Giacosa, F.

Heinz, A.

Rischke, D. H.

GSI Repository

Inhomogeneous condensation in nuclear matter∗Achim Heinz, Francesco Giacosa, and Dirk H. RischkeITP, Frankfurt am Main, GermanyIntroductionSpontaneous breaking of chiral symmetry is a nonpertur-bative phenomenon in the QCD vacuum as well as at lowtemperature and densities. Hadronic theories of the low en-ergy regime have to take this into account [1]. Chiral sym-metry breaking appears in the hadron spectrum as a masssplitting of so-called chiral partners.A re-occurring topic in the literature is the possibilitythat the order parameter for the chiral transition is a func-tion of spatial coordinate [2]. A fruitful Ansatz to de-scribe inhomogeneous condensation is the chiral-densitywave (CDW).We re-investigate the question of inhomogeneous con-densation at nonzero density in the extended Linear SigmaModel (eLSM) where the baryons are introduced as paritydoublets [3, 4]. The eLSM successfully describes hadronvacuum phenomenology both in the meson and baryon sec-tor, it is therefore a natural choice for non-zero densitystudies including the CDW [5].Non-zero density studyIn the two-flavor case, Nf = 2, the scalar and pseu-doscalar mesons are described by the matrixΦ = (σ + ıηN )t0 + (~a0 + ı~π) · ~t ,and the vector and axial-vector mesons byV μ = ωμt0 + ~ρμ · ~t , Aμ = fμ1 t0 + ~aμ1 · ~t ,where ~t = ~τ/2, with the vector of Pauli matrices ~τ , andt0 = 12/2. The model is invariant under the chiral groupSU(2)R×SU(2)L. The chiral condensate φ = 〈σ〉 = Zfπemerges upon spontaneous chiral symmetry breaking in themesonic sector, where fπ ' 92.4 MeV is the pion decayconstant and Z ' 1.67 is the wave-function renormaliza-tion constant of the pseudoscalar fields.We now make the following Ansatz for the condensates,which is of the form of a chiral-density wave:〈σ〉 = φ cos(2fx) , 〈π〉 = φ sin(2fx) , (1)In the limit f → 0 we obtain the usual homogeneous con-densation.The baryons are introduced as two parity doublets Ψ 1and Ψ2, which transform according to the mirror assign-ment:Ψ1,R → UR Ψ1,R , Ψ1,L → UL Ψ1,L , (2)Ψ2,R → UL Ψ2,R , Ψ2,L → UR Ψ2,L . (3)∗Work supported by HGS-HIRe and HIC4FAIR.The mirror assignment allows for an additional chirally in-variant mass term [6]:m0(Ψ¯1,LΨ2,R − Ψ¯1,RΨ2,L − Ψ¯2,LΨ1,R + Ψ¯2,RΨ1,L).(4)900 950 1000 1050 1100Μ MeV050100150Φ, Χ0 MeVCDWhomogeneousphaseFigure 1: The condensates φ and χ¯ are shown as functionsof μ.In Fig. 1 the condensates φ and χ¯ are shown as func-tions of μ. For μ = 923 MeV a first-order phase transi-tion to the nuclear matter ground state takes place and atμ = 973 MeV a transition to the CDW phase occurs. Interms of density, the onset of inhomogeneous condensationis at 2.4ρ0. Then, a mixed phase is realized between 2.4ρ0to 10.4ρ0. However somewhere in the mixed phase the de-confinement phase transition should occur.OutlookFurther studies of the model at zero and non-zero densi-ties should be performed to test for general forms of inho-mogeneous condensation. The eLSM should be extendedto Nf = 3 in the baryon sector.References[1] S. Gasiorowicz et al. Rev. Mod. Phys. 41, 531 (1969).[2] A. B. Migdal, Rev. Mod. Phys. 50, 107 (1978).[3] D. Parganlija et al. Phys. Rev. D 82, 054024 (2010);[4] S. Gallas et al. Phys. Rev. D 82, 014004 (2010).[5] A. Heinz et al. arXiv:1312.3244 [nucl-th].[6] C. DeTar et al. Phys. Rev. D 39, 2805 (1989).GSI SCIENTIFIC REPORT 2013 THEORY-13doi:10.15120/GR-2014-1-THEORY-13 265

Inhomogeneous condensation in nuclear matter

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Inhomogeneous condensation in nuclear matter

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