First-order Chiral Phase Transition Research Articles

Convergence of Ginzburg–Landau Expansions: Superconductivity in the Bardeen–Cooper–Schrieffer Theory and Chiral Symmetry Breaking in the Nambu–Jona-Lasinio Model

Abstract We study the convergence of the Ginzburg–Landau (GL) expansion in the context of the Bardeen–Cooper–Schrieffer (BCS) theory for superconductivity and the Nambu–Jona-Lasinio (NJL) model for chiral symmetry breaking at finite temperature T and chemical potential μ. We present derivations of the all-order formulas for the coefficients of the GL expansions in both systems under the mean-field approximation. We show that the convergence radii for the BCS gap Δ and dynamical quark mass M are given by Δconv = πT and $M_{\rm conv} = \sqrt{\mu ^2 + (\pi T)^2}$, respectively. We also discuss the implications of these results and the quantitative reliability of the GL expansion near the first-order chiral phase transition.

Gravitational Waves from Nnaturalness

We study the prospects for probing the Nnaturalness solution to the electroweak hierarchy problem with future gravitational wave observatories. Nnaturalness, in its simplest incarnation, predicts N copies of the Standard Model with varying Higgs mass parameters. We show that in certain parameter regions the scalar reheaton transfers a substantial energy density to the sector with the smallest positive Higgs squared mass while remaining consistent with bounds on additional effective relativistic species. In this sector, all six quarks are much lighter than the corresponding QCD confinement scale, allowing for the possibility of a first-order chiral symmetry-breaking phase transition and an associated stochastic gravitational wave signal. We consider several scenarios characterizing the strongly-coupled phase transition dynamics and estimate the gravitational wave spectrum for each. Pulsar timing arrays (SKA), spaced-based interferometers (BBO, Ultimate-DECIGO, μAres, asteroid ranging), and astrometric measurements (THEIA) all have the potential to explore new regions of Nnaturalness parameter space, complementing probes from next generation cosmic microwave background radiation experiments.

Probing the QCD phase transition with hadron multiplicity ratios

We investigate the impact of a first-order chiral phase transition and critical point on hadron multiplicity ratios. We model the dynamical expansion of the hot and dense matter created in a heavy ion collision with a Bjorken hydrodynamics expansion coupled to the explicit evolution of the chiral order parameter at center-of-mass energies from 2 to 7 GeV. Hereby, the chiral dynamics is implemented using a Langevin equation including dissipation and noise. We find a strong enhancement of the entropy-per-baryon S/A at lowest energies which is created at the non-equilibrium first-order phase transition. By mapping the initial and final S/A to a hadron resonance gas, we can quantify the shift of hadron multiplicity ratios.

Supercool exit: Gravitational waves from QCD-triggered conformal symmetry breaking

Classically conformal Standard Model extensions predict an intriguing thermal history of the early universe. In contrast to the common paradigm, the onset of the electroweak phase transition can be significantly delayed while the universe undergoes a period of thermal inflation. Then, a first-order chiral phase transition could not only trigger electroweak symmetry breaking but also initiate the exit from supercooling. To study the dynamics of this scenario, we focus on low-energy quark-based QCD effective models that exhibit a first-order transition. While a large amount of latent heat is naturally involved if thermal inflation ends, we find that a supercooling period prior to the QCD scale considerably enhances the timescale of the transition. This enhancement implies great observational prospects at future gravitational wave observatories. Our results are readily applicable to a wide class of scale-invariant SM extensions, as well as strongly coupled dark sectors.

