Chiral Critical End Point Research Articles

Locating the critical endpoint of QCD: Mesonic backcoupling effects

We study the effects of pion and sigma meson backcoupling on the chiral order parameters and the QCD phase diagram and determine their effect on the location of the chiral critical endpoint. To this end, we solve a coupled set of truncated Dyson-Schwinger equations for Landau gauge quark and gluon propagators with ${N}_{\mathrm{f}}=2+1$ dynamical quark flavors and explicitly backcoupled mesons. The corresponding meson bound-state properties and the quark-meson Bethe-Salpeter vertices are obtained from their homogeneous Bethe-Salpeter equation. We find chiral-restoration effects of the pion and/or sigma meson backcoupling and observe a (small) shift of the critical endpoint towards smaller chemical potentials. The curvature of the chiral crossover line decreases. Our results indicate that the location of the critical endpoint in the phase diagram is mainly determined by the microscopic degrees of freedom of QCD (in contrast to its critical properties).

Finite-density QCD transition in a magnetic background field

Using numerical simulations of lattice QCD with physical quark masses, we reveal the influence of magnetic-field background on chiral and deconfinement crossovers in finite-temperature QCD at low baryonic density. In the absence of thermodynamic singularity, we identify these transitions with inflection points of the approximate order parameters: normalized light-quark condensate and renormalized Polyakov loop, respectively. We show that the quadratic curvature of the chiral transition temperature in the ``temperature--chemical potential'' plane depends rather weakly on the strength of the background magnetic field. At weak magnetic fields, the thermal width of the chiral crossover gets narrower as the density of the baryon matter increases, possibly indicating a proximity to a real thermodynamic phase transition. Remarkably, the curvature of the chiral thermal width flips its sign at $eB_{\mathrm{fl}} \simeq 0.6\,\mathrm{GeV}^2$, so that above the flipping point $B > B_{\mathrm{fl}}$, the chiral width gets wider as the baryon density increases. Approximately at the same strength of magnetic field, the chiral and deconfining crossovers merge together at $T \approx 140\,\mathrm{MeV}$. The phase diagram in the parameter space ``temperature-chemical potential-magnetic field'' is outlined, and single-quark entropy and single-quark magnetization are explored. The curvature of the chiral thermal width allows us to estimate an approximate position of the chiral critical endpoint at zero magnetic field: $(T_c^{\text{CEP}}, \mu_B^{\text{CEP}})= (100(25)\, \text{MeV},\ 800(140)\,\text{MeV})$.

Phase Diagram, Scalar-Pseudoscalar Meson Behavior and Restoration of Symmetries in (2 + 1) Polyakov-Nambu-Jona-Lasinio Model

We explore the phase diagram and the modification of mesonic observables in a hot and dense medium using the (2 + 1) Polyakov-Nambu-Jona-Lasinio model. We present the phase diagram in the ( T , μ B ) -plane, with its isentropic trajectories, paying special attention to the chiral critical end point (CEP). Chiral and deconfinement transitions are examined. The modifications of mesonic observables in the medium are explored as a tool to analyze the effective restoration of chiral symmetry for different regions of the phase diagram. It is shown that the meson masses, namely that of the kaons, change abruptly near the CEP, which can be relevant for its experimental search.

Modeling chiral criticality and its consequences for heavy-ion collisions

We explore the critical fluctuations near the chiral critical endpoint (CEP) in a chiral effective model and discuss possible signals of the CEP, recently explored experimentally in nuclear collision. Particular attention is paid to the dependence of such signals on the location of the phase boundary and the CEP relative to the chemical freeze-out conditions in nuclear collisions. We argue that in effective models, standard freeze-out fits to heavy-ion data should not be used directly. Instead, the relevant quantities should be examined on lines in the phase diagram that are defined self-consistently, within the framework of the model. We discuss possible choices for such an approach.

