Chiral Phase Transition Research Articles

Probing exotic phases via stochastic gravitational wave spectra

Abstract Stochastic backgrounds of gravitational waves (GWs) from the pre-BBN era offer a unique opportunity to probe the universe beyond what has already been achieved with the Cosmic Microwave Background (CMB). If the source is short in duration, the low frequency tail of the resulting GW spectrum follows a universal frequency scaling dependent on the equation of state of the universe when modes enter the horizon. We demonstrate that the distortion of the equation of state due to massive particles becoming non-relativistic can lead to an observable dip in the GW spectrum. To illustrate this effect, we consider a first order chiral symmetry breaking phase transition in the weak-confined Standard Model (WCSM). The model features a large number of pions and mostly elementary fermions with masses just below the critical temperature for the phase transition. These states lead to a 20% dip in the GW power. We find potential sensitivity to the distortions in the spectrum to future GW detectors such as LISA, DECIGO, BBO, and μAres.

Exploring the chiral and deconfinement phase transitions in a self-consistent PNJL model

Exploring the chiral and deconfinement phase transitions in a self-consistent PNJL model

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.

Interplay of baryonic chiral partners in fluctuations of netbaryon number density

In this contribution, we use the parity doublet model to investigate the fluctuations of the net-baryon number density. We discuss the systematics of the susceptibilities and their ratios for nucleons of positive and negative parity, as well as their correlator. We demonstrate that the fluctuations of positiveparity nucleon do not reflect the fluctuations of the total net-baryon number at the chiral phase transition.

Microscopic origin of criticality at macroscale in QCD chiral phase transition

We reveal that the criticality of the chiral phase transition in QCD at the macroscale arises from the microscopic energy levels of its fundamental constituents, the quarks. We establish a novel relation between cumulants of the chiral order parameter (i.e., chiral condensate) and correlations among the energy levels of quarks (i.e., eigenspectra of the massless Dirac operator), which naturally leads to a generalization of the Banks-Casher relation. Based on this novel relation and through (2+1)-flavor lattice QCD calculations using the HISQ action with varying light quark masses in the vicinity of the chiral phase transition, we demonstrate that the correlations among the infrared part of the Dirac eigenspectra exhibit same universal scaling behaviors as expected of the cumulants of the chiral condensate. We find that these universal scaling behaviors extend up to the physical values of the up and down quark masses.

Shear viscosity coefficient of magnetized QCD medium with anomalous magnetic moments near chiral phase transition

Shear viscosity coefficient of magnetized QCD medium with anomalous magnetic moments near chiral phase transition

Temperature and volume dependence of pion-pion scattering lengths* *Supported by the Fostering Program in Disciplines Possessing Novel Features for Natural Science of Sichuan University (2020SCUNL209)

The s-wave pion-pion scattering lengths and are studied at finite temperature and in finite spatial volume under the framework of the Nambu–Jona-Lasinio model. The behavior beyond the pseudo transition temperature is investigated using proper time regularization. The scattering length exhibits singularity near the Mott temperature, and is a continuous but non-monotonic function of temperature. We present the effect of finite volume on the scattering length and find that can be negative and its singularity disappears at small volumes, which may hint at the existence of a chiral phase transition with decreasing volume.

A new technique to incorporate multiple fermion flavors in tensor renormalization group method for lattice gauge theories

We propose a new technique to incorporate multiple fermion flavors in the tensor renormalization group method for lattice gauge theories, where fermions are treated by the Grassmann tensor network formalism. The basic idea is to separate the site tensor into multiple layers associated with each flavor and to introduce the gauge field in each layer as replicas, which are all identified later. This formulation, after introducing an appropriate compression scheme in the network, enables us to reduce the size of the initial tensor with high efficiency compared with a naive implementation. The usefulness of this formulation is demonstrated by investigating the chiral phase transition and the Silver Blaze phenomenon in 2D Abelian gauge theories with Nf flavors of Wilson fermions up to Nf = 4.

Splitting of chiral and deconfinement phase transitions induced by rotation

Splitting of chiral and deconfinement phase transitions induced by rotation

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

(Pseudo) Scalar mesons in a self-consistent NJL model* *X.W. is supported by the Start-up Funding of Jiangsu University(4111190010) and the Natural Science Foundation of China (12147103)

In this study, we investigate the mass spectra of π and σ mesons at finite chemical potential using the self-consistent NJL model and the Fierz-transformed interaction Lagrangian. The model introduces an arbitrary parameter α to reflect the weights of the Fierz-transformed interaction channels. We show that, when α exceeds a certain threshold value, the chiral phase transition transforms from a first-order one to a smooth crossover, which is evident from the behaviors of the chiral condensates and meson masses. Additionally, at a high chemical potential, the smaller the value of α, the higher the masses of the π and σ mesons. Moreover, the Mott and dissociation chemical potentials increase with the increase in α. Thus, the meson mass emerges as a valuable experimental observable for determining the value of α and investigating the properties of the chiral phase transition in dense QCD matter.

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.

CFTs with $\mathbf{U(m)\times U(n)}$ global symmetry in 3D and the chiral phase transition of QCD

Conformal field theories (CFTs) with U(m)\times U(n)U(m)×U(n) global symmetry in d=3d=3 dimensions have been studied for years due to their potential relevance to the chiral phase transition of quantum chromodynamics (QCD). In this work such CFTs are analyzed in d=4-\varepsilond=4−ε and d=3d=3. This includes perturbative computations in the \varepsilonε and large-nn expansions as well as non-perturbative ones with the numerical conformal bootstrap. New perturbative results are presented and a variety of non-perturbative bootstrap bounds are obtained in d=3d=3. Various features of the bounds obtained for large values of nn disappear for low values of nn (keeping m<nm<n fixed), a phenomenon which is attributed to a transition of the corresponding fixed points to the non-unitary regime. Numerous bootstrap bounds are found that are saturated by large-nn results, even in the absence of any features in the bounds. A double scaling limit is also observed, for mm and nn large with m/nm/n fixed, both in perturbation theory as well as in the numerical bootstrap. For the case of two-flavor massless QCD existing bootstrap evidence is reproduced that the chiral phase transition may be second order, albeit associated to a universality class unrelated to the one usually discussed in the \varepsilonε expansion. Similar evidence is found for the case of three-flavor massless QCD, where we observe a pronounced kink.

Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States.

The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo-based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.

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.

The finite volume effects on the critical endpoint of chiral phase transition in Nambu–Jona-Lasinio model with different regularization schemes

In this paper, we study the influence of different regularization schemes on the critical endpoint (CEP) of chiral phase transition within a cubic box with volume [Formula: see text]. A two-flavor Nambu–Jona-Lasinio model at finite temperature [Formula: see text] and chemical potential [Formula: see text] is adopted as the effective model of the strong interacting matter. Due to the finite volume of the box, the momentum integral in gap equation is replaced by discrete summation, and an anti-periodic boundary condition for quark field is applied. We employ the Schwinger’s proper time and the Pauli–Villars regularization (PVR) schemes, respectively. It is found that the first-order phase transition line displays an intriguing “staircase” behavior, and eventually disappears as [Formula: see text] increases. In particular, there is no existence of the CEP for both regularization schemes in infinite volume limit [Formula: see text]. However, for the finite volume, the locations of the CEPs with proper time and PVR are determined, respectively.

Influence of gauge boson mass on dynamical mass generation and chiral phase transition in thermal QED3

In this work, we quantitatively explore how a finite gauge boson mass affects dynamical mass generation and the chiral phase transition in thermal QED3. To this end, we numerically solve the Dyson–Schwinger equations by considering the contributions coming from the wave function renormalization and the spatial part of the boson propagator at first and then compute the chiral condensate and some of thermodynamic quantities. It is found that the wave function renormalization and the spatial part of the boson propagator are crucial for the numerical solutions of the dressing functions and the value of critical temperature. The behaviors of the thermodynamic quantities and the chiral condensate as a function of temperature consistently imply that the chiral phase transition is none other than a second order one. That critical temperature decreases with increasing gauge boson mass verifies that the gauge boson mass will weaken the interactions between fermions and so suppress dynamical mass generation.

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.

Chiral phase transition of a dense, magnetized and rotating quark matter

We investigate the chiral symmetry restoration/breaking of a dense, magnetized and rotating quark matter within the Nambu Jona–Lasinio model including Nf=2 and Nc=3 numbers of flavors and colors, respectively. Imposing the spectral boundary conditions as well as the positiveness of energy levels lead to a correlation between the magnetic and rotation fields such that strongly magnetized plasma can not rotate anymore. We solve the gap equation at zero and finite temperature. At finite temperature and baryon chemical potential μB, we sketch the phase diagrams Tc(μB) and Tc(RΩ) in different cases. As a result, we always observe inverse-rotational catalysis mean to decrease Tc by increasing RΩ. But the magnetic field has a more complex structure in the phase diagram. For slowly rotating plasma, we find that Tc decreases by increasing eB, while in the fast rotating plasma we see that Tc increases by increasing eB. Also, we locate exactly the position of Critical End Point by solving the equations of first and second derivatives of effective action with respect to the order parameters, simultaneously.

Magnetic catalysis in the ( 2+1 )-dimensional Gross-Neveu model

We study the Gross-Neveu model in $2+1$ dimensions in an external magnetic field $B$. We first summarize known mean-field results, obtained in the limit of large flavor number $N_\mathrm{f}$, before presenting lattice results using the overlap discretization to study one reducible fermion flavor, $N_\mathrm{f}=1$. Our findings indicate that the magnetic catalysis phenomenon, i.e., an increase of the chiral condensate with the magnetic field, persists beyond the mean-field limit for temperatures below the chiral phase transition and that the critical temperature grows with increasing magnetic field. This is in contrast to the situation in QCD, where the broken phase shrinks with increasing $B$ while the condensate exhibits a non-monotonic $B$-dependence close to the chiral crossover, and we comment on this discrepancy. We do not find any trace of inhomogeneous phases induced by the magnetic field.