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We investigate the gravitational wave spectrum induced by first-order QCD phase transitions including the deconfinement phase transition in the pure gluon system and Friedberg-Lee model, and chiral phase transition in the quark-meson model and Polyakov quark-meson model. The gravitational wave power spectra are sensitive to the phase transition rate $\beta/H$. All QCD models predict a rather large phase transition rate in the order of $\beta/H\sim10^4$ at high temperature region, and the produced gravitational waves lie in the peak frequency region of $10^{-4}-0.01 {\rm Hz}$, corresponding to an energy spectrum in the range of $10^{-8}-10^{-7}$, which can be detected by LISA and Taiji. If a high baryon density is generated through Affleck-Dine baryogenesis or other mechanisms, the baryon chemical potential significantly reduces the phase transition rate, potentially dropping it to the order of $\beta/H\sim 10^1$, leading to the production of nanohertz gravitational waves. Furthermore, a critical quark chemical potential exists with a zero phase transition rate $\beta/H=0$, indicating that the false vacuum will not decay, thus supporting the formation of primordial quark nuggets in the early universe., Comment: 22 pages

The first-order QCD phase transition at high temperature features a large transition rate in the magnitude of $\beta/H \sim 10^4$ with induced stochastic gravitational waves typically lying in the LISA range. High baryon density in the early universe can be generated through Affleck-Dine baryogenesis. The baryon chemical potential enhances the potential barrier and significantly reduces the transition rate, which decreases from infinity at the critical end point (CEP) to zero at the critical nucleation point (CNP). Nanohertz gravitational waves can be produced in a narrow window of high baryon chemical potential with transition rate in the order of $\beta/H \sim 10^1$. When the phase transition rate reaches zero, the false vacuum of high baryon density quark matter is unlikely to decay and can persist over cosmological time scales. Therefore the primordial quark nuggets (PQN) can form and survive in the early universe as the seeds of compact stars, thereby dramatically accelerating the evolution of compact stars and the formation of galaxies, which may explain the high red-shift massive galaxies observed by the James Webb Space Telescope., Comment: 3 figures

The properties of QCD matter at finite isospin densities are investigated employing holographic hard-wall and soft-wall AdS/QCD models. It is confirmed that at high enough isospin densities, charged pions start to condense and the pion superfluid phase appears in the system. It is shown that the chiral condensate and the pion condensate can be transformed to each other and form a `chiral circle' in the superfluid phase. We derived the Equation of State (EoS) for pionic matter, calculated the normalized trace anomaly $\Delta$ and $(\epsilon-3p)/m_\pi^4$, and analyzed the sound speed and adiabatic index. Additionally, we provided data on the mass-radius relation and tidal deformability of pion stars. The results indicate that the holographic models align well with lattice QCD concerning isospin density, axial-vector condensation, EoS, and trace anomaly, though discrepancies in sound speed and adiabatic index emerge at higher isospin chemical potentials. The holographic models closely match those from chiral perturbation theory ($\chi$PT), suggesting that they can be considered as five-dimensional description of $\chi$PT., Comment: 24 pages, 5 figures

We discuss the effect of the quark anomalous magnetic moment (AMM) on the neutral dense quark matter under magnetic fields based on the Nambu-Jona-Lasinio (NJL) model at finite baryon density. To address its correlation with the chiral symmetry, we consider a simplified situation: the model includes the two-quark flavors under constant magnetic fields, and incorporates the effective interaction of the quark AMM linked to the spontaneous chiral symmetry breaking. We then examine the equation of state (EoS) in cases with and without magnetization for anatomizing the thermodynamic quantities. Without the magnetization, a small magnetic field stiffens the EoS, but with increasing the magnetic field, the EoS tends to soften. The stiffness of the EoS is found to be influenced by the magnetic effect on the critical chemical potential of the chiral phase transition and the quark number density at this critical point. As a result, the mass and radius of the neutral dense quark matter increase with the small magnetic field but turn to decrease as the magnetic field further increases. By including the quark AMM, the critical chemical potential is decreased and the quark number density takes a smaller value. Thus, for the stronger magnetic fields, the quark AMM suppresses the softening effect of the magnetic field on the EoS, leading to increased mass and radius compared to when the quark AMM is absent. In contrast, for the small magnetic field, the contribution of the quark AMM to the EoS is marginal. When the magnetization is taken into account, the magnetic effect on the stiffness of the EoS is overshadowed by the contribution of the magnetization, and the significance of the quark AMM also becomes invisible in the mass-radius relation., Comment: 16 pages, 7 figures