Influence of the vector interaction and an external magnetic field on the isentropes near the chiral critical end point

The location of the critical end point (CEP) and the isentropic trajectories in the QCD phase diagram are investigated. We use the (2+1) Nambu$-$Jona-Lasinio model with the Polyakov loop coupling for different scenarios, namely by imposing zero strange quark density, which is the case in the ultra relativistic heavy-ion collisions, and $\beta$-equilibrium. The influence of strong magnetic fields and of the vector interaction on the isentropic trajectories around the CEP is discussed. It is shown that the vector interaction and the magnetic field, having opposite effects on the first-order transition, affect the isentropic trajectories differently: as the vector interaction increases, the first-order transition becomes weaker and the isentropes become smoother; when a strong magnetic field is considered, the first-order transition is strengthened and the isentropes are pushed to higher temperatures. No focusing of isentropes in region towards the CEP is seen.

Sensitivity of predictions in an effective model: Application to the chiral critical end point position in the Nambu-Jona-Lasinio model

The measurement of the position of the chiral critical end point (CEP) in the QCD phase diagram is under debate. While it is possible to predict its position by using effective models specifically built to reproduce some of the features of the underlying theory (QCD), the quality of the predictions (\textit{e.g.}, the CEP position) obtained by such effective models, depends on whether solving the model equations constitute a well- or ill-posed inverse problem. Considering these predictions as being inverse problems provides tools to evaluate if the problem is ill-conditioned, meaning that infinitesimal variations of the inputs of the model can cause comparatively large variations of the predictions. If it is ill-conditioned, it has major consequences because of finite variations that could come from experimental and/or theoretical errors. In the following, we shall apply such a reasoning on the predictions of a particular Nambu--Jona-Lasinio model within the mean field + ring approximations, with special attention to the prediction of the chiral CEP position in the $(T-\mu)$ plane. We find that the problem is ill-conditioned (\idest very sensitive to input variations) for the $T$-coordinate of the CEP, whereas, it is well-posed for the $\mu$-coordinate of the CEP. As a consequence, when the chiral condensate varies in a $10$ MeV range, $\mu_{CEP}$ varies far less. As an illustration to understand how problematic this could be, we show that the main consequence when taking into account finite variation of the inputs, is that the existence of the CEP itself cannot be predicted anymore: for a deviation as low as 0.6 \% with respect to vacuum phenomenology (well within the estimation of the first correction to the ring approximation) the CEP may or may not exist.

Quark Number Susceptibility around the Chiral Critical End Point

We calculate the quark number susceptibility (QNS) around the chiral critical end point (CEP). The CEP is found to be located at (μc, Tc) = (80 MeV, 148 MeV) where μc and Tc are the critical chemical potential and temperature, respectively. The QNS is found to have the highest and sharpest peak at the CEP. It is also found that, when the chemical potential μ is in the range of 60 MeV≤ μ ≤ 110 MeV, the QNS near the transition temperature is larger than the free field result, which indicates that the space-like damping mode dominates the degree of freedom of motion near the CEP.

Recovering the chiral critical endpoint via delocalization of quark interactions

We show that for the lower branch of the quark condensate and values higher than approximately $\ensuremath{-}(250\text{ }\text{ }\text{MeV}{)}^{3}$ the chiral critical endpoint in the Nambu--Jona-Lasinio model does not occur in the phase diagram. By using lattice motivated nonlocal quark interactions, we demonstrate that the critical endpoint can be recovered. We study this behavior for a range of condensate values and find that the variation in the position of the critical endpoint is more pronounced as the condensate is increased.

Phase diagram in an external magnetic field beyond a mean-field approximation

The phase structure of the Polyakov loop-extended chiral quark-meson model is explored in a nonperturbative approach, beyond a mean-field approximation, in the presence of a magnetic field. We show that by including meson fluctuations one cannot resolve the qualitative discrepancy on the dependence of the crossover transition temperature in a nonzero magnetic field between effective model predictions and recent lattice results [1]. We compute the curvature of the crossover line in the $T\ensuremath{-}{\ensuremath{\mu}}_{B}$ plane at a nonzero magnetic field and show that the curvature increases with increasing magnetic field. On the basis of QCD inequalities, we also argue that, at least in the large ${N}_{c}$ limit, a chiral critical end point and, consequently, a change from crossover to a first-order chiral phase transition are excluded at zero baryon chemical potential and nonzero magnetic field.

