arXiv subjects

Gaoqing Cao

Publications and source records attributed to Gaoqing Cao.

At least 19 recordsLinked to original sources

arXiv2026

Dilepton emission assists the search for the QCD critical point

In this work, we propose that dilepton emission rate (DER) could possibly carry the characteristic structures associated with the chiral criticality of the QCD system based on the extended Polyakov-quark-meson model. The model could successfully capture two main mechanisms for dilepton production, $π^+π^-$ and quark-antiquark annihilations on one hand, and self-consistently account for chiral transition and (de-)confinement on the other hand. All the moments of the DER peak exhibit extremal features similar to those of light-quark mass along the chemical freeze-out lines, thus the DER can reflect the change of chiral symmetry and criticality. However, the DER is relatively too low to produce a sufficient number of thermal dileptons in each heavy-ion collision, which prevents the implementation of event-by-event measurements of the moments. As an alternative, we propose to study the baseline-subtracted DER: For a given low center of mass of dileptons, the reduced baseline-subtracted DER exhibits a nonmonotonic behavior in the region where the light-quark mass changes most rapidly.

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arXiv2026

QCD phase transition at finite isospin density and magnetic field within the three-flavor NJL model

Previously, the QCD phase transition at finite isospin density and magnetic field was explored within the two-flavor Nambu--Jona-Lasinio model. This work extends the study to the more realistic three-flavor case, where not only strange quark contributions but also quark mass splitting in a strong magnetic field are fully taken into account. Adopting the Ginzburg-Landau approximation and the Landau representation for fermion propagators, we re-explore the transitions from the normal chiral symmetry breaking phase to pion superfluidity or rho superconductivity. Unlike the previous study, we project the mesonic fields onto the eigenstates of a charged point particle in a magnetic field and prove that the corresponding self-energies from quark loops are gauge invariant and degenerate with respect to the extra transverse degrees of freedom. However, the numerical results are qualitatively consistent with previous findings: as the isospin chemical potential increases, pion superfluidity is favored at small magnetic fields, while rho superconductivity is favored at large magnetic fields. In the three-flavor model, since the lowest energy of the rho meson increases with stronger magnetic field, the corresponding critical isospin chemical potential also increases with the magnetic field.

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arXiv2026

Charged pseudoscalar mesons in a strong magnetic field under the Weinberg model

Recent lattice QCD simulations have further validated their earlier unusual findings: The lowest energies of charged pseudoscalar mesons $π^\pm$ and $K^\pm$ decrease at stronger magnetic field, though quasiparticle approximation assumes an increasing feature. We address this long-standing puzzle by employing the chiral effective Weinberg model, in which pseudoscalar and vector mesons exhibit intrinsic mutual couplings. Under this framework, charged pseudoscalar mesons deviate from pure quasiparticle behavior due to their interactions with neutral pseudoscalar and charged vector mesons. By incorporating the modifications induced by neutral pseudoscalar-charged vector loops, we demonstrate that the lowest energies of $π^\pm$ and $K^\pm$ indeed decrease at stronger magnetic field in both the lowest- and full-Landau-level calculations. However, instabilities emerge under a fixed mesonic coupling constant, and appear unavoidable when attempting to reproduce the observed peak structures. In contrast to the quark-antiquark meson description in models such as the NJL model, our results support the conjecture that a charged pseudoscalar meson could effectively form a molecular bound state of a neutral pseudoscalar meson and a charged vector meson in the strong magnetic field regime.

