We compute the QCD phase diagram in the plane of the chiral chemical potential and temperature using the linear sigma model coupled to quarks and to the Polyakov loop. The chiral chemical potential accounts for effects of imbalanced chirality due to QCD sphaleron transitions which may emerge in heavy-ion collisions. We found three effects caused by the chiral chemical potential: the imbalanced chirality (i) tightens the link between deconfinement and chiral phase transitions; (ii) lowers the common critical temperature; (iii) strengthens the order of the phase transition by converting the crossover into the strong first order phase transition passing via the second order end-point. Since the fermionic determinant with the chiral chemical potential has no sign problem, the chirally imbalanced QCD matter can be studied in numerical lattice simulations.

6 pages, 4 figures, RevTeX 4.1