Chiral Phase Transition In QCD Research Articles

Microscopic Encoding of Macroscopic Universality: Scaling Properties of Dirac Eigenspectra near QCD Chiral Phase Transition

Microscopic Encoding of Macroscopic Universality: Scaling Properties of Dirac Eigenspectra near QCD Chiral Phase Transition

Spin polarization and anomalous magnetic moment in a ( 2+1 )-flavor Nambu–Jona-Lasinio model in a thermomagnetic background

We investigate the magnetized QCD matter and chiral phase transition in a ($2+1$)-flavor Nambu--Jona-Lasinio (NJL) model at finite temperature and chemical potential by comparing the contributions from the tensor spin polarization (TSP) and anomalous magnetic moment (AMM) of quarks. For light $u$ and $d$ quarks, when TSP and AMM are not considered, the magnetized system is characterized by magnetic catalysis. The introduction of TSP will further enhance the magnetic catalytic characteristics. On the other hand, when AMM is introduced, the phase-transition temperature decreases with the magnetic field, which is the feature of inverse magnetic catalysis. The phase diagram of $u$ and $d$ quarks will change from the crossover phase transition to the first order phase transition with the increase of magnetic field and chemical potential when AMM is induced. The phase diagram will not change from the crossover phase transition to the first-order phase transition when TSP is induced. For the phase diagram of strange $s$ quark, whether TSP or AMM is induced, the phase diagram will keep a crossover phase transition with the increase of magnetic field and chemical potential.

Fate of the first-order chiral phase transition in QCD: Implications for dark QCD studied via a Nambu–Jona-Lasinio model

The first-order nature of the chiral phase transition in QCD-like theories can play crucial roles to address a dark side of the Universe, where the created out-of equilibrium is essential to serve as cosmological and astrophysical probes such as gravitational wave productions, which have extensively been explored. This interdisciplinary physics is built based on a widely-accepted conjecture that the thermal chiral phase transition in QCD-like theories with massless (light) three flavors is of first order. We find that such a first order feature may not hold, when ordinary or dark quarks are externally coupled to a weak enough background field of photon or dark photon (which we collectively call a ``magnetic" field). We assume that a weak ``magnetic" background field could be originated from some ``magnetogenesis" in the early Universe. We work on a Nambu-Jona-Lasinio model which can describe the chiral phase transition in a wide class of QCD-like theories. We show that in the case with massless (light) three flavors, the first-order feature goes away when $2 f_\pi^2 \lesssim eB ( \ll (4 \pi f_\pi)^2)$, where $eB$ is the ``magnetic" field strength and $f_\pi$ the pion decay constant at the vacuum. This disappearance is the generic consequence of the presence of the ``magnetically" induced scale anomaly and the ``magnetic" catalysis for the chiral symmetry breaking, and would impact or constrain modeling dark QCD coupled to an external ``magnetic" field.

Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model

We analyze a two-body non-Hermitian two-site Sachdev–Ye–Kitaev (SYK) model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of second-order phase transitions, which is a consequence of the factorization of the partition function into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways: first in terms of the single-particle energies and second by solving the Schwinger–Dyson equations of the two-site model. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can also be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the free energy are due to the chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases, the free energy is determined by the spectral density. The chaotic four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. On the other hand, the low-temperature free energy of the two-body SYK model is not flat; in fact, it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive in the low-temperature phase, which most likely is a consequence of the non-hermiticity.

Nonextensive effects on QCD chiral phase transition with a chiral chemical potential* *Supported by the National Natural Science Foundation of China (12005192) and the Project funded by China Postdoctoral Science Foundation (2020M672255, 2020TQ0287)

In this study, we investigate the QCD chiral phase diagram in the presence of a chiral chemical potential based on nonextensive statistical mechanics. A feature of this new statistic is a dimensionless nonextensivity parameter q, which summarizes all possible effects violating the assumptions of Boltzmann-Gibbs (BG) statistics (when , it returns to the BG case). Within the nonextensive Polyakov-Nambu-Jona-Lasinio model, we find that as increases, the critical end point (CEP) in the plane continues to in the plane, and nonextensive effects have a significant impact on the evolution from the CEP to . Generally, with an increase in q, both the CEP and move in the direction of a lower temperature T and larger chemical potential μ (). In addition, we find that chiral charge density generally increases with T, μ, , and q. Our study may provide useful hints about lattice QCD and relativistic heavy-ion collision experiments.

Dynamics of the O(4) critical point in QCD

We perform a Langevin simulation of the $O(4)$ critical point, which lies in the dynamic universality class of ``model G.'' This is the dynamic universality class of the chiral phase transition in QCD with two massless flavors. The axial charge and the order parameter ${\ensuremath{\phi}}_{a}=(\ensuremath{\sigma},\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\pi}})$ exhibit a rich dynamical interplay, which reflects the qualitative differences in the hydrodynamic effective theories above and below ${T}_{c}$. From the axial charge correlators on the critical line we extract a dynamical critical exponent of $\ensuremath{\zeta}=1.47\ifmmode\pm\else\textpm\fi{}0.01(\text{stat.})$, which is compatible with the theoretical expectation of $\ensuremath{\zeta}=d/2$ (with $d=3$) when systematic errors are taken into account. At low temperatures, we quantitatively match the $O(4)$ simulations to the superfluid effective theory of soft pions.