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arXiv2026

QCD phase transition at finite isospin density and magnetic field

The QCD phase transition is explored at finite isospin density and magnetic field within the extended two-flavor Nambu--Jona-Lasinio model. By adopting the Ginzburg-Landau approximation, we study the transitions from normal chiral symmetry breaking phase to pion superfluidity or rho superconductivity. To avoid the artificial divergence for a large isospin chemical potential, we adopt the Landau representation rather than the proper-time one for the fermion propagators in a constant magnetic field. For the Landau representation, the same cutoff to the Landau energies, rather than to Landau levels, should be adopted to regularize the divergences from the summations over Landau levels. Then, the Ginzburg-Landau coefficients for pion and rho mesons are worked out both analytically and numerically in random phase approximation. The results show that pion superfluidity is favored for a small magnetic field while rho superconductivity is favored for a large magnetic field when increasing isospin chemical potential, in line with the magnetic enhancement (deduction) of the lowest energy of $π^+ (ρ^{+})$ meson. The novel rho superconductivity phase at large magnetic field and finite isospin density implies an interesting and nontrivial interplay between QCD and QED.

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arXiv2025

Single-flavor heavy baryons in a strong magnetic field

In this work, we study the properties of single-flavor heavy baryons, $Ω_{\rm ccc}$ and $Ω_{\rm bbb}$, in a strong magnetic field. For that sake, we simply treat the baryons as quark-diquark two-body systems, and a systematic formalism is developed to deal with two-body Schr$\ddot{\text o}$dinger equations in a magnetic field. It is found that: 1. The orbital properties of $Ω_{\rm bbb}$ are almost not affected by the magnetic field. 2. $Ω_{\rm ccc}$ is more tightly bound in the presence of a magnetic field. 3. The magnetic-spin effect dominates over the magnetic-orbital effect. Applying to peripheral heavy ion collisions, $Ω_{\rm ccc}$ is much better than $Ω_{\rm bbb}$ to explore the magnetic effect, and the discovery of $Ω_{\rm ccc}$ could be more promising.

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arXiv2025

Moat regimes within a $2+1$ flavor Polyakov-quark-meson model

To better understand recent predictions on the moat regime of quantum chromodynamics (QCD) matter, this paper extends the previous work within the two-flavor quark-meson (QM) model to the more realistic $2+1$ flavor Polyakov-quark-meson (PQM) model. Mainly, two effects are further taken into account: strange quark and confinement coded through Polyakov loop. Model parameters are chosen to consistently reproduce the pseudocritical temperature from lattice QCD, $T_{\rm C}\sim 156~ {\rm MeV}$, and the baryon chemical potential at the critical end point (CEP) from FRG-QCD, $μ_{\rm B(CEP)}\sim 635~ {\rm MeV}$. It is found that the basic features of moat regimes for $σ$ and $π$ mesons remain similar to those from QM model: Moat regimes cover the region where temperature or baryon chemical potential is large; reentrances occur around the critical baryon chemical potential of chiral transition at zero temperature. Thus, the FRG-QCD results can still not be well understood, especially why the CEP should locate at the entrances of moat regimes for $σ$ and $π$ mesons. Nevertheless, some basic features can be understood qualitatively, and it is consistent that the pole energies are increasing functions of momenta in the whole $T-μ_{\rm B}$ plane. The moat regime and pole energy of $K$ mesons are also studied with the features similar.

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arXiv2024

Extended Nambu--Jona-Lasinio model for quark and nuclear matters

In this work, we extend the two-flavor Nambu--Jona-Lasinio model to one capable of exploring quark and nuclear matter consistently. With an extra term standing for quark-nucleon interactions, nucleons could automatically emerge as color-singlet three-quark entities by following a process similar to mesons. Besides the quark part in mean field approximation, both mesons and nucleons could contribute to the thermodynamic potential thus possibly give rise to quarkyonic matter beyond mean field. In the study, two kinds of "confining" couplings are adopted for the new interaction term and two different quark masses are considered for comparison. It turns out that only confined nuclear matter or deconfined quark matter is possible for all the cases at zero temperature, thus quarkyonic matter is not favored at all. Even more strictly, only the case with stronger confinement effect and a smaller quark mass admits a physical first-order phase transition from nuclear matter to quark matter around twice saturation density.

