Abstract
We investigate the effect of strange quark degrees of freedom on the formation of inhomogeneous chiral condensates in a three-flavor Nambu--Jona-Lasinio model in mean-field approximation. A Ginzburg-Landau study complemented by a stability analysis allow us to determine in a general way the location of the critical and Lifshitz points, together with the phase boundary where the (partially) chirally restored phase becomes unstable against developing inhomogeneities, without resorting to specific assumptions on the shape of the chiral condensate. We discuss the resulting phase structure and study the influence of the bare strange-quark mass $m_s$ and the axial anomaly on the size and location of the inhomogeneous phase compared to the first-order transition associated with homogeneous matter. We find that, as a consequence of the axial anomaly, critical and Lifshitz point split. For realistic strange-quark masses the effect is however very small and becomes sizeable only for small values of $m_s$.
Highlights
Mapping the phase diagram of QCD at nonvanishing temperature T and quark chemical potential μ is one of the major goals in strong interaction physics [1,2]
A GinzburgLandau study complemented by a stability analysis allows us to determine in a general way the location of the critical and Lifshitz points, together with the phase boundary where the chirally restored phase becomes unstable against developing inhomogeneities, without resorting to specific assumptions on the shape of the chiral condensate
We investigated within the NJL model how the formation of inhomogeneous chiral condensates is affected by the inclusion of strange quarks, which are coupled to the light flavors via a KMT determinant interaction, mimicking the effects of the axial anomaly
Summary
Mapping the phase diagram of QCD at nonvanishing temperature T and quark chemical potential μ is one of the major goals in strong interaction physics [1,2]. LatticeQCD calculations revealed that chiral symmetry, which is spontaneously broken in vacuum, gets approximately restored at high temperature via a smooth crossover transition [3]. At low temperature but nonvanishing chemical potential, standard lattice Monte Carlo techniques are not applicable. In this regime, one has to rely on other approaches to QCD, like Dyson-Schwinger equations [4] or the Functional Renormalization Group (FRG) [5], or on effective models, like the Nambu–Jona-Lasinio (NJL) or the quark-meson model. Assuming spatially uniform chiral condensates, these approaches typically predict a first-order phase transition from the chirally broken to the (approximately) restored phase, ending at a critical end point [4,5,6,7]. We will refer to both the tricritical point and the critical end point as the “critical point” (CP) in the following
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