Abstract
We discuss the influence of a helicity imbalance on the phase diagram of dense QCD at finite temperature. We argue that the helical chemical potential is a thermodynamically relevant quantity in theories with the mass gap generation. Using the linear sigma model coupled to quarks, we show that the presence of the helical density substantially affects the phase diagram of dense quark matter. A moderate helical density makes the chiral phase transition softer while shifting the critical endpoint towards lower temperatures and higher baryon chemical potentials. As the helical density increases, the segment of the first-order transition disappears, and the chiral transition becomes a soft crossover. At even higher helical chemical potentials, the first-order transition reappears again at the zero-density finite-temperature transition and extends into the interior of the phase diagram. This evolution of the chiral transition reflects the existence of a thermodynamic duality between helical and vector (baryonic) chemical potentials. We also show that the presence of the helicity imbalance of quark matter increases the curvature of the chiral pseudocritical line in QCD.
Highlights
Unusual properties of quark-gluon plasma attract intensive attention of the scientific community
Using the linear sigma model coupled to quarks, we show that the presence of the helical density substantially affects the phase diagram of dense quark matter
In order to keep our calculations as simple as possible, and noticing that our work is concentrated on the analysis of the new effects that could be brought by the inclusion of the helical degrees of freedom rather than on a detailed analysis of the temperature-density phase diagram, we continue to work with the Nf 1⁄4 2 flavors following Ref. [32]
Summary
Unusual properties of quark-gluon plasma attract intensive attention of the scientific community. The axial symmetry, which is respected by the massless Dirac Hamiltonian, is broken at the quantum level via an axial anomaly This feature leaves an imprint on the particularities of the meson spectrum [10] and generates anomalous transport effects in the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions [11,12]. As we discuss at the end of the paper, the net helicity is expected to be a reasonably good quantum number to characterize the thermal evolution of the quark-gluon plasma until the hadronization time It is well-known that the helicity of massless quarks is conserved in perturbative QCD interactions due to the vector nature of the coupling between quarks and gluons We employ the ðþ; −; −; −Þ signature for the space-time metric and the convention ε0123 1⁄4 þ1 for the Levi-Civita symbol
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