Remarks on the QCD-electroweak phase transition in a supercooled universe

In extensions of the Standard Model with no dimensionful parameters the electroweak phase transition can be delayed to temperatures of order 100 MeV. Then the chiral phase transition of QCD can proceed with 6 massless quarks. The top-quark condensate destabilizes the Higgs potential through the Yukawa interaction, triggering the electroweak transition. Based on the symmetries of massless QCD, it has been argued that the chiral phase transition is first order. We point out that the top-Higgs Yukawa interaction is nonperturbatively large at the QCD scale, and that its effect on the chiral phase transition may not be negligible, violating some of the symmetries of massless QCD. The remaining symmetries indicate that top quarks condense in a second-order phase transition, but top condensation might also be triggered by a first-order symmetry-breaking transition in the light-quark sector.

Detecting scale anomaly in chiral phase transition of QCD: new critical endpoint pinned down

Violation of scale symmetry, scale anomaly, being a radical concept in quantum field theory, is of importance to comprehend the vacuum structure of QCD, and should potentially contribute to the chiral phase transition in thermal QCD, as well as the chiral and U(1) axial symmetry. Though it should be essential, direct evidence of scale anomalies has never been observed in the chiral phase transition. We propose a methodology to detect a scale anomaly in the chiral phase transition, which is an electromagnetically induced scale anomaly: apply a weak magnetic field background onto two-flavor massless QCD with an extremely heavy strange quark, first observe the chiral crossover; second, adjusting the strange quark mass to be smaller and smaller, observe the second-order chiral phase transition, and then the first-order one in the massless-three flavor limit. Thus, the second-order chiral phase transition, observed as the evidence of the quantum scale anomaly, is a new critical endpoint. It turns out that this electromagnetic scale anomaly gets most operative in the weak magnetic field regime, rather than a strong field region. We also briefly address accessibility of lattice QCD, a prospected application to dense matter system, and implications to astrophysical observations, such as gravitational wave productions provided from thermomagnetic QCD-like theories.

Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density

The thermal restoration of chiral symmetry in QCD is known to proceed by an analytic crossover, which is widely expected to turn into a phase transition with a critical endpoint as the baryon density is increased. In the absence of a genuine solution to the sign problem of lattice QCD, simulations at zero and imaginary baryon chemical potential in a parameter space enlarged by a variable number of quark flavours and quark masses constitute a viable way to constrain the location of a possible non-analytic phase transition and its critical endpoint. In this article I review recent progress towards an understanding of the nature of the transition in the massless limit, and its critical temperature at zero density. Combined with increasingly detailed studies of the physical crossover region, current data bound a possible critical point to μB ≳ 3T.

On the order of the QCD chiral phase transition for different numbers of quark flavours

The nature of the QCD chiral phase transition in the limit of vanishing quark masses has remained elusive for a long time, since it cannot be simulated directly on the lattice and is strongly cutoff-dependent. We report on a comprehensive ongoing study using unimproved staggered fermions with Nf ∈ [2, 8] mass-degenerate flavours on Nτ ∈ {4, 6, 8} lattices, in which we locate the chiral critical surface separating regions with first-order transitions from crossover regions in the bare parameter space of the lattice theory. Employing the fact that it terminates in a tricritical line, this surface can be extrapolated to the chiral limit using tricritical scaling with known exponents. Knowing the order of the transitions in the lattice parameter space, conclusions for approaching the continuum chiral limit in the proper order can be drawn. While a narrow first-order region cannot be ruled out, we find initial evidence consistent with a second-order chiral transition in all massless theories with Nf ≤ 6, and possibly up to the onset of the conformal window at 9 ≲ {N}_{mathrm{f}}^{ast } ≲ 12. A reanalysis of already published mathcal{O} (a)-improved Nf = 3 Wilson data on Nτ ∈ [4, 12] is also consistent with tricritical scaling, and the associated change from first to second-order on the way to the continuum chiral limit. We discuss a modified Columbia plot and a phase diagram for many-flavour QCD that reflect these possible features.

Nonuniform-temperature effects on the phase transition in an Ising-like model

In this study, we investigate the spatially nonuniform-temperature effects on the QCD chiral phase transition in the heavy-ion collisions. Since the QCD effective theory and the Ising model belong to the same universality class, we start our discussion by mimicking the QCD effective potential with an Ising-like effective potential. In contrast to the dynamical slowing down effects which delays the phase transition from quark-gluon-plasma to hadron gas, the spatially nonuniform-temperature effects show a possibility to lift the phase transition temperature. Besides, both the fluctuations and the correlation length are enhanced in the phase transition region. Furthermore, the critical phenomena is strongly suppressed like as the critical slowing down effects. The underlying mechanism is the nonzero-momentum mode fluctuations of the order parameter induced by the nonuniform temperature. Our study provides a method to evaluate the nonuniform-temperature effects, and illustrate its potential influence on analyzing the QCD phase transition signals at RHIC.

