Fate of the topological susceptibility in two-color dense QCD

Abstract

We explore the topological susceptibility at finite quark chemical potential and zero temperature in two-color QCD (QC2D) with two flavors. Through the Ward-Takahashi identities of QC2D, we find that the topological susceptibility in the vacuum solely depends on three observables: the pion decay constant, the pion mass, and the η mass in the low-energy regime of QC2D. Based on the identities, we numerically evaluate the topological susceptibility at finite quark chemical potential using the linear sigma model with the approximate Pauli-Gursey SU(4) symmetry. Our findings indicate that, in the absence of U(1)A anomaly effects represented by the Kobayashi-Maskawa-’t Hooft-type determinant interaction, the topological susceptibility vanishes in both the hadronic and baryon superfluid phases. On the other hand, when the U(1)A anomaly effects are present, the constant and nonzero topological susceptibility is induced in the hadronic phase, reflecting the mass difference between the pion and η meson. Meanwhile, in the superfluid phase it begins to decrease smoothly. The asymptotic behavior of the decrement is fitted by the continuous reduction of the chiral condensate in dense QC2D, which is similar to the behavior observed in hot three-color QCD matter. In addition, effects from the finite diquark source on the topological susceptibility are discussed. We expect that the present study provides a clue to shed light on the role of the U(1)A anomaly in cold and dense QCD matter.