thepseudoscalar mesonsπ, K and the scalar diquarks Ua, Da, Sa in theframework of the coupled rainbow Schwinger–Dyson equation and ladderBethe–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 thetimelike region are absent which implements confinement naturally.The Bethe–Salpeter wavefunctions of the pseudoscalarmesons π, K, and the scalar diquarks Ua, Da, Sahave the same type (Gaussian type) momentum dependence,center around zero momentum and extend to the energy scale aboutq2 = 1 GeV2, which happens to be the energy scale for the chiralsymmetry breaking, the strong interactions in the infrared regionresult in bound (or quasi-bound) states. The numerical results forthe masses and decay constants of the π and K mesons canreproduce the experimental values, and the ground state masses of thescalar diquarks Ua, Da, Sa are consistent with the existingtheoretical calculations. We suggest a new Lagrangian which mayexplain the uncertainty of the masses of the scalar diquarks.