arXiv subjects

Yu-xin Liu

Publications and source records attributed to Yu-xin Liu.

At least 19 recordsLinked to original sources

arXiv2026

Extracting freeze-out conditions in beam energy scan via functional QCD

Fluctuations of conserved charges provide a link between high quality theoretical results and precision measurements of heavy ion collisions. We compare results for ratios of the lowest order baryon number susceptibilities from functional QCD approaches to proton number cumulants extracted from experiments. We find that they meet at a specific temperature and chemical potential for each collision energy. This is indicative of the respective freeze-out point. From this self-consistent determination of the freeze-out parameters we extract a prediction for the kurtosis on the freeze-out line. We find quantitative agreement with experimental data where available, despite comparing apples (baryons) with oranges (protons). At a collision energy around 5 GeV, our kurtosis exhibits a peak structure indicative of the critical end point of QCD.

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arXiv2026

Flavor dependence of chiral symmetry breaking and the conformal window

We investigate the phase structure of Quantum Chromodynamics (QCD) in the vacuum as a function of quark flavor number $N_f$ within the chiral limit. By self-consistently solving the coupled DSEs for the quark and gluon propagators in a minimal QCD scheme, we elucidate the nonperturbative dynamics governing dynamical chiral symmetry breaking. Our calculations determine a critical flavor number of $N_f^c=6.81$ which marks the chiral symmetry restoration of quarks. Further analysis reveals the critical exponents of the chiral condensate as $ -\langle\bar{\psi} {\psi}\rangle\sim |N_f-N_f^c|^{0.53(9)}$, characterized the second order feature of this phase transition of chiral symmetry. Additionally, we discuss the implications for the walking regime towards the conformal window at larger flavor.

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arXiv2025

The Dichotomous Nature of the $\sigma$ Meson and the Nucleon D-Term

Employing a symmetry-preserving contact-interaction formulation of the Dyson-Schwinger equations in quantum chromodynamics (QCD), we examine the identity of the $\sigma$ meson and its implications for the gravitational structure of hadrons. In this framework, the scalar meson emerges as the chiral partner of the pion, with both states' properties tightly connected to the mechanisms of mass generation in QCD. We find that, above a critical coupling that triggers dynamical chiral symmetry breaking, the D-terms of the constituent quark, the pion, and $\sigma$ saturate at fixed values $D_{q,\pi,\sigma}=-1/3,-1,-7/3$. By examining the coupling strength evolution of the D-terms, this pattern follows naturally once a dual nature for the $\sigma$ meson is recognized: it behaves both as a quark-antiquark composite and as a dilaton arising from spontaneous scale symmetry breaking. This unified picture yields the prediction $D_N\sim -3$ for the nucleon D-term, consistent with contemporary lattice-QCD, continuum, and dispersive studies.

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arXiv2025

Revisiting the first-order QCD phase transition in dense strong interaction matter

We revisit the phase structure and thermodynamics of QCD in the low temperature and high density region, where a strong, first-order phase transition is expected beyond the critical end point. By solving the quark gap equation in the continuum QCD approach, we reveal the coexistence of the multi-phases both in the microscopic dynamics of chiral symmetry breaking and also in the thermodynamic observables, which manifests the existence of spinodal decomposition during the first-order QCD phase transitions. We also analyse the interface structure of the co-exist Nambu and Wigner phases in the isothermal process during the first-order transition. In particular, the interface tension and interface entropy density are extracted from the isothermal trajectories, which further allows for an analysis on the formation of nuclear bubble, including the bubble radius and its stability at different temperatures. Our predictions may serve as useful inputs for further investigations in heavy-ion physics or astrophysics research.