Baryon-rich QCD matter

Properties of high-density strong-interaction matter of relevance for astrophysical scenarios that involve neutron stars are discussed. It is argued that theoretical and experimental insights from the small baryo-chemical potential (µB ) and high-temperature regions of the QCD phase diagram can guide realistic model building at high density, as this regime is currently not accessible to first-principles numerical calculations of the QCD partition function. Special attention is payed to the chiral properties of high-density matter and the nature of a possible first-order chiral phase transition. In this transition hadronic parity-partners, in particular baryons, become spectrally degenerate with finite (pole) masses, as expected from general insight into the mass generation in QCD. Possible signals in heavy-ion dielectron production at beam energies of a few GeV are discussed. Based on evidence for an emergent ”chiral spin symmetry” above the pseudo-critical chiral transition temperature at small µB , speculations on the physical state of dense hadronic matter beyond the chiral phase transition are presented.

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.

Enhanced pion-to-proton ratio at the onset of the QCD phase transition

The pion-to-proton ratio is identified as a potential signal for a non-equilibrium first-order chiral phase transition in heavy-ion collisions, as the pion multiplicity is directly related to entropy production. To showcase this effect, a non-equilibrium Bjorken expansion starting from realistic initial conditions along a Taub adiabat is used to simulate the entropy production. Different dynamical criteria to determine the final entropy-per-baryon number are investigated and matched to a hadron resonance gas model along the chemical freeze out curve to obtain the final pion and proton numbers. We detect a strong enhancement of their multiplicity ratio at the energies where the system experiences a strong phase transition as compared to a smooth crossover which shows almost no enhancement.

Probing Compressed Baryonic Matter

The objective of the compressed baryonic matter (CBM) experiment at the future Facility for Antiproton and Ion Research (FAIR) in Darmstadt, Germany, is the investigation of the fundamental properties of strongly interacting matter. Of particular interest for our understanding of compact stellar objects is the determination of the equation-of-state (EOS) at high baryon densities and the exploration of the microscopic degrees-of-freedom under these conditions. The results of these laboratory experiments will complement astronomical observations, which also constrain the high-density EOS. Recent results of QCD-based calculations suggest that a possible first-order chiral phase transition should be observable in heavy-ion collisions at FAIR energies. This article reviews relevant observables from heavy-ion collisions and describes the detector configuration and the physics performance of the CBM experiment.

Mesons and diquarks in a color superconducting regime

The behavior of the mesons and diquarks is studied at finite temperatures, chemical potentials and densities, notably when the color superconductivity is taken into account. The Nambu and Jona-Lasinio model complemented by a Polyakov loop (PNJL description) has been adapted in order to model them in this regime. This paper focuses on the scalar and pseudoscalar mesons and diquarks, in a three-flavor and three-color description, with the isospin symmetry and at zero strange density. An objective of this work is to underline the modifications carried out by the color superconducting regime on the used equations and on the obtained results. It has been observed that the two-flavor color-superconducting (2SC) phase affects the masses and the coupling constants of the mesons and diquarks in a non-negligible way. This observation is particularly true at high densities and low temperatures for the pions, [Formula: see text] and the diquarks [ud] whose color is rg. This reveals that the inclusion of the color superconductivity in the modeling is relevant to describe the mesons and diquarks near the first-order chiral phase transition.

Compressibility of quark matter under strong magnetic field in the NJL model

The compressibility of magnetized quark matter is investigated in the SU(2) NJL model. The increases of the chemical potential and the temperature can reduce the compressibility, and lead to the much stiffer equation of state. The variation of the compressibility with the magnetic field will depend on the phase region. Due to the anisotropic structure, the compressibility is different in the directions parallel and perpendicular to the field. The discontinuity of longitudinal compressibility with the chemical potential and the temperature captures the signature of a first-order chiral phase transition and the crossover at high temperature. Moreover, the magnetic-field-and-temperature running coupling would have an important effect on the position of the phase transition. Under the lowest landau level approximation at zero temperature, the longitudinal compressibility has a direct inverse proportional relation to the magnetic field strength and the chemical potential square as ${\ensuremath{\kappa}}_{\mathrm{LLL},\ensuremath{\chi}}^{\ensuremath{\parallel}}\ensuremath{\propto}1/(eB{\ensuremath{\mu}}^{2})$.

