# Darmstadt 2016 – wissenschaftliches Programm

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# HK: Fachverband Physik der Hadronen und Kerne

## HK 66: Heavy Ion Collision and QCD Phases XIII

### HK 66.3: Vortrag

### Freitag, 18. März 2016, 14:45–15:00, S1/01 A04

**Vacuum-fluctuation effects on inhomogeneous chiral symmetry breaking** — •Michael Buballa^{1}, Stefano Carignano^{2}, and Bernd-Jochen Schaefer^{3} — ^{1}TU Darmstadt — ^{2}INFN Gran Sasso — ^{3}Justus-Liebig-Universität Gießen

Various model studies suggest that the phase diagram of strong-interaction matter contains an inhomogeneous region where the chiral condensate is non-uniform in space. Most of these studies have been performed in the mean-field approximation. As a first step to include fluctuation effects, we investigate the phase structure of the quark-meson (QM) model in the so-called extended mean-field approximation, where the Dirac-sea contributions of the quarks are taken into account. In contrast to the frequently employed Nambu--Jona-Lasinio (NJL) model the QM model is renormalizable, so that the results eventually become independent of the cutoff parameter. Compared with the case where the Dirac sea is neglected, we find that the inhomogeneous phase shrinks, but in general does not disappear. It turns out, however, that the inhomogeneous phase is particularly sensitive to a proper choice of the renormalization conditions, fixing meson pole masses, rather than curvature masses. With that choice the Lifshitz point of the inhomogeneous phase coincides with the tricritical point if the ratio between sigma-meson and constituent quark mass in vacuum is chosen to be 2, corresponding to the fixed mass ratio in the NJL model. Finally, we uncover a general instability of the model, indicating that further improvements of the approximation scheme, in particular including bosonic fluctuations, are necessary.