Topological susceptibility at zero temperature and finite temperature in the Nambu–Jona-Lasinio model

Abstract

We consider the three flavor Nambu-Jona-Lasinio model with the 't Hooft interaction incorporating the U(1) A anomaly. In order to set the coupling strength of the 't Hooft term, we employ the topological susceptibility χ instead of the η ′ meson mass. The value for χ is taken from lattice simulations.We also calculate χ at finite temperature within the model. Comparing it with the lattice data, we extract information about the behavior of the U(1) A anomaly at finite temperature. We conclude that within the present framework, the effective restoration of the U(1) A symmetry does not necessarily take place even at high temperature where the chiral symmetry is restored.11.30. Rd, 12.39.Fe

Formation ofη′(958)-Mesic Nuclei and AxialUA(1)Anomaly at Fin

“…There is another theoretical work with a linear σ model [18]. Theoretical predictions by other authors also reported the similar consequences [19,20] and supported the possible change of the η ′ properties at finite density as well as at finite temperature.…”

“…We treat V 0 as a parameter and estimate its reasonable running range using the theoretical evaluation of the η ′ mass shift at ρ 0 as V 0 = 0 ∼ −150 MeV [15,19,20]. We estimate the imaginary strength W 0 from analysis of γp → η ′ p data [29].…”

UA(1)anomaly in hot and dense QCD and the critical surface

“…In the large N c (number of colors) limit, χ t is related to the η ′ mass through the Witten-Veneziano mass formula [11], 2N f χ t /f 2 π = m 2 η + m 2 η ′ − 2m 2 K , so it can be used to probe the U A (1) anomaly. The NJL model calculation [10] reproduced the lattice data [12] above the critical temperature up to 1.5 times the chiral phase transition temperature with temperature independent 't Hooft coupling constant. This implies that, at least in the NJL model, the effective U A (1) restoration does not necessarily take place near the chiral transition.…”

“…Note that in Ref. [10], the T independent g * D was found to be able to reproduce the T dependence of the topological susceptibility. Without knowing the functional form of g * D (µ), we plot the critical curves in the (µ, m = m ud = m s ) space with different constant g * D 's in Fig.…”

“…[10], where the topological susceptibility χ t , a correlator of topological charges, was considered. In the large N c (number of colors) limit, χ t is related to the η ′ mass through the Witten-Veneziano mass formula [11], 2N f χ t /f 2 π = m 2 η + m 2 η ′ − 2m 2 K , so it can be used to probe the U A (1) anomaly.…”