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arXiv2025

Lee--Yang edge singularities in Nonlocal Nambu--Jona-Lasinio Model

We investigate the QCD phase diagram and the associated Lee--Yang edge singularities using the two-flavor nonlocal Nambu--Jona-Lasinio model extended to complex chemical potential. There exists a strong correlation between the chiral phase transition and the structure of the effective potential in the complex order parameter plane, serving as a criterion to differentiate crossover from first-order transitions. Typically, the Lee--Yang edge singularities can be understood as a generalization of the critical end-point (CEP) between crossover and first-order transitions, where the positive Nambu phase and the Wigner phase coalesce. We further analyze the scaling behavior near the CEP by extracting the critical exponent associated with the Lee--Yang singularities. Additionally, we confirm that the extrapolation of the Lee--Yang edge singularity trajectories provides an effective method of determining the CEP location, even at a small real chemical potential. This provides a viable method for exploring regions of the QCD phase diagram that remain inaccessible to lattice QCD.

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arXiv2025

Dynamical instability and transport peak of chiral matter from holography

We study dynamical properties of strongly coupled chiral matter by using holographic method. We demonstrate, at both linear and nonlinear levels, that perturbations on thermodynamically unstable backgrounds within the spinodal region of chiral first-order phase transitions exhibit dynamic instability. The corresponding magnitude of dynamic instability can be characterized by the critical momentum. Furthermore, we found that, within a certain temperature range, the quasi-normal mode spectrum contains purely imaginary diffusive modes. As spatial momentum increases, a transition occurs in the system's long-time dynamics. The dominant contribution shifts from diffusive mode to propagating mode. When the diffusive mode becomes dominant, the spectral function exhibits a transport peak structure in the low-frequency region. A heuristic argument suggests that this particular transition can be related to the chiral symmetry breaking and restoration.

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arXiv2025

The equation of state and surface tension of QCD in the first order phase transition region

We build up a complete description of QCD phase structure by applying the parametrization of the chiral and deconfinement order parameters upon the calculations from functional QCD approaches. In particular in the first order phase transition region at high chemical potential, both the phase transition line using Maxwell construction and the coexistence boundary lines from the spinodal decompostion are determined. We compute the thermodynamic quantities including the number density, the energy density, the pressure and also the free energy for both stable and unstable phases of QCD. Additionally, after applying a phenomenological description of the inhomogeneity of the QCD free energy, we obtain the surface tension of the first order phase transition of QCD.

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arXiv2025

Lee Yang edge singularities of QCD in association with Roberge-Weiss phase transition and chiral phase transition

We study the Quantum Chromodynamics (QCD) phase transitions in the complex chemical potential plane in the framework of Dyson-Schwinger equation approach, in the presence of a constant gluonic background field that represents confining dynamics. We solve the quark gap equation and the background field equation self consistently, which allows us to directly explore the confinement phase transition and furthermore, evaluate the impact of the back-coupling of confinement on chiral symmetry breaking. Moreover, within such a coupled framework towards the complex chemical potential region, we demonstrate the emergence of Roberge-Weiss (RW) symmetry and investigate the trajectory of Lee-Yang edge singularities (LYES). Our analysis reveals that the LYES scaling behavior is similar to our previous findings without the background field condensate. However, a significant difference from our earlier work is that the trajectory of LYES terminates when the imaginary part of the singularity becomes $1/3 \, \pi T$. We elaborate that this cut-off behavior is caused by the RW symmetry that is symmetric to the imaginary chemical potential $\mu_i=1/3 \, \pi T$.

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arXiv2025

Finite density signatures of confining and chiral dynamics in QCD thermodynamics and fluctuations of conserved charges

We evaluate thermodynamic observables such as pressure, baryon number, entropy and energy density, as well as the second and fourth order baryon number cumulants in the phase structure of QCD. The intertwined confinement and chiral dynamics is resolved within functional QCD, aiming for quantitative accuracy at larger densities. Specifically it is shown that the self-consistent resolution of the confining gluonic background is crucial in particular for even the qualitative properties of the cumulants. Our results are in quantitative agreement with lattice and functional QCD benchmarks at vanishing and small chemical potentials. Moreover, they offer novel insights in the dynamics at larger chemical potentials including the regime of the critical end point. A welcome by-product of this analysis is the computation of the Polyakov loop potential in finite density QCD, which, alongside the aforementioned observables, can be used as input and benchmark for effective theory computations at finite density.

