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A non-perturbative effect of gluons for scalar diquark in the Schwinger-Dyson formalism

The diquark has been considered to be important effective degrees of freedom in hadron physics, especially for multi-quark physics and the structure of heavy hadronic states. Using the Schwinger-Dyson formalism, we investigate the non-perturbative effect of gluons for scalar diquarks with renormalization-group improved coupling in the Landau gauge. Here, we treat the scalar diquark as an effective degree of freedom with a peculiar size, while the diquark is originally a bound-state-like object of two quarks. Since the diquark has a non-zero color charge, it strongly interacts with gluons. We evaluate the gluonic non-perturbative effect to the diquark, considering the size effect of the diquark. We investigate the mass function of the diquark in both cases with a constant bare diquark mass and twice of the running quark self-energy. It is found that the diquark, especially the small diquark, obtains a large effective mass by the gluonic dressing effect. The scalar diquark mass seems to be dynamically generated by the non-perturbative effect, although it does not have the chiral symmetry.