arXiv subjects

Bikai Gao

Publications and source records attributed to Bikai Gao.

At least 19 recordsLinked to original sources

arXiv2026

Evidence for a Continuous Hadron--Quark Transition in Cold Dense Matter

Statistical evidence for a continuous hadron-quark transition is found in this work. Confronting microscopic descriptions connecting the Parity Doublet Model and the Nambu--Jona-Lasinio model with observationally constrained non-parametric equations of state, Bayesian model comparison decisively favors a boundary-free crossover over the conventional first-order Maxwell construction ($Δ\ln\mathcal{Z} \sim +7.20$) and fixed-boundary crossover ($Δ\ln\mathcal{Z} \sim +5.16 $). The preferred crossover decouples the intermediate stiffening from the intrinsic stiffness of each phase, allowing both sectors to exhibit physical self-consistency. The chiral-invariant nucleon mass is large, $M_0 = 834^{+28}_{-92}\text{ MeV}$, as expected for a substantial baryon mass surviving chiral restoration. While the quark sector accommodates a small pairing gap $Δ_{\rm CFL} = 88^{+83}_{-59}\text{ MeV}$ consistent with perturbative QCD limits, avoiding the excessively large gaps $Δ_{\rm CFL} \gtrsim 200\text{ MeV}$ required by the other constructions. These results demonstrate that a realistic unified description represents a continuous transition deviating substantially from isolated effective models of hadrons and quarks. Exploring genuine phase boundaries is therefore necessary through the emergence of spinodal instