Phase diagram of helically imbalanced QCD matter

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.

The Chiral Phase Transitions of Helical Matter

“…We show that close to the phase transition, it is possible to distinguish between normal and helical matter not only in terms of the densities, but also in terms of the susceptibilities that indeed measure the fluctuations of the conserved quantities. Our results have some overlap with [24], and we agree with that reference whenever we compute similar quantities. One of our conclusions is that helical density makes the chiral phase transition softer.…”

“…The phase diagram of a system with unbalanced helicity at T = 0 has been studied in [24] for the first time: here we confirm the results of [24] and in addition to this, we analyze how the vacuum renormalized term of the thermodynamic potential affects the picture. In the upper panel of Fig.…”

“…( 16), the thermodynamic potential at µ = 0 and µ H = 0 is equivalent to that at µ = 0 and µ H = 0. This duality has been observed noticed in [24] for the first time.…”

“…The finite temperature thermodynamic potential is standard: following [24] to take into account the helical as well as the number chemical potentials, we get…”

“…Within the local density approximation, the thermodynamic potential for an unbounded system rotating with angular velocity ω along the z−axis, temperature T = 1/β and helical chemical potential µ H can be obtained from [24,36,38,40], that is…”