hep-ph↗

arXiv2025

Illustrating the liquid gas transition of nuclear matter in QCD

We demonstrate that the liquid-gas transition of nuclear matter can be rigorously described with the quantum chromodynamics by combining the quark gap equation and the Faddeev equation of nucleon. Our investigation focuses on this transition at zero temperature and finite chemical potential, revealing a finite difference between the gas and liquid solution of the quark propagator. This difference emerges from the shift of the nucleon pole mass in medium, which is generated in the nucleon channel of the quark gap equation. We prove that such a difference is precisely the contour contribution from the shift of the nucleon pole. The resulting discontinuity manifests as a first-order phase transition and fundamentally determines both the nuclear binding energy and the saturation density. We then derive an analytical relation between the binding energy and the sigma term of the nucleon, yielding a binding energy of $E/A=15.9\,\textrm{MeV}$. Furthermore, by establishing the relation between the nuclear saturation density and the vector charge of nucleon in association with the binding energy, we determine the saturation density to be $n_{\textrm{B}}^{0}=0.15\,\textrm{fm}^{-3}$.

nucl-th↗

arXiv2024

A quantitative analysis of Gravitational Wave spectrum sourced from First-Order Chiral Phase Transition of QCD

We investigate the cosmological first-order chiral phase transition of QCD, and for the first time calculate its parameters which can fully determine the gravitational wave spectrum. With the state-of-the-art calculation from the functional QCD method, we found that the large chemical potential of QCD phase transition results in very weak and fast first-order phase transitions at the temperature lower than $\mathcal{O}(10^2)$ MeV. These results further suggest that the GW signals of NANOGrav are very unlikely sourced from the chiral phase transition of QCD.

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arXiv2024

The effective potential of composite operator in the first order region of QCD phase transition

We propose a method to determine the effective potential of QCD from the gap equation, by introducing the homotopy method between the solutions of the equation of motion. Via this method, the effective potential beyond the bare vertex approximation is obtained, which then generalizes the Cornwall, Jackiw and Tomboulis (CJT) effective potential for the bilocal composite operators. Moreover, the extended effective potential is set to be a function of self energy instead of the propagator, which is the key point for the potential to be bounded from below. We then investigate the extended effective potential in the cases of phase transition of the QCD vacuum with a small current quark mass, and the first-order phase transition of QCD at finite temperature and high baryon chemical potential. In the former case, the effective potential shows as an inflection point at the critical mass where the multiple solutions of the Dyson-Schwinger equation (DSE) vanishes, which is consistent with that obtained by solving the DSE directly. For the latter case, the in-medium properties, such as the latent heat and the difference of trace anomaly, of QCD is obtained.

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arXiv2023

Dynamical and finite-size effects on the criterion of first-order phase transition

To identify first-order phase transitions in the dynamical process similar to the relativistic heavy-ion collisions, we investigate the dynamical behaviors of the first-order phase transition criterion in the Fokker-Planck framework. In the thermodynamic limit, the criterion can be expressed as combinations of cumulants or coefficients of an Ising-like effective potential. Our study reveals that factors such as phase transition scenarios, initial temperature, system volume, relaxation rate, and evolution trajectory have great impacts on the criterion, a larger initial temperature, a smaller volume, a larger relaxation rate, or bending of the trajectory will all lead to a reduction of the first-order phase transition signal, while volume expansion over time preserves signal integrity. Analysis along a hypothetical freezeout line shows that the signal is possibly preserved at relatively large chemical potentials.

nucl-th↗

arXiv2023

Chemical freeze-out parameters via functional renormalization group approach

We study the freeze-out parameters in a QCD-assisted effective theory that accurately captures the quantum and in-medium effects of QCD at low energies. Functional renormalization group approach is implemented in our work to incorporate the non-perturbative quantum, thermal and density fluctuations. By analyzing the calculated baryon number susceptibility ratios $χ_{2}^{B}/χ_{1}^{B}$ and $χ_{3}^{B}/χ_{2}^{B}$, we determine the chemical freeze-out temperatures and baryon chemical potentials in cases of hard thermal or dense loop improved $μ$-dependent glue potential and $μ$-independent glue potential. We calculate the ${χ_{4}^{B}}/{χ_{2}^{B}}\, (κσ^{2})$ and ${χ_{6}^{B}}/{χ_{2}^{B}}$ along the freeze-out line for both cases. It's found that $κσ^{2}$ exhibits a nonmonotonic behavior in low collision energy region and approach to one for lower collision energy. ${χ_{6}^{B}}/{χ_{2}^{B}}$ shows a similar complicated behavior in our calculation.

hep-ph↗

arXiv2023

Determining Hadron-Quark Phase Transition Chemical Potential via Astronomical Observations

We propose a scheme to determine the chemical potential and baryon number density of the hadron-quark phase transition in cold dense strong interaction matter (compact star matter). The hadron matter is described with the relativistic mean field theory, and the quark matter is described with the Dyson-Schwinger equation approach of QCD. To study the first-order phase transition, we take the sound speed as the interpolation objective to construct the equation of state in the middle density region. With the maximum mass, the tidal deformability and the radius of neutron stars being taken as calibration quantities, the phase transition chemical potential is constrained to a quite small range. And the most probable value of the phase transition chemical potential is found.

hep-ph↗

arXiv2022

Revealing the Signal of QCD Phase Transition in Heavy-Ion Collisions

We propose a novel method to construct the Landau thermodynamic potential directly from the fluctuations measured in heavy-ion collisions. The potential is capable of revealing the signal of the critical end-point (CEP) and the first order phase transition (FOPT) of QCD in the system even away from the phase transition region. With the available experimental data, we show that the criterion of the FOPT is negative for most of the collision energies which indicates no signal of FOPT. The data at $\sqrt{s_\mathrm{NN}}=7.7$ GeV with 0-5% centrality shows a different behavior and the mean value of the data satisfies the criterion. However, the uncertainty is still too large to make a certain conclusion. The higher order fluctuations are also required for confirming the signal. We emphasize therefore that new measurements with higher precision for the $C_{1,...,6}$ within 0-5% centrality in the vicinity of $\sqrt{s_\mathrm{NN}}=7.7$ GeV are in demand which may finally reveal the signal of QCD phase transition.

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arXiv2022

Exposing the effect of $p$-wave in pion triplet under the strong magnetic field

The static properties, masses and decay constants, of pseudoscalar meson triplet in a strongly magnetized medium are studied through the Dyson-Schwinger equation approach treatment of a contact interaction. Complementary to the usual vector-vector form, a symmetry-preserving formulation of couplings has been proposed in this work, without modifying the quark propagator, to control the strength of the $p$-wave component of Bethe-Salpeter amplitude. It is found that, with the help of flexible auxiliary interaction, our simple model is able to reproduce the observation in the lattice QCD simulation, where the spectra of the charged pseudo-scalar meson shows a non-monotonic behavior as the magnetic field grows. The discovery of this work implies the strong magnetic field affects the inner structure of mesons dramatically.

hep-ph↗

arXiv2022

A Flavor Change Study based on Dyson-Schwinger Equation

We study the flavor change effects using the Dyson-Schwinger (DS) equation in a multi-flavor system. By taking the Electroweak interaction as perturbation into conditions, the $\text{SU(4)}_\text{L}\rightarrow\text{SU(2)}_\text{L}\otimes\text{SU(2)}_\text{L}\rightarrow\text{SO(2)}_\text{L}\otimes\text{SO(2)}_\text{L}$ symmetry breaking chain is studied. Under this symmetry breaking pattern fermion masses are split, and we can identify the fermions with different masses as different generations. Quark mass spectrum is then given. Meanwhile, there are a total of fifteen Goldstones but only four of them are independent. The Goldstones have electric charges $0$, $0$, $+1$, $-1$, respectively. One of them becomes pseudo-Nambu-Goldstone boson (pNGB) and gains a mass due to the Electroweak interaction perturbation. It can be identified as the Higgs boson. The other three Goldstones maintain massless and will be eaten by gauge bosons to give $W^\pm$ and $Z^0$ masses via Schwinger mechanism. Thus, the Goldstones can take the role of the Higgs boson.

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