Role of U(1) axial anomaly in two-color dense QCD

The anomaly of U(1) axial symmetry is an important element of the quantum chromodynamics (QCD), which affects the hadron mass spectrum and the chiral phase transition in QCD matter. However, its role in the baryonic QCD matter is not well understood compared to hot medium. In this talk, I will discuss the role of the U(1) axial anomaly by exploring the topological susceptibility at finite quark chemical potential and zero temperature in two-color QCD with two flavors. By using the Ward-Takahashi identities of QCD, we find that the topological susceptibility in hadronic phase is described by only three observables: the pion decay constant, the pion mass, and the eta meson mass in the low-energy regime of two-color QCD. Based on the identities, we numerically evaluate the topological susceptibility at finite quark chemical potential using the linear sigma model which undergoes the baryon superfluid phase transition. Our findings indicate that the nonzero topological susceptibility is induced by the presence of the U(1) axial anomalous interaction, reflecting the mass difference between the pion and eta meson. Moving on to the superfluid phase, it turns to decrease smoothly. The asymptotic behavior of the decrement is fitted by the continuous reduction of the chiral condensate in dense two-color QCD. In addition, effects from the finite diquark source on the topological susceptibility will be also discussed.