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arXiv2024

Heavy-flavor mesons in a strong electric field

Very strong electromagnetic field can be generated in peripheral relativistic heavy ion collisions. This work is devoted to exploring the interplay between the effects of a constant external electric field and confining potential on heavy-flavor mesons. As the corresponding vector potential linearly depends on one spatial coordinate for a constant electric field, it might be able to overcome the linear confining potential of QCD and induce deconfinement. To perform analytic calculations and for comparison, one and two dimensional systems are studied together with the realistic three dimensional systems. The one dimensional Schr$\ddot{\text o}$dinger equation can be solved analytically with the help of Airy functions, and deconfinement is indeed realized when the electric field is larger than the string tension. Focus on the confining case, the two and three dimensional Schr$\ddot{\text o}$dinger equations can be solved analytically in large $r$ limit with the help of elliptic cosine/sine functions, and the wave functions are dominated by the region antiparallel to the electric field. When a more realistic potential is applied, a non-monotonic feature is found for $Υ(2S)$ and $Υ(3S)$-like mesons with increasing electric field.

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arXiv2024

Topological transition in a parallel electromagnetic field

In this work, we attack the problem of "chiral phase instability" ($χ$PI) in a quantum chromodynamics (QCD) system under a parallel and constant electromagnetic field. The $χ$PI refers to that: When $I_2\equiv{\bf E\cdot B}$ is larger than the threshold $I_2^c$, no homogeneous solution can be found for $σ$ or $π^0$ condensate, and the chiral phase (or angle) $θ$ becomes unstable. Within the two-flavor chiral perturbation theory, we obtain an effective Lagrangian density for $θ(x)$ where the chiral anomalous Wess-Zumino-Witten term is found to play a role of "source" to the "potential field" $θ(x)$. The Euler-Lagrangian equation is applied to derive the equation of motion for $θ(x)$, and physical solutions are worked out for several shapes of system. In the case $I_2>I_2^c$, it is found that the $χ$PI actually implies an inhomogeneous QCD phase with $θ(x)$ spatially dependent. By its very nature, the homogeneous-inhomogeneous phase transition is of pure topological and second order at $I_2^c$. Finally, the work is extended to the three-flavor case, where an inhomogeneous $η$ condensation is also found to be developed for $I_2>I_2^c$. Correspondingly, there is a second critical point, $I_2^{c'}=24.3I_2^c$, across which the transition is also of topological and second order by its very nature.

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arXiv2024

Kaon superfluidity in the early universe

Previously, it was found that pion superfluidity could be realized in the QCD epoch of the early universe, when lepton flavor asymmetry $|l_{\rm e}+l_μ|$ is large enough to generate a charge chemical potential $|μ_{\rm Q}|$ larger than vacuum pion mass. By following the same logic, kaon superfluidity might also be possible when $|l_{\rm e}+l_μ|$ is so large that $|μ_{\rm Q}|$ becomes larger than vacuum kaon mass. Such a possibility is checked by adopting Ginzburg-Landau approximation within the three-flavor Polyakov--Nambu--Jona-Lasinio model. Consider the case with full chemical balance, though kaon superfluidity could be stable compared to the chiral phases with only $σ$ condensations, it would get killed by the more favored homogeneous pion superfluidity. If we introduce mismatch between $s$ and $d$ quarks, kaon superfluidity would require so large $s$ quark density that such a state is impossible in the early universe.

