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We suggest the idea, supported by concrete calculations within chiral models,that the critical endpoint of the phase diagram of Quantum Chromodynamics withthree colors can be detected, by means of Lattice simulations ofgrand-canonical ensembles with a chiral chemical potential, $\mu_5$, conjugatedto chiral charge density. In fact, we show that a continuation of the criticalendpoint of the phase diagram of Quantum Chromodynamics at finite chemicalpotential, $\mu$, to a critical end point in the temperature-chiral chemicalpotential plane, is possible. This study paves the way of the mapping of thephases of Quantum Chromodynamics at finite $\mu$, by means of the phases of afictitious theory in which $\mu$ is replaced by $\mu_5$.

The Critical End Point of Quantum Chromodynamics Detected by Chirally Imbalanced Quark Matter