In order to prove the existence of a critical end point (CEP) in the QCD phase diagram it is sufficient to demonstrate that at zero temperature $T=0$ a first order phase transition exists as a function of the baryochemical potential $\mu$, since it is established knowledge from ab-initio lattice QCD simulations that at $\mu=0$ the transition on the temperature axis is a crossover.
We present the argument that the observation of a gap in the mass-radius relationship for compact stars which proves the existence of a so-called third family (aka "mass twins") will imply that the $T=0$ equation of state of compact star matter exhibits a strong first order transition with a latent heat that satisfies $\Delta\epsilon/\epsilon_c > 0.6$. Since such a strong first order transition under compact star conditions will remain first order when going to symmetric matter, the observation of a disconnected branch (third family) of compact stars in the mass-radius diagram proves the existence of a CEP in QCD. Modeling of such compact star twins is based on a QCD motivated NJL quark model with high order interactions together with the hadronic DD2-MEV model fulfilling nuclear observables. Further approaches include multipolytrope EoS description and constant speed of sound for the quark matter EoS. Moreover, astrophysical applications of high mass twins phenomenon are presented.
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