QCD chiral phase transition and critical exponents within the nonextensive Polyakov-Nambu-Jona-Lasinio model * *Supported by the National Natural Science Foundation of China (12005192) and the Project funded by China Postdoctoral Science Foundation (2020M672255, 2020TQ0287)

We present a nonextensive version of the Polyakov-Nambu-Jona-Lasinio model that is based on nonextentive statistical mechanics. This new statistics model is characterized by a dimensionless nonextensivity parameter q that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs (BG) statistics (for , it returns to the BG case). Based on the nonextensive Polyakov-Nambu-Jona-Lasinio model, we discussed the influence of nonextensive effects on the curvature of the phase diagram at and especially on the location of the critical end point (CEP). A new and interesting phenomenon we found is that with an increase in q, the CEP position initially shifts toward the direction of larger chemical potential and lower temperature. However, when q is larger than a critical value , the CEP position moves in the opposite direction. In other words, as q increases, the CEP position moves in the direction of smaller chemical potential and higher temperature. This U-turn phenomenon may be important for the search of CEP in relativistic heavy-ion collisions, in which the validity of BG statistics is questionable due to strong fluctuations and long-range correlations, and nonextensive effects begin to manifest themselves. In addition, we calculated the influence of the nonextensive effects on the critical exponents and found that they remain almost constant with q.

QCD susceptibilities in the presence of the chiral chemical potential

In this paper, chiral chemical potential [Formula: see text] is introduced to investigate the QCD susceptibilities and chiral phase transition within the Polyakov-loop-extended Nambu–Jona-Lasinio models in the mean-field approximation. We concentrate on the effect of chiral chemical potential on the phase diagram and the QCD susceptibilities. Moreover, it is worth noting that chiral chemical potential has more and more prominent impact on the susceptibilities and the phase diagram with the decrease of temperature based on our results, which coincides with the prediction that the chiral symmetry is dynamically broken in the first-order phase transition region and gets partly restored in the crossover region.

Effect of the chiral phase transition on axion mass and self-coupling

We compute the effect of the chiral phase transition of QCD on the axion mass and self-coupling; the coupling of the axion to the quarks at finite temperature is described within the Nambu--Jona-Lasinio model. We find that the axion mass decreases with temperature, following the response of the topological susceptibility, in agreement with previous results obtained within chiral perturbation theory at low and intermediate temperatures. As expected, the comparison with lattice data shows that chiral perturbation theory fails to reproduce the topological susceptibility around the chiral critical temperature, while the Nambu--Jona-Lasinio model offers a better qualitative agreement with these data, hence a more reliable estimate of the temperature dependence of the axion mass in the presence of a hot quark medium. We complete our study by computing the temperature dependence of the self-coupling of the axion, finding that this coupling decreases at and above the phase transition. The model used in our work as well as the results presented here pave the way to the computation of the in-medium effects of hot and/or dense quark-gluon plasma on the axion properties.

Mass sensitivity of the three-flavor chiral phase transition

The mass sensitivity of the chiral phase transition of QCD with and without axial $U_A(1)$-symmetry breaking at vanishing and finite quark chemical potential is investigated. To focus on the low-energy sector of QCD, a quark-meson model with three dynamical quark flavors is employed. Non-perturbative quantum fluctuations are taken into account with the functional renormalization group. The inherent ambiguities in fixing the low-energy model parameters away from the physical mass point and their consequences for spontaneous chiral symmetry breaking are discussed in detail and a heuristic parameter fixing scheme motivated by chiral perturbation theory is proposed. The influence of vacuum and thermal fluctuations of quarks and mesons on the order of the chiral phase transition is additionally assessed with a mean-field analysis.

Finite volume effects on the QCD chiral phase transition in the finite size dependent Nambu-Jona-Lasinio model * * Supported by the National Natural Science Foundation of China (11475085, 11535005, 11690030) and the National Major state Basic Research and Development (2016YFE0129300)

The effective Lagrangian of a finite volume system should, in principle, depend on the system size. In the framework of the Nambu-Jona-Lasinio (NJL) model, by considering the influence of quark feedback on the effective coupling, we obtain a modified NJL model so that its Lagrangian depends on the volume. Based on the modified NJL model, we study the influence of finite volume on the chiral phase transition at finite temperature, and find that the pseudo-critical temperature of crossover is much lower than that obtained in the normal NJL model. This clearly shows that the volume dependent effective Lagrangian plays an important role in the chiral phase transitions at finite temperature.

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.