Chiral Phase Transition In QCD Research Articles

Studies on proper time regularization and the QCD chiral phase transition

We investigate the finite-temperature and zero quark chemical potential QCD chiral phase transition of strongly interacting matter within the two-flavor Nambu–Jona-Lasinio (NJL) model as well as the proper time regularization. We use two different regularization processes, as discussed in Refs. 36 and 37, separately, to discuss how the effective mass M varies with the temperature T. Based on the calculation, we find that the M of both regularization schemes decreases when T increases. However, for three different parameter sets, quite different behaviors will show up. The results obtained by the method in Ref. 36 are very close to each other, but those in Ref. 37 are getting farther and farther from each other. This means that although the method in Ref. 37 seems physically more reasonable, it loses the advantage in Ref. 36 of a small parameter dependence. In addition, we also, find that two regularization schemes provide similar results when T [Formula: see text] 100 MeV, while when T is larger than 100 MeV, the difference becomes obvious: the M calculated by the method in Ref. 36 decreases more rapidly than that in Ref. 37.

Does the chiral magnetic effect change the dynamic universality class in QCD?

In QCD matter under an external magnetic field, the chiral magnetic effect (CME) leads to the collective gapless mode called the chiral magnetic wave (CMW). Since dynamic universality class generally depends on low-energy gapless modes, it is nontrivial whether the CME and the resulting CMW change that of the second-order chiral phase transition in QCD. To address this question, we study the critical dynamics near the chiral phase transition in massless two-flavor QCD under an external magnetic field. By performing the dynamic renormalization-group analysis within the ϵ expansion, we find that the presence of the CME changes the dynamic universality class to that of model A. We also show that the transport coefficient of the CME is not renormalized by the critical fluctuations of the order parameter.

Density-Dependence of Nuclear Symmetry Energy: Role of QCD Chiral Phase Transition

The density-dependence of symmetry energy is of particular importance to many problems in nuclear physics and astrophysics. By using the functional path integral method, we show explicitly the relation between nuclear symmetry energy and isospin susceptibility. The latter one is found to be a probe to the QCD chiral phase transition. We further found in the Nambu-Jona-Lasinio model calculations that, the nuclear symmetry energy has an abrupt change at the critical nuclear density where the chiral symmetry restores partially.

QCD chiral phase transition from noninteger numbers of flavors

Attempts to extract the order of the chiral transition of QCD at zero chemical potential, with two dynamical flavors of massless quarks, from simulations with progressively decreasing pion mass, have remained inconclusive because of their increasing numerical cost. In an alternative approach to this problem, we consider the path integral as a function of continuous number ${N}_{\mathrm{f}}$ of degenerate quarks. If the transition in the chiral limit is first order for ${N}_{\mathrm{f}}\ensuremath{\ge}3$, a second-order transition for ${N}_{\mathrm{f}}=2$ then requires a tricritical point in between. This, in turn, implies tricritical scaling of the critical boundary line between the first-order and crossover regions as the chiral limit is approached. Noninteger numbers of fermion flavors are easily implemented within the staggered fermion discretization. Exploratory simulations at $\ensuremath{\mu}=0$ and ${N}_{\mathrm{f}}=2.8$, 2.6, 2.4, 2.2, 2.1, on coarse ${N}_{\ensuremath{\tau}}=4$ lattices, indeed show a smooth variation of the critical mass mapping out a critical line in the ($m$, ${N}_{\mathrm{f}}$) plane. For the smallest masses, the line appears consistent with tricritical scaling, allowing for an extrapolation to the chiral limit.

Low temperature electroweak phase transition in the Standard Model with hidden scale invariance

We discuss a cosmological phase transition within the Standard Model which incorporates spontaneously broken scale invariance as a low-energy theory. In addition to the Standard Model fields, the minimal model involves a light dilaton, which acquires a large vacuum expectation value (VEV) through the mechanism of dimensional transmutation. Under the assumption of the cancellation of the vacuum energy, the dilaton develops a very small mass at 2-loop order. As a result, a flat direction is present in the classical dilaton-Higgs potential at zero temperature while the quantum potential admits two (almost) degenerate local minima with unbroken and broken electroweak symmetry. We found that the cosmological electroweak phase transition in this model can only be triggered by a QCD chiral symmetry breaking phase transition at low temperatures, T≲132 MeV. Furthermore, unlike the standard case, the universe settles into the chiral symmetry breaking vacuum via a first-order phase transition which gives rise to a stochastic gravitational background with a peak frequency ∼10−8 Hz as well as triggers the production of approximately solar mass primordial black holes. The observation of these signatures of cosmological phase transitions together with the detection of a light dilaton would provide a strong hint of the fundamental role of scale invariance in particle physics.

