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

TL;DR

This paper explores how non-perturbative gluon effects influence the mass and properties of scalar diquarks using the Schwinger-Dyson formalism, revealing significant mass generation especially for small diquarks.

Contribution

It introduces a non-perturbative analysis of gluonic effects on scalar diquarks considering their size, using the Schwinger-Dyson approach with renormalization-group improved coupling.

Findings

Small diquarks gain large effective mass from gluonic dressing.

Scalar diquark mass is dynamically generated by non-perturbative effects.

Gluonic effects are significant despite the absence of chiral symmetry.

Abstract

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.