Relevant gluonic energy scale of spontaneous chiral symmetry breaking from lattice QCD

TL;DR

This study investigates which gluon momentum components are crucial for spontaneous chiral symmetry breaking in lattice QCD, highlighting the significant role of zero-momentum and infrared gluons in generating the chiral condensate.

Contribution

It identifies the specific gluon energy scales that induce chiral symmetry breaking, emphasizing the importance of zero and infrared momentum components.

Findings

Removing zero-momentum gluons reduces the chiral condensate by about 40%.

Infrared nonzero-momentum gluons also significantly contribute to chiral symmetry breaking.

The results reveal a strong link between infrared gluons and zero-mode quarks.

Abstract

We analyze which momentum component of the gluon field induces spontaneous chiral symmetry breaking in lattice QCD. After removing the high-momentum or low-momentum component of the gluon field, we calculate the chiral condensate and observe the roles of these momentum components. The chiral condensate is found to be drastically reduced by removing the zero-momentum gluon. The reduction is about 40% of the total in our calculation condition. The nonzero-momentum infrared gluon also has a sizable contribution to the chiral condensate. From the Banks-Casher relation, this result reflects the nontrivial relation between the infrared gluon and the zero-mode quark.