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Register a new userThe Critical End Point of Quantum Chromodynamics Detected by Chirally Imbalanced Quark Matter
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Authors
Marco Ruggieri
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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 with three colors can be detected, by means of Lattice simulations of grand-canonical ensembles with a chiral chemical potential, $mu_5$, conjugated to chiral charge density. In fact, we show that a continuation of the critical endpoint of the phase diagram of Quantum Chromodynamics at finite chemical potential, $mu$, to a critical end point in the temperature-chiral chemical potential plane, is possible. This study paves the way of the mapping of the phases of Quantum Chromodynamics at finite $mu$, by means of the phases of a fictitious theory in which $mu$ is replaced by $mu_5$.
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We show that the nonlocal two-flavor Nambu--Jona-Lasinio model predicts the enhancement of both chiral and axial symmetry breaking as the chiral imbalance of hot QCD matter, regulated by a chiral chemical potential $mu_5$, increases. The two crossovers are reasonably close to each other in the range of $mu_5$ examined here and the pseudocritical temperatures rise with $mu_5$. The curvatures of the chiral and axial crossovers for the chiral quark chemical potential approximately coincide and give $kappa_5 simeq - 0.011$. We point out that the presence of $mu_5$ in thermodynamic equilibrium is inconsistent with the fact that the chiral charge is not a Noether-conserved quantity for massive fermions. The chiral chemical potential should not, therefore, be considered as a true chemical potential that sets a thermodynamically stable environment in the massive theory, but rather than as a new coupling that may require a renormalization in the ultraviolet domain. The divergence of an unrenormalized chiral density, corr{coming from zero-point fermionic fluctuations,} is a consequence of this property. We propose a solution to this problem via a renormalization procedure.
Observations from collisions of heavy-ion at relativistic energies have established the formation of a new phase of matter, Quark Gluon Plasma (QGP), a deconfined state of quarks and gluons in a specific region of the temperature versus baryonic chemical potential phase diagram of strong interactions. A program to study the features of the phase diagram, such as a possible critical point, by varying the collision energy ($sqrt{s_{rm NN}}$), is performed at the Relativistic Heavy-Ion Collider (RHIC) facility. Non-monotonic variation with $sqrt{s_{rm NN}}$ of moments of the net-baryon number distribution, related to the correlation length and the susceptibilities of the system, is suggested as a signature for a critical point. We report the first evidence of a non-monotonic variation in kurtosis $times$ variance of the net-proton number (proxy for net-baryon number) distribution as a function of $sqrt{s_{rm NN}}$ with 3.1$sigma$ significance, for head-on (central) gold-on-gold (Au+Au) collisions measured using the STAR detector at RHIC. Non-central Au+Au collisions and models of heavy-ion collisions without a critical point show a monotonic variation as a function of $sqrt{s_{rm NN}}$.
Strongly interacting matter undergoes a crossover phase transition at high temperatures $Tsim 10^{12}$ K and zero net-baryon density. A fundamental question in the theory of strong interactions, Quantum Chromodynamics (QCD), is whether a hot and dense system of quarks and gluons displays critical phenomena when doped with more quarks than antiquarks, where net-baryon number fluctuations diverge. Recent lattice QCD work indicates that such a critical point can only occur in the baryon dense regime of the theory, which defies a description from first principles calculations. Here we use the holographic gauge/gravity correspondence to map the fluctuations of baryon charge in the dense quark-gluon liquid onto a numerically tractable gravitational problem involving the charge fluctuations of holographic black holes. This approach quantitatively reproduces ab initio results for the lowest order moments of the baryon fluctuations and makes predictions for the higher order baryon susceptibilities and also for the location of the critical point, which is found to be within the reach of heavy ion collision experiments.
The magnetized phase diagram for three-flavor quark matter is studied within the Polyakov extended Nambu--Jona-Lasinio model. The order parameters are analyzed with special emphasis on the strange quark condensate. We show that the presence of an external magnetic field induces several critical endpoints (CEPs) in the strange sector, which arise due to the multiple phase transitions that the strange quark undergoes. The spinodal and binodal regions of the phase transitions are shown to increase with external magnetic field strength. The influence of strong magnetic fields on the isentropic trajectories around the several CEPs is analyzed. A focusing effect is observed on the region towards the CEPs that are related with the strange quark phase transitions. Compared to the chiral transitions, the deconfinement transition turns out to be less sensitive to the external magnetic field and the crossover nature is preserved over the whole phase diagram.
We study the effect of periodic boundary conditions on chiral symmetry breaking and its restoration in Quantum Chromodynamics. As an effective model of the effective potential for the quark condensate, we use the quark-meson model, while the theory is quantized in a cubic box of size $L$. After specifying a renormalization prescription for the vacuum quark loop, we study the condensate at finite temperature, $T$, and quark chemical potential, $mu$. We find that lowering $L$ leads to a catalysis of chiral symmetry breaking. The excitation of the zero mode leads to a jump in the condensate at low temperature and high density, that we suggest to interpret as a gas-liquid phase transition that takes place between the chiral symmetry broken phase (hadron gas) and chiral symmetry restored phase (quark matter). We characterize this intermediate phase in terms of the increase of the baryon density, and of the correlation length of the fluctuations of the order parameter: for small enough $L$ the correlation domains occupy a substantial portion of the volume of the system, and the fluctuations are comparable to those in the critical region. For these reasons, we dub this phase as the {it subcritical liquid}. The qualitative picture that we draw is in agreement with previous studies based on similar effective models. We also clarify the discrepancy on the behavior of the critical temperature versus $L$ found in different models.
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