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I will discuss how the functional renormalization group can be used to include beyond mean-field fluctuations in cold quark matter, with a special focus on diquark pairing and color superconductivity. Within the quark-meson-diquark model, I will examine how these fluctuations affect the QCD phase structure and their astrophysical implications for neutron stars with quark matter cores. Finally, I will present preliminary results aimed at constraining the parameters of such effective models based on non-perturbative first-principle QCD.

L. Heitz