Magnetic fields in heavy-ion collisions are pivotal and subject to diverse factors. In this study, we quantitatively investigate the impact of fluid vorticity on the evolution of magnetic fields in the 20-50\% centrality class in Au+Au collisions, with collision energies of $\sqrt{s_{NN}}=(7.7, 14.5, 19.6, 27, 39, 62.4, 200)$ GeV. Our results indicate that fluid vorticity leads to a delay in the evolution of the magnetic field, in which this effect becomes more pronounced as the collision energy decreases. Additionally, we have calculated the mean magnetic field values on the freeze-out hypersurface for various collision energies. Our simulation results align with the values inferred from experimental data of $\bar{\Lambda}-\Lambda$, within the error margins.

We propose a novel mechanism that the spin alignment of vector meson $\phi$ and $K^{*0}$ in most central heavy ion collisions is induced by intrinsic QCD dynamics without external vortical/ magnetic fields. The local spin density fluctuation of quarks due to the axial-vector and tensor interactions between quarks can induce the spin alignments of vector meson. It is found that axial-vector interaction results in $\rho_{00}<1/3$ for the spin alignment of $\phi$ meson, while tensor interaction results in $\rho_{00}>1/3$. We argue that the spin alignment of $K^{*0}$ due to the spin density fluctuation from flavor-mixing would be a signature or hint of instanton., Comment: 9 pages,4 figures

We investigate the effects of rotation on deconfinement and chiral phase transitions in the framework of dynamical holographic QCD model. Instead of transforming to the rotating system by Lorentz boost, we construct an anisotropic gravitational background by incorporating the rotating boundary current. We firstly investigate the pure gluon system under rotation to extract deconfinement phase transition from the Polyakov loop then add 2-flavor probe for chiral restoration phase transition from the chiral condensate. It is observed that at low chemical potentials, the deconfinement phase transition of pure gluon system is of first order and the chiral phase transition of 2-flavor system is of crossover. Both the critical temperatures of deconfinement and chiral phase transitions decrease/increase with imaginary/real angular velocity ($\Omega_I/\Omega$) as $T/T_c\sim 1- C_2 \Omega_I^2$ and $T/T_c\sim 1+ C_2 \Omega^2$, which is consistent with lattice QCD results. In the temperature-chemical potential $T-\mu$ phase diagram, the critical end point (CEP) moves towards regions of higher temperature and chemical potential with real angular velocity.

QCD phase diagram in the $T - \mu$ plane and the equation of state for pure gluon, 2-flavor, 2+1-flavor systems, and 2+1+1-flavor systems have been investigated using the Einstein-Maxwell-Dilaton (EMD) framework at finite temperature and chemical potential. By inputting lattice QCD data for the equation of state and baryon susceptibility at zero chemical potential into holographic model, all the parameters can be determined with the aid of machine learning algorithms. Our findings indicate that the deconfinement phase transition is of first order for the pure gluon system with critical temperature $T_c = 0.265 \rm GeV$ at vanishing chemical potential. The phase transition for the 2-flavor, 2+1-flavor systems, and 2+1+1-flavor systems are crossover at vanishing chemical potential and first-order at high chemical potential, and the critical endpoint(CEP) in the $T - \mu$ plane locates at ($\mu_B^c$=0.46 GeV, $T^c$=0.147 GeV), ($\mu_B^c$ = 0.74 GeV, $T^c$ = 0.094 GeV), and ($\mu_B^c$= 0.87 GeV,$T^c$ = 0.108 GeV), respectively. Additionally, the thermodynamic quantities of the system for different flavors at finite chemical potential are presented in this paper. It is observed that the difference between the 2+1 flavor and 2+1+1 flavor systems is invisible at vanishing chemical potential and low temperature. The location of CEP for 2+1+1 flavor system deviates explicitly from that of the 2+1 flavor system with the increase of chemical potential. Both 2+1 flavor and 2+1+1 flavor systems differ significantly from the 2-flavor system.

The bubble wall velocity in the first order phase transition plays an important role in determining both the amplitude and the pivot frequency of stochastic gravitational wave background. In the framework of the minimal left-right symmetric model, we study the wall velocity when the first order phase transition can occur. The wall velocity can be determined by matching the distribution functions in the free particle approximation and the local thermal equilibrium approximation. It is found that the wall velocity can be determined in the range $ 0.2 < v_w < 0.5 $ for the parameter space with the first order phase transition. It is also found that for the case when the wall velocity is close to the speed of sound, the peak amplitude of gravitational wave spectrum can be larger than that in the runaway case. Moreover, It is also found that there exists an approximate power law between the wall velocity and pressure difference between broken and symmetry phases, and the power index is equal to 0.41 or so., Comment: 22 pages, 12 figures

In the SMASH-CLVisc-hybrid framework, including SMASH for the initial conditions and the hadronic rescattering stage, and CLVisc for the quark gluon plasma (QGP) evolution, we investigate net baryon number fluctuations via considering the equation of state (EoS) with and without a critical end point (CEP) in the QCD phase transition. Specifically, two distinct QCD EoS are utilized: one with smooth crossover derived from NEOS and another with a critical end point sourced from the rPNJL model. Our results show that non-monotonic behavior of $\kappa\sigma^2$ is not observed above the collision energy $7.7 {\rm GeV}$, nor are there explicit differences between the EoS characterized by crossover and that by CEP. This could be attributed to the significant deviation of the freeze-out line from the location of CEP. It is also found that the pure SMASH result of $\kappa \sigma^2$ is positive and close to zero at 3 GeV, which is different from the negative value observed from STAR.

In the framework of Nambu--Jona-Lasinio model beyond mean field approximation, the effects of pion fluctuations on (inverse) magnetic catalysis and magnetic susceptibility are studied. The negative magnetic susceptibility at low temperature is observed when contributions from both neutral and charged pions are taken into account. In weak field approximation, it is observed that at finite temperature, the magnetic inhibition effect in the chiral limit, resulting from the difference between the transverse and longitudinal velocities of neutral pions, converts to weak magnetic catalysis when considering a non-zero current quark mass. Moreover, the magnetic catalysis is amplified by the charged pions., Comment: 16 pages, 8 figures

By using the extrapolation method, a polarized Polykov-loop potential at finite real angular velocity is constructed from the lattice results at finite imaginary angular velocity. The chiral and deconfinement phase transitions under rotation have been simultaneously investigated in the Polarized-Polyakov-loop Nambu-Jona-Lasinio (PPNJL) model. It is observed that both critical temperatures of deconfinement and chiral phase transition increase with the angular velocity, which is in consistent with lattice results. The spin alignment of vector meson has the negative deviation of $\rho_{00} -1/3$ under rotation, and the deviation in the PPNJL model is much more significant than that in the NJL model and the quark coalescence model, which revealing the important role of rotating gluons on the quark polarization., Comment: 10 pages, 6 figures

Based on lattice QCD results of equation of state (EOS) and baryon number susceptibility at zero baryon chemical potential, and supplemented by machine learning techniques, we construct the analytic form of the holographic black hole metric in the Einstein-Maxwell-Dilaton (EMD) framework for pure gluon, 2-flavor, and 2+1-flavor systems, respectively. The dilaton potentials solved from Einstein equations are in good agreement with the extended non-conformal DeWolfe-Gubser-Rosen (DGR) type dilaton potentials fixed by lattice QCD EOS, which indicates the robustness of the EMD framework. The predicted critical endpoint (CEP) in the 2+1-flavor system is located at $(T^c$=0.094GeV, $\mu^c_B$=0.74GeV), which is close to the results from the realistic Polyakov-Nambu-Jona-Lasinio(PNJL) model, the functional renormalization group, and the holographic model with extended DeWolfe-Gubser-Rosen dilaton potential.

We investigate the effect of charm quark on the chiral phase transition of light quarks at finite temperature based on the four-flavor soft-wall holographic QCD model. In the massless limit, we find that the thermal chiral phase transition is of the second order in the four-quark flavor system. In the case with the massive charm quark and the massless light and strange quarks, the order of the phase transition changes to the first order. This is due to the quark flavor symmetry breaking which is associated with the violation of the $U(1)$ axial symmetry. Once the light and strange quarks get massive, the explicit chiral symmetry breaking becomes eminent, then the crossover phase transition is realized at the physical quark masses. We also map the order of the phase transition on a phase diagram in the quark mass plane where the light- and strange-quark masses are degenerate but differ from the value of the charm quark mass. This phase diagram is an extension of the conventional Columbia plot to the four-quark flavor system. The critical exponents related to the chiral phase transition are also addressed., Comment: We have updated some parts of the text and added a subsection on critical exponents

Built upon the state-of-the-art model a multiphase transport (AMPT), we develop a new module of chiral anomaly transport (CAT), which can trace the evolution of the initial topological charge of gauge field created through sphaleron transition at finite temperature and external magnetic field in heavy ion collisions. The eventual experimental signals of chiral magnetic effect(CME) can be measured. The CAT explicitly shows the generation and evolution of the charge separation, and the signals of CME through the CAT are quantitatively in agreement with the experimental measurements in Au+Au collision at $\sqrt{s}=200 {\rm GeV}$, and the centrality dependence of the CME fraction follows that of the fireball temperature., Comment: 7 pages, 6 figures

We investigate semileptonic form factors of $D_{(s)}$ meson from a modified soft-wall 4-flavor holographic model. The model successfully reproduces the masses and decay constants of various mesons, including $\rho$, $K^*$, $D^*$, $D_s^*$, $a_1$, $K_1$, $f_1$, $D_1$,$D_{s1}$, $\pi$, $K$, $\eta$, $D$, and $D_s$. Moreover, we study the semileptonic decay processes $D^{+} \to (\pi, K, \eta) l^{+} \nu_{l}$ and $D_{s}^{+} \to ( K, \eta) l^{+} \nu_{l}$, associated with the vector meson exchange, as well as $D_{(s)}^{+} \to K^{} l^{+} \nu_{l}$, associated with the vector and axial vector meson exchange. The form factors $f_{+}(q^{2})$ for $D \to\pi$ and $D_{(s)}\to K$ decays agree excellently with experimental and lattice data, outperforming other theoretical approaches. The $f_{+}(q^{2})$ form factor for $D^{+} \to \eta $ is compatible with experimental data, while a slight discrepancy is observed for $D_{s}^{+} \to \eta $ at large $q^{2}$. Additionally, we predict the vector form factors $V(q^{2})$ and $A_{1}(q^{2})$ for $D \to K^{}$ and $D_{s} \to K^{}$ decays, respectively. The results agree well with other approaches and lattice data at maximum recoil ($q^{2}=0$)., Comment: arXiv admin note: text overlap with arXiv:2308.14975

In this study, we employ a modified soft-wall holographic model with four flavors to investigate the meson spectra, decay constants, electromagnetic form factors, and charge radius of various mesons. We obtain the spectra for vector, axial vector, and pseudoscalar mesons. Decay constants are calculated and compared with experimental and lattice QCD data. The pion and kaon electromagnetic form factors are compared with the experimental data, and a good agreement is achieved for the kaon at low $Q^{2}$. For the charmed mesons, the electromagnetic form factors of the $D$ and $D_{s}$ and electric form factors of the $D^{*}$ and $D_{s}^{*}$ are well consistent with the lattice QCD data. Moreover, the electric, magnetic, and quadrupole form factors are predicted for the $\rho$, $K^{*}$, $a_1$, $K_1$, $D_1$, and $D_{s1}$ mesons. Furthermore, the charge radius of the vector, axial vector, and pseudoscalars, including the strange and charmed mesons, are computed.

There has been significant interest in recent years in studying the spin polarization of hyperons in heavy-ion collisions. However, describing the dynamic spin polarization of quarks in quark-gluon plasma fireballs in detail presents a significant challenge. In this study, we conducted a phenomenological investigation of the dynamical spin polarization of quarks induced by the magnetic field at the pre-thermal stage in heavy-ion collisions using the recently developed theoretical tool of chiral kinetic theory. This study presents a comprehensive analysis of the dynamic process of quark spin polarization induced by magnetic fields. Our findings demonstrate that the spin polarization of quarks is highly sensitive to the interactions between quarks. These interactions can delay the decay of the early spin polarization vector while accelerating the decay of the later spin polarization vector. Specifically, our simulations model the detailed process of how magnetic fields polarize quarks within the fireball by the average spin vector and reveal that quark interactions lead to an acceleration effect on the average spin, causing it to rapidly increase from zero before being rapidly destroyed. Notably, the induced magnetic field in the fireball has an incomplete electromagnetic response effect, and its increase in the opposite direction of the external magnetic field decaying has a delay effect.

The chiral and deconfinement phase transitions under rotation have been simultaneously investigated in the Polyakov-Nambu-Jona-Lasinio (PNJL) model. An interesting observation has been found that the chiral phase transition is catalyzed and the deconfinement phase transition is decelerated by rotation, therefore a chiral symmetric but confined phase is induced by rotation, which indicates that chiral dynamics and gluon dynamics can be split by rotation., Comment: 9 pages, 5 figures

Two critical end points (CEPs) of the chiral phase transition and the nuclear liquid-gas phase transition show up at finite baryon chemical potential. The kurtosis $\kappa\sigma^2$ of baryon number fluctuation on the $T-\mu_B$ plane is positive on the first-order side and negative on the crossover side along the phase boundary. The freeze-out line extracted from the heavy ion collisions crosses between these two phase boundaries, one can observe a peak of $\kappa\sigma^2$ around the collision energy $5 {\rm GeV}$ near the CEP of the chiral phase transition, and negative $\kappa\sigma^2$ at low collision energies due to the CEP of the nuclear liquid-gas phase transition. This expalains the experimental measurement of $\kappa\sigma^2$ at the collision energies of 2.4 GeV at HADES and 3 GeV and 7.7-200 GeV at STAR for most central collision. Thus we propose that the baryon number fluctuation $\kappa\sigma^2$ can be used as a probe of nuclear matter phase structure at high baryon density., Comment: 5 pages, 3 figures

We calculated the masses of neutral and charged pion and pion decay constants under an extra magnetic field at zero temperature. The quantum fluctuations are integrated through the functional renormalization group. We consider the quark and meson propagators in the Landau level representation and weak-field expansion, respectively. The neutral pion mass monotonically decreases with the magnetic field, while the charged pion mass monotonically increases with the magnetic field. The pion decay constant and the quark mass show the magnetic catalysis behavior at vanishing temperature. The neutral pion mass and pion decay constant are quantitatively in agreement with the lattice QCD results in the region of $eB < 1.2 {\rm GeV}^2$, and no non-monotonic mass behavior for charged pion has been observed in this framework., Comment: 10 pages, 5 figures

Vorticities in heavy-ion collisions (HICs) are supposed to induce spin alignment and polarization phenomena of quarks and mesons. In this work, we analyze the spin alignment of vector mesons $\phi$ and $\rho$ induced by rotation from quark dynamics in the framework of the Nambu-Jona-Lasinio (NJL) model. The rotating angular velocity induces mass splitting of spin components for vector $\phi,\rho$ mesons $M_{\phi,\rho}(\Omega)\simeq M_{\phi,\rho}(\Omega=0)-s_{z}\Omega$. This behavior contributes to the spin alignment of vector mesons $\phi,\rho$ in an equilibrium medium and naturally explains the negative deviation of $\rho_{00}-1/3$ for vector mesons. Incidentally, the positive deviation of $\rho_{00}-1/3$ under the magnetic field can also be easily understood from quark dynamics., Comment: 12 pages, 8 figures

Anomalous magnetic moment (AMM) of quarks in presence of an external magnetic field has been explored using a nonlocal Nambu\textemdash Jona-Lasinio (NJL) model. Various strengths of AMM differing in orders of magnitude are used in the literature. We explore them in our nonlocal framework to decide on their strength. We checked the validity of using constant AMM of quarks and investigate two different temperature and magnetic field dependent forms. The forms are taken as the AMM being proportional to the i) meanfield and the ii) square of the meanfield. On comparison with the lattice data for both the condensate averages and differences, it turns out that the second choice is the most suitable one, in such an effective model scenario. In the process, we also keep track of the phase diagram in the $T-eB$ plane arising from our model calculation. The outcome is reasonable as far as the lattice QCD result is concerned., Comment: 13 pages, 8 captioned figures, Comments are welcome