Fluctuation-induced modifications of the phase structure in ( 2+1 )-flavor QCD

The low-energy sector of QCD with $N_f = 2\!+\!1$ dynamical quark flavors at non-vanishing chemical potential and temperature is studied with a non-perturbative functional renormalization group method. The analysis is performed in different truncations in order to explore fluctuation-induced modifications of the quark-meson correlations as well as quark and meson propagators on the chiral phase transition of QCD. Depending on the chosen truncation significant quantitative implications on the phase transition are found. In the chirally symmetric phase, the quark flavor composition of the pseudoscalar $(\eta,\eta^{\prime})$-meson complex turns out to be drastically sensitive to fluctuation-induced modifications in the presence of the axial $U(1)_A$ anomaly. This has important phenomenological consequences for the assignment of chiral partners to these mesons.

Proper time regularization and the QCD chiral phase transition

We study the QCD chiral phase transition at finite temperature and finite quark chemical potential within the two flavor Nambu–Jona-Lasinio (NJL) model, where a generalization of the proper-time regularization scheme is motivated and implemented. We find that in the chiral limit the whole transition line in the phase diagram is of second order, whereas for finite quark masses a crossover is observed. Moreover, if we take into account the influence of quark condensate to the coupling strength (which also provides a possible way of how the effective coupling varies with temperature and quark chemical potential), it is found that a CEP may appear. These findings differ substantially from other NJL results which use alternative regularization schemes, some explanation and discussion are given at the end. This indicates that the regularization scheme can have a dramatic impact on the study of the QCD phase transition within the NJL model.

Chiral phase transition of QCD with Nf = 2 + 1 flavors from holography

Chiral phase transition for three-flavor Nf = 2 + 1 QCD with mu = md ≠ ms is investigated in a modified soft-wall holographic QCD model. Solving temperature dependent chiral condensates from equations of motion of the modified soft-wall model, we extract the quark mass dependence of the order of chiral phase transition in the case of Nf = 2 + 1, and the result is in agreement with the “Columbia Plot”, which is summarized from lattice simulations and other non-perturbative methods. First order phase transition is observed around the three flavor chiral limit mu/d = 0, ms = 0, while at sufficient large quark masses it turns to be a crossover phase transition. The first order and crossover regions are separated by a second order phase transition line. The second order line is divided into two parts by the mu/d = ms line, and the ms dependence of the transition temperature in these two parts are totally contrast, which might indicate that the two parts are governed by different universality classes.

Necessary Condition for Emergent Symmetry from the Conformal Bootstrap.

We use the conformal bootstrap program to derive the necessary conditions for emergent symmetry enhancement from discrete symmetry (e.g., Z_{n}) to continuous symmetry [e.g., U(1)] under the renormalization group flow. In three dimensions, in order for Z_{2} symmetry to be enhanced to U(1) symmetry, the conformal bootstrap program predicts that the scaling dimension of the order parameter field at the infrared conformal fixed point must satisfy Δ_{1}>1.08. We also obtain the similar necessary conditions for Z_{3} symmetry with Δ_{1}>0.580 and Z_{4} symmetry with Δ_{1}>0.504 from the simultaneous conformal bootstrap analysis of multiple four-point functions. As applications, we show that our necessary conditions impose severe constraints on the nature of the chiral phase transition in QCD, the deconfinement criticality in Néel valence bond solid transitions, and anisotropic deformations in critical O(n) models. We prove that some fixed points proposed in the literature are unstable under the perturbation that cannot be forbidden by the discrete symmetry. In these situations, the second-order phase transition with enhanced symmetry cannot happen.

Stable Yang-Lee zeros in a truncated fugacity series from the net baryon number multiplicity distribution

We investigate Yang-Lee zeros of grand partition functions as truncated fugacity polynomials of which coefficients are given by the canonical partition functions $Z(T,V,N)$ up to $N \leq N_{\text{max}}$. Such a partition function can be inevitably obtained from the net-baryon number multiplicity distribution in relativistic heavy ion collisions, where the number of the event beyond $N_{\text{max}}$ has insufficient statistics, as well as canonical approaches in lattice QCD. We use a chiral random matrix model as a solvable model for chiral phase transition in QCD and show that the closest edge of the distribution to real chemical potential axis is stable against cutting the tail of the multiplicity distribution. The similar behavior is also found in lattice QCD at finite temperature for Roberge-Weiss transition. In contrast, such a stability is found to be absent in the Skellam distribution which does not have phase transition. We compare the number of $N_{\text{max}}$ to obtain the stable Yang-Lee zeros with those of critical higher order cumulants.

Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial–vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson–Schwinger equations.

Inverse Magnetic Catalysis in the three-flavor NJL model with axial-vector interaction

In this paper we explore the chiral phase transition in QCD within the three-flavor Nambu-Jona-Lasinio model with a negative coupling constant in the isoscalar axial-vector channel, which is associated with a polarized instanton--anti-instanton molecule background. The QCD phase diagram described in this scenario shows a new first order phase transition around the transition temperature ${T}_{c}$ toward a phase without chiral condensates, but with nontrivial dynamic chiral chemical potentials for the light quarks, spontaneously giving rise to local charge parity violation and local chirality imbalance. The corresponding critical temperature ${T}_{5c}$ for this phase transition decreases with the magnetic field and it gives a natural explanation to the inverse magnetic catalysis effect for light quarks when incorporating a reasonable value of the coupling constant in the isoscalar axial-vector channel. Furthermore, when the isoscalar axial-vector interaction is dominant in the light quark sector and suppressed in the strange quark sector, it is found that there is no inverse magnetic catalysis for strange quark condensate, which agrees with lattice results.

