Mesonic and nucleon fluctuation effects at finite baryon density

Abstract: Mesonic and nucleon fluctuation effects are investigated in medium. We couple the nucleon field to the $2+1$ flavor meson model and investigate the finite temperature and density behavior of the system, in particular, the axial anomaly function. Somewhat contrary to earlier expectations we find that it tends to strengthen at finite density. At lower temperatures nucleon density fluctuations can cause a relative difference in the $U_A(1)$ axial anomaly of about $20\%$. This has important consequences on the mesonic spectra, especially on the $\eta-\eta'$ system, as we observe no drop in the $\eta'$ mass as a function of the baryochemical potential, irrespective of the temperature. Based on the details of chiral symmetry restoration, it is argued that there has to be a competition between underlying QCD effects of the anomaly and fluctuations of the low energy hadronic degrees of freedom, and the fate of the $U_A(1)$ coefficient should be decided by taking into account both effects simultaneously.