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We suggest a new Bayesian analysis using disjunct M-R constraints forextracting probability measures for cold, dense matter equations of state. Oneof the key issues of such an analysis is the question of a deconfinementtransition in compact stars and whether it proceeds as a crossover or rather asa first order transition. The latter question is relevant for the possibleexistence of a critical endpoint in the QCD phase diagram under scrutiny inpresent and upcoming heavy-ion collision experiments.

Mass and radius constraints for compact stars and the QCD phase diagram