Cumulants of the chiral order parameter in a nonequilibrium Bjorken expansion with a QCD critical point

To understand experimentally obtained net-proton number cumulants in the search for the QCD critical point, we study a dynamical model based on an effective quark-meson Lagrangian with chiral symmetry. We investigate the evolution of the expanding medium created in a heavy-ion collision using a spatially homogeneous fluid and a time-dependent order parameter, the sigma field evolved by a Langevin equation. We extract cumulants of the sigma field along a parametrized freeze-out curve and match the obtained freeze-out points to corresponding beam energies. These cumulants can be related to cumulants of the net-proton number through the sigma-proton coupling to provide a qualitative comparison to experimental data from STAR’s beam energy scan program. We demonstrate that the presence of the spinodal or mixed phase region around the first-order chiral phase transition allows for a wide interval of cumulants at the lowest beam energies.

Enhanced yield ratio of light nuclei in heavy ion collisions with a first-order chiral phase transition

Using a transport model that includes a first-order chiral phase transition between the partonic and the hadronic matter, we study the development of density fluctuations in the matter produced in heavy ion collisions as it undergoes the phase transition, and their time evolution in later hadronic stage of the collisions. Using the coalescence model to describe the production of deuterons and tritons from nucleons at the kinetic freeze out, we find that the yield ratio $ N_\text{t}N_\text{p}/ N_\text{d}^2$, where $N_\text{p}$, $N_\text{d}$, and $N_\text{t}$ are, respectively, the proton, deuteron, and triton numbers, is enhanced if the evolution trajectory of the produced matter in the QCD phase diagram passes through the spinodal region of a first-order chiral phase transition.

Restoration of chiral symmetry in cold and dense Nambu-Jona-Lasinio model with tensor renormalization group

We analyze the chiral phase transition of the Nambu-Jona-Lasinio model in the cold and dense region on the lattice, developing the Grassmann version of the anisotropic tensor renormalization group algorithm. The model is formulated with the Kogut-Susskind fermion action. We use the chiral condensate as an order parameter to investigate the restoration of the chiral symmetry. The first-order chiral phase transition is clearly observed in the dense region at vanishing temperature with μ/T ∼ O(103) on a large volume of V = 10244. We also present the results for the equation of state.

Chiral pasta: Mixed phases at the chiral phase transition

Interiors of neutron stars are ultra-dense and may contain a core of deconfined quark matter. Such a core connects to the outer layers smoothly or through a sharp microscopic interface or through an intermediate macroscopic layer of inhomogeneous mixed phases, which is globally neutral but locally contains electrically charged domains. Here I employ a nucleon-meson model under neutron star conditions that shows a first-order chiral phase transition at large densities. In the vicinity of this chiral transition I calculate the free energies of various mixed phases - different 'pasta structures' - in the Wigner-Seitz approximation. Crucially, chirally broken nuclear matter and the approximately chirally symmetric phase (loosely interpreted as quark matter) are treated on the same footing. This allows me to compute the interface profiles of bubbles, rods, and slabs fully consistently, taking into account electromagnetic screening effects and without needing the surface tension as an input. I find that the full numerical results tend to disfavor mixed phases compared to a simple step-like approximation used frequently in the literature and that the predominantly favored pasta structure consists of slabs with a surface tension $\Sigma \simeq 6\, {\rm MeV}/{\rm fm}^2$.

Fluctuations, criticality and nonequilibrium effect of the QCD matter

The multiplicity distributions of net-baryon number fluctuation in the first-order chiral phase transition associated with the nonequlibrium effect are investigated within the improved Polyakov–Nambu–Jona–Lasinio model. Compared with the idealized first-order transition in equilibrium, the calculation indicates that the density fluctuations in the metastable and unstable regions are more violent, which possibly affects the statistical distributions of density fluctuation in later stage of an expanding system. Signals induced by the first-order phase transition and those from the nonequilibrium effect are discussed in detail, which could be exploited to identify the first-order phase transition. Besides, the critical exponents of the thermodynamic quantities at both the critical end point and spinodal boundary are investigated.