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arXiv2023

Effects of imaginary and real rotations on QCD matters

Inspired from perturbative calculations, this work introduces imaginary ($Ω_{\rm I}$) and real ($Ω$) rotation effects to the pure $SU(3)$ gauge potentials simply through variable transformations: The empirical Polyakov loop (PL) potentials can be rewritten as functions of the imaginary chemical potentials of gluons and ghosts $(q_{\rm ij})$, and the transformations are taken as $q_{\rm ij}\rightarrow q_{\rm ij}\pmΩ_{\rm I}/T$ and $q_{\rm ij}\rightarrow q_{\rm ij}\pm i\,Ω/T$, respectively. For the PL potential of Fukushima $(V_1)$, a smaller imaginary rotation $Ω_{\rm I}$ tends to suppress PL at all temperature and the deconfinement transition keeps of first order. However, for the PL potential of Munich group $(V_2)$, $Ω_{\rm I}$ tends to enhance PL at low temperature $T$, consistent with lattice simulations; but suppress PL at high $T$, consistent with perturbative calculations. Moreover, the deconfinement alters from first order to crossover with increasing $Ω_{\rm I}$ as is expected from lattice simulations. On the other hand, the real rotation $Ω$ tends to enhance PL at relatively low $T$ for both potentials, and the (pseudo-)critical temperature decreases with $Ω$ as expected. Therefore, we find that analytic continuation of the phase diagram from imaginary to real rotation is not necessarily valid in the non-perturbative region. Finally, we apply the more successful PL potential $V_2$ to the Polyakov--Nambu-Jona-Lasinio (PNJL) model and discover that $Ω_{\rm I}$ tends to break chiral symmetry while $Ω$ tends to restore it. Especially, the modified model is even able to qualitatively explain the lattice result that a larger $T$ would catalyze chiral symmetry breaking for a large $Ω_{\rm I}$.

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arXiv2023

Self-consistent thermodynamic potential for magnetized QCD matter

Within the two-flavor Nambu--Jona-Lasinio model, we derive a self-consistent thermodynamic potential $Ω$ for a QCD matter in an external magnetic field $B$. To be consistent with Schwinger's renormalization spirit, counter terms with vacuum quark mass are introduced into $Ω$ and then the explicit $B$-dependent parts can be regularized in a cutoff-free way. Following that, explicit expressions of gap equation and magnetization can be consistently obtained according to the standard thermodynamic relations. The formalism is able to reproduce the paramagnetic feature of a QCD matter without ambiguity. For more realistic study, a running coupling constant is also adopted to account for the inverse magnetic catalysis effect. It turns out that the running coupling would greatly suppress magnetization at large $B$ and is important to reproduce the temperature enhancement effect to magnetization. The case with finite baryon chemical potential is also explored: no sign of first-order transition is found by varying $B$ for the running coupling and the de Haas-van Alphen oscillation shows up in the small $B$ region.

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arXiv2023

First-order QCD transition in a primordial magnetic field

Recalling the expectation of an extremely strong primordial magnetic field $H$, we recheck transitions among the phases of chiral symmetry restoration ($χSR$), chiral symmetry breaking ($χSB$), and pion superfluidity ($πSF$)in the QCD epoch of the early Universe. For homogeneous phases in a finite $H$, a sensible scheme is adopted to determine the phase boundaries of $πSF$, which is also superconductivity phase itself. In the first part, the QCD phase diagrams are studied in detail within the chiral effective Polyakov-Nambu--Jona-Lasinio model and the transitions involving $πSF$ are found to be of first order at relatively small $H$. As expected from the Meissner effect, the regime of $πSF$ shrinks with increasing $H$ and completely vanishes beyond a threshold value. In the second part, the bubble dynamics is illuminated for the stronger first-order transition, $χSR\rightarrowπSF$, in the more convenient Polyakov-quark-meson model. The coupled equations of motion of pion condensate and magnetic field are solved consistently to give the bubble structure. Then, based on bubble collisions, we explore gravitational wave (GW) emission by developing a simple toy model in advance; and the characteristic frequency of the relic GW is estimated to be of the order $0.1-1\,{\rm K}$ or $10^9-10^{10}\,{\rm Hz}$ in our galaxy.

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arXiv2022

Quarkyonic matter state of neutron stars

This work extends our previous study of isospin symmetric quarkyonic matter to quarkyonic neutron matter which might be relevant to the inner cores of neutron stars. The vector-isovector $ρ$ mesons are introduced to the model mainly to account for isospin density interactions, just like $ω$ meson for baryon density interactions. The modified Lagrangian still preserves approximate chiral symmetry which could be significantly broken at lower density. And new free parameters are fixed by adopting the experimental constraints on the symmetry energy and its slope at saturation density. Eventually, the pressure, mass-radius relation, and tidal deformability are explored in advance for the quarkyonic neutron stars. While the pressure and tidal deformability are well consistent with experimental and observational restrictions, the mass-radius relation is unable to reproduce the observed two solar mass of PSR J0740+6620.

