Abstract
Our understanding of the dynamics and the phase structure of dense strong-interaction matter is to a large extent still built on the analysis of low-energy models, such as those of the Nambu-Jona-Lasinio-type. In this work, we analyze the emergence of the latter class of models at intermediate and low energy scales from fundamental quark-gluon interactions. To this end, we study the renormalization group flow of a Fierz-complete set of four-quark interactions and monitor their strength at finite temperature and quark chemical potential. At small quark chemical potential, we find that the scalar-pseudoscalar interaction channel is dynamically rendered most dominant by the gauge degrees of freedom, indicating the formation of a chiral condensate. Moreover, the inclusion of quark-gluon interactions leaves a significant imprint on the dynamics as measured by the curvature of the finite-temperature phase boundary which we find to be in accordance with lattice QCD results. At large quark chemical potential, we then observe that the dominance pattern of the four-quark couplings is changed by the underlying quark-gluon dynamics, without any fine-tuning of the four-quark couplings. In this regime, the scalar-pseudoscalar interaction channel becomes subleading and the dominance pattern suggests the formation of a chirally symmetric diquark condensate. In particular, our study confirms the importance of explicit $U_{\mathrm{A}}(1)$ breaking for the formation of this type of condensate at high densities.
Highlights
Low-energy models of the theory of the strong interaction are still considered very valuable for a variety of reasons
In the high-density regime, which is at least difficult to access with lattice Monte Carlo techniques, the Nambu–JonaLasinio (NJL) model [1,2] and its various variations and relatives, such as quarkmeson (QM) models, allow us to gain some insight into the plethora of symmetry-breaking patterns that may potentially be realized in this regime; see Refs. [9,10,11,12] for reviews
Working in the chiral limit, the only parameter of our study in the UAð1Þ-symmetric limit is given by the strong coupling gs which we fixed at a large initial UV scale in the perturbative regime. With this setting at hand, we found that the inclusion of gluodynamics leads to an increase of the critical temperatures at large quark chemical potential in comparison to the results from a corresponding Fierz-complete NJL model study
Summary
Low-energy models of the theory of the strong interaction (quantum chromodynamics, QCD) are still considered very valuable for a variety of reasons. In full QCD, the values of the four-quark couplings are no longer fundamental parameters since these self-interactions are fluctuation induced by the dynamics of the gauge fields Taking this aspect into account, the aforementioned issue associated with the determination of model parameters—such as ambiguities related to the possibility to Fierz transform given initial conditions and the potential existence of more than one parameter set reproducing well a given set of low-energy observables, or the dependence of the initial conditions on external control parameters—can, in principle, be resolved. Including gauge dynamics and resolving the fundamental microscopic d.o.f. allows the initialization of the RG flow at a large scale Λ associated with the perturbative regime, which effectively corresponds to starting in the vacuum as we have T=Λ ≪ 1 and μ=Λ ≪ 1 In this way, the finite UV extent as implied by the validity bound of NJL-type models is surmounted, and the limit on the range of applicability in terms of external parameters is lifted.
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