22aDC-9 共形ブートストラップで解くQCDカイラル相転移

22aDC-9 共形ブートストラップで解くQCDカイラル相転移

Chiral phase transition with a chiral chemical potential in the framework of Dyson-Schwinger equations

Within the framework of Dyson-Schwinger equations (DSEs), we discuss the chiral phase transition of QCD with a chiral chemical potential $\mu_5$ as an additional scale. We focus especially on the issues related to the widely accepted as well as interested critical end point (CEP). With the help of a scalar susceptibility, we find that there might be no CEP$_5$ in the $T-\mu_5$ plane, and the phase transition in the $T-\mu_5$ plane might be totally crossover when $\mu<50$ MeV, which has apparent consistency with the Lattice QCD calculation. Our study may also provide some useful hints to some other studies related to $\mu_5$.

Realistic implementation of chiral magnetic wave in heavy ion collisions

A chiral magnetic wave (CMW) is a gapless collective excitation of chiral charges along the direction of magnetic field in the quark-gluon plasma that arises from the triangle anomaly of QCD. We perform a reliable study of the CMW in a realistic simulation of heavy ion collisions, and find that the CMW contributions to the charge-dependent elliptic flow of pions, $\ensuremath{\Delta}{v}_{2}\ensuremath{\equiv}{v}_{2}({\ensuremath{\pi}}^{\ensuremath{-}})\ensuremath{-}{v}_{2}({\ensuremath{\pi}}^{+})$, linearly depending on the net charge asymmetry ${A}_{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\equiv}({N}_{+}\ensuremath{-}{N}_{\ensuremath{-}})/({N}_{+}+{N}_{\ensuremath{-}})$ with a positive slope $r$, is comparable to the recent experimental results from the Relativistic Heavy Ion Collider (RHIC). We identify a ``freeze-out hole effect,'' which is a direct consequence of the propagation of the CMW during the realistic evolution of the fireball, as the dominant physics effect responsible for a sizable contribution from the CMW to the slope parameter $r$, and emphasize that a proper treatment of the freeze-out condition is crucial in any reliable computation of the CMW contribution to the slope parameter $r$. We also implement a chiral phase transition effect in our study, which illustrates the sensitivity of the results to chiral phase transition temperature, and suggest that the CMW can be an important probe of the QCD chiral phase transition. Our results on the impact parameter dependence compare well with the RHIC experiments. We also give predictions for the Large Hadron Collider (LHC) energy.

A Model Study of the Chiral Phase Diagram of QCD

In this paper we study the chiral phase transition of QCD at finite temperature and density by using the rank-2 confining separable gluon propagator model in the framework of Dyson-Schwinger Equations. The critical end point is located at (T_CEP, {\mu}_CEP) = (69 MeV, 270.3 MeV). It is also found that the first order phase transition might not end at one point, but experiences a two-phase coexisting meta-stable state. A comparison with the results in the previous literature is given.

The Wigner solution of quark gap equation and chiral phase transition of QCD at finite temperature and nonzero chemical potential

By employing some modification to the normal NJL model, we discuss the Wigner solution of quark gap equation at finite temperature and chemical potential when the current quark mass m is nonzero. The discovery of the coexistence of the Nambu solution and the Wigner solution at finite temperature and chemical potential beyond the chiral limit is of great importance in the study of the chiral phase transition of QCD. Using the pressure difference between Nambu phase and Wigner phase (or in other words, the bag constant) as an order parameter for chiral phase transition, we draw a possible phase diagram based on our calculations.

Influence of an inhomogeneous and expanding medium on signals of the QCD phase transition

According to a fluid dynamic expansion of the fireball we investigate how the inhomogeneity of the system influences the chiral phase transition of QCD. We compare the averaged values of the order parameter in equilibrium with that of a homogeneous system. If the temperature is averaged over a certain region of the fireball the corresponding correlation length does not diverge in an expansion with a critical point.

QCD Thermodynamics with Domain-Wall Fermions

The study of the QCD chiral phase transition on the lattice has been hampered in the past by the lack of a chiral-invariant fermion formulation. Only recently has it become possible to perform fully dynamical simulations with chiral formulations such as domain-wall and overlap fermions. Here we present results for various chiral observables at finite temperature that were obtained using domain-wall fermions. We also present results showing that the axial anomaly is still present even above the chiral phase transition. Lastly, we show our results for the Dirac spectrum at finite temperature and speculate on the mechanism of U(1)A breaking beyond the chiral phase transition.

Chiral phase transition of QCD at finite chemical potential

In the framework of Dyson-Schwinger equation (DSE) approach, we propose a chemical potential dependent effective gluon propagator and the quark gap equation is solved with such a gluon propagator. It is found for the first time in DSE approach that with light current quark mass m not equal 0, the Wigner solution will appear at some chemical potential mu(W). Based on this, the chiral phase transition at finite chemical potential is studied and the result shows that it is a first-order phase transition. The results are compared with the known results in the literature.