Chiral transition in a finite system and possible use of finite-size scaling in relativistic heavy ion collisions

We investigate finite-size effects on the chiral phase diagram of strong interactions within the linear sigma model coupled to quarks. We estimate the modification of the pseudocritical transition line and isentropic trajectories for sizes that are representative of the systems created in relativistic heavy-ion collision experiments. The corrections are clearly non-negligible and might significantly affect signatures of the chiral critical endpoint based on estimates for an infinite system. We argue that a finite-size scaling analysis should be tested in the process of data analysis of the Beam Energy Scan program at RHIC and in future experiments at FAIR-GSI, through the use of full scaling plots and a chi-squared method as tools for searching the critical endpoint.

Fluctuations and isentropes near the chiral critical endpoint

Isentropic trajectories crossing the chiral phase transition near the critical endpoint (CEP) are studied for two light quark flavors. The calculations are performed within an effective chiral model with quark–meson interactions, belonging to the same universality class as QCD. We confront mean-field thermodynamics with the functional renormalization group approach, where fluctuations are properly taken into account. We establish a connection between modifications of the isentropic trajectories found in mean-field calculations at the crossover transition near the CEP and the order of the phase transition in the chiral limit. Furthermore, the isentropes obtained with the renormalization group are completely smooth at the crossover transition and do not in any way reflect the proximity of the CEP. In particular, our results do not show the recently conjectured focusing of isentropes from the crossover region towards the critical endpoint.

Quarkyonic matter and chiral symmetry breaking

The appearance of a new phase of QCD, Quarkyonic Matter in the limit of large number of colors is studied within Nambu–Jona-Lasinio effective chiral model coupled to the Polyakov loop. The interplay of this novel QCD phase with chiral symmetry restoration and color deconfinement is discussed. We find that at vanishing temperature and at large N c , the quarkyonic transition occurs at densities only slightly lower than that expected for the chiral transition. This property is also shown to be valid at finite temperature if the temperature is less than that of deconfinement. The position and N c -dependence of chiral critical end point is also discussed.

The chiral critical point ofNf= 3 QCD at finite density to the order (μ/T)4

QCD with three degenerate quark flavours at zero baryon density exhibits a first order thermal phase transition for small quark masses, which changes to a smooth crossover for some critical quark mass mc0, i.e. the chiral critical point. It is generally believed that as an (even) function of quark chemical potential, the critical point mc(μ) moves to larger quark masses, constituting the critical endpoint of a first order phase transition in theories with m ≥ mc0. To test this, we consider a Taylor expansion of mc(μ) around μ = 0 and determine the first two coefficients from lattice simulations with staggered fermions on Nt = 4 lattices. We employ two different techniques: a) calculating the coefficients directly from a μ = 0 ensemble using a novel finite difference method, and b) fitting them to simulation data obtained for imaginary chemical potentials. The μ2 and μ4 coefficients are found to be negative by both methods, with consistent absolute values. Combining both methods gives evidence that also the μ6 coefficient is negative. Hence, on coarse Nt = 4 lattices a three-flavour theory with m > mc0 does not possess a chiral critical endpoint for quark chemical potentials μ T. Simulations on finer lattices are required for reliable continuum physics. Possible implications for the QCD phase diagram are discussed.

Spectral functions in theσchannel near the critical end point

Spectral functions in the $\sigma$-channel are investigated near the chiral critical end point (CEP), that is, the point where the chiral phase transition ceases to be first-ordered in the $(\mu,T)$-plane of the QCD phase diagram. At that point the $\sigma$ meson becomes massless in spite of explicit breaking of the chiral symmetry. It is expected that experimental signatures peculiar to CEP can be observed through spectral changes in the presence of abnormally light $\sigma$ mesons. As a candidate, the invariant-mass spectrum for diphoton emission is estimated with the chiral quark model incorporated. The results show the characteristic shape with a peak in the low energy region, which may serve as a signal for CEP. However, we find that the diphoton multiplicity is highly suppressed by infrared behaviors of the $\sigma$ meson. Experimentally, in such a low energy region below the threshold of two pions, photons from $\pi^0\to2\gamma$ are major sources of the background for the signal.