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arXiv2021

Gauge independence of pion masses in a magnetic field within the Nambu--Jona-Lasinio model

We investigate the properties of neutral and charged pions in a constant background magnetic field mainly at zero temperature within the Nambu--Jona-Lasinio model. In the previous calculations, the Ritus method, involving Schwinger phases in a fixed gauge, was employed within the momentum-space random phase approximation (RPA)~[Phys. Lett. B $\textbf{782}$, 155-161 (2018)]. However, gauge invariance of the charged pion masses has not yet been examined. In this work, by adopting the linear response theory based on the imaginary-time path integral formalism, we derive the correlation functions for pions in the coordinate space, where the corresponding Schwinger phases show up automatically. At sufficiently large imaginary time $τ$, the meson correlation function approaches an exponential form $\sim\exp(-E_{\rm G}τ)$, where $E_{\rm G}$ is the ground-state energy of the one-meson state and hence determined as the meson mass. Furthermore, we show that the mass of the charged pions is gauge independent, i.e., independent of the choice of the vector potential for the magnetic field. Actually, we also find that the momentum-space RPA is equivalent to the imaginary-time method used here.

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arXiv2021

Reentrant pion superfluidity and cosmic trajectories within PNJL model

In this work, we self-consistently explore the possibility of charged pion superfluidity and cosmic trajectories in early Universe under the framework of Polyakov-Nambu--Jona-Lasinio model. By taking the badly constrained lepton flavor asymmetries $l_{\rm e}$ and $l_μ$ as free parameters, the upper boundaries of pion superfluidity phase are consistently found to be around the pseudocritical temperature at zero chemical potentials. So the results greatly support the choice of $T=0.16~{\rm GeV}$ as the upper boundary of pion superfluidity in the previous lattice QCD study. Take $l_{\rm e}+l_μ=-0.2$ as an example, we demonstrate the features of pion condensation and the associated cosmic trajectories with the evolution of early Universe. While the trajectory of electric chemical potential reacts strongly at both the lower and upper boundaries of reentrant pion superfluidity, the trajectories of other chemical potentials only respond strongly at the upper boundary.

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arXiv2021

Recent progresses on QCD phases in a strong magnetic field -- views from Nambu--Jona-Lasinio model

In this review, we summarize recent progress on the possible phases of quantum chromodynamics (QCD) in the presence of a strong magnetic field, mainly from the views of the chiral effective Nambu--Jona-Lasinio model. Four kinds of phase transitions are explored in detail: chiral symmetry breaking and restoration, neutral pseudoscalar superfluidity, charged pion superfluidity and charged rho superconductivity. In particular, we revisit the unsolved problems of inverse magnetic catalysis effect and competition between the chiral density wave and solitonic modulation phases. It is shown that useful results can be obtained by adopting self-consistent schemes.

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arXiv2021

Connecting Theory to Heavy Ion Experiment

Only a fraction of all $Λ$ and $\barΛ$ hyperons detected in heavy ion collisions are produced from the hot and dense matter directly at the hadronization. These hyperons are called the {\em primary} hyperons. The rest of the hyperons are products of the decays of heavier hyperon states, which in turn are produced at the hadronization. As such, the polarization of only primary hyperons can be described with the formulae introduced in Sect. 8. For the rest of the hyperons, the polarization transfer in the decays has to be computed, and convoluted with the polarization of the mother hyperon. In this chapter, a derivation of the polarization transfer coefficients, as well as the computation of the mean polarization of all $Λ$ hyperons detected in the experiment, is presented. The chapter is concluded with the calculation of the resonance contributions to the global and local $Λ$ polarizations.

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