Heavy holographic QCD

We study the phase structure of the Witten-Sakai-Sugimoto model in the plane of temperature and baryon chemical potential, including the effect of a nonzero current quark mass. Our study is performed in the decompactified limit of the model, which, at least regarding the chiral phase transition, appears to be closer to real-world QCD than the original version. Following earlier studies, we account for the quark mass in an effective way based on an open Wilson line operator whose expectation value is identified with the chiral condensate. We find that the quark mass stabilizes a configuration with string sources and point out that this phase plays an important role in the phase diagram. Furthermore, we show that the quark mass breaks up the first-order chiral phase transition curve and introduces critical points to the phase diagram. Similarities of the phase structure to other holographic approaches and to lattice simulations of “heavy QCD” are found and discussed. By making holographic QCD more realistic, our results open the door to a better understanding of real-world strongly coupled hot and dense matter.

Quarks and light (pseudo-)scalar mesons at finite chemical potential

We investigate the properties of light scalar and pseudoscalar mesons at finite (light) quark chemical potential. To this end we solve a coupled set of (truncated) Dyson-Schwinger equations for the quark and gluon propagators in Landau-gauge QCD and extend earlier results for $ N_{\mathrm{f}} = 2+1$ dynamical quark flavors to finite chemical potential at zero temperature. We then determine the meson bound state masses, wave functions, and decay constants for chemical potentials below the first-order phase transition from their homogeneous Bethe-Salpeter equation. We study the changes in the quark dressing functions and Bethe-Salpeter wave functions with chemical potential. In particular, we trace charge-conjugation parity breaking. Furthermore, we confirm the validity of the Silver-Blaze property: all dependencies of colored quantities on chemical potential cancel out in observables and we observe constant masses and decay constants up to and into the coexistence region of the first-order chiral phase transition.

Role of vector interaction and axial anomaly in the PNJL modeling of the QCD phase diagram

Effects of a flavor singlet vector interaction in the Polyakov–Nambu–Jona-Lasinio (PNJL) Model are studied in combination with the axial U(1) breaking Kobayashi–Maskawa–ʼt Hooft interaction, using an improved, consistent cutoff scheme. We confirm that the first-order chiral phase transition at moderate baryon chemical potentials and its critical point, a generic feature of NJL-type models without vector coupling, disappear for sufficiently large vector coupling strength gv. New results are presented concerning the curvature of the crossover boundary in the T–μ plane close to μ=0 and its dependence on gv.

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.

Nuclear chiral dynamics and phases of QCD

This presentation starts with a brief review of our current picture of QCD phases, derived from lattice QCD thermodynamics and from models based on the symmetries and symmetry breaking patterns of QCD. Typical approaches widely used in this context are the PNJL and chiral quark-meson models. It is pointed out, however, that the modeling of the phase diagram in terms of quarks as quasiparticles misses important and well known nuclear physics constraints. In the hadronic phase of QCD governed by confinement and spontaneously broken chiral symmetry, in-medium chiral effective field theory is the appropriate framework, with pions and nucleons as active degrees of freedom. Nuclear chiral thermodynamics is outlined and the liquid–gas phase transition is described. The density and temperature dependence of the chiral condensate is deduced. As a consequence of two- and three-body correlations in the nuclear medium, no tendency towards a first-order chiral phase transition is found at least up to twice the baryon density of normal nuclear matter and up to temperatures of about 100 MeV. Isospin-asymmetric nuclear matter and neutron matter are also discussed. An outlook is given on new tightened constraints for the equation-of-state of cold and highly compressed matter as implied by a recently observed two-solar-mass neutron star.