The simplest version of the dynamical holographic QCD model is described by adding the KKSS model action on a dilaton-graviton coupled background, in which the AdS$_5$ metric is deformed by the gluon condensation and further deformed by the chiral condensation. In this framework, both the chiral symmetry breaking and linear confinement can be realized, the light-flavor hadron spectra and the pion form factor were investigated but it was difficult to reconcile the light-flavor hadron spectra and pion form factor. By considering the anomalous 5-dimension mass correction of the scalar field from QCD running coupling, it is found that the light flavor hadron spectra and pion form factor can be described well simultaneously, especially the ground state and lower excitation states of scalar, pseudo scalar and axial vector meson spectra are improved, but the vector meson spectra is not sensitive to the anomalous 5-dimension mass correction of the scalar field., Comment: 14 pages, 5 figures

The magnetic fields in heavy-ion collisions are important ingredients for many interesting phenomena, such as the Chiral Magnetic Effect, Chiral Magnetic Wave, the directed flow $v_1$ of $D^0$ mesons and the splitting of the spin polarization of the $\Lambda$/$\bar{\Lambda}$. Quantitative studies of these phenomena however suffer from limited understanding on the dynamical evolution of these fields in the medium created by the collisions, which remains a critical and challenging problem. The initial magnetic fields from the colliding nuclei decay very fast in the vacuum but their lifetime could be extended through medium response due to electrically conducting quarks and antiquarks. Here we perform a detailed analysis of such medium effect on the dynamical magnetic fields by numerically solving the Maxwell's equations concurrently with the expanding medium described by viscous hydrodynamics, under the assumption of negligible back reaction of the fields on the fluid evolution. Our results suggest a considerable enhancement of late time magnetic fields, the magnitude of which depends sensitively on the fireball expansion as well as the medium electric conductivity both before and during hydrodynamic stage., Comment: 15 pages, 7 figures

We investigate the bounce solution in the holographic QCD and electroweak models with first-order phase transition. The strength parameter $\alpha$, inverse duration time $\beta/H$, and bubble wall velocity $v_w$ in the gravitational wave power spectra are calculated by holographic bounce solution. In contrast to the results of field theory, we find the parameter $\alpha$ is about $\mathcal{O}(1)$ and $\beta/H$ is about $10^4$, which imply that the phase transition is fast and strong. The critical, nucleation and percolation temperatures of the phase transition are close to each other in the holographic model. In addition, the velocity $v_w$ is found to be less than the sound speed of the plasma $c_{s}=1/\sqrt{3}$, which corresponds to the deflagration scenario. For QCD phase transition, the gravitational wave power spectrum can reach $10^{-13}-10^{-14}$ around the peak frequency of 0.01 Hz, which can be detected by BBO and Ultimate-DECIGO. For electroweak phase transition, the gravitational wave power spectrum can reach $10^{-12}-10^{-16}$ around the peak frequency $1-10$ Hz. Moreover, the primordial black hole is not favorable for formation due to the large parameter $\beta/H$ and small velocity $v_w$.

We study the anisotropies of gravitational waves induced by weak hypermagnetic fields which are randomly distributed and oriented during the electroweak phase transition in the early universe. The theory setup of this study is the standard model plus a real singlet scalar field, which can produce the needed strongly first order electroweak phase transition. Then we investigate how the hypermagnetic fields can convert to magnetic fields and we compute the departure of energy difference between the symmetric phase and the broken phase when the magnetic fields are turned on. It is found that the presence of the hypermagnetic fields can increase the Euclidean action, thus can decrease nucleation temperature, which can lead to a supercool plasma. We point out that the hypermagnetic field can enhance the gravitational wave production from a first order electroweak phase transition and the inhomogeneity of primordial hypermagnetic field can lead to anisotropies of gravitational waves. By examining three well-motivated distribution of hypermagnetic fields, we calculate the corresponding angular power spectra of stochastic gravitational wave background and find they can be significantly larger than the contributions of the Sachs-Wolfe effects and integrated Sachs-Wolfe effects. Our results show that the anisotropies of gravitational wave could provide a novel probe to the primordial hypermagnetic field in the electroweak phase transition epoch., Comment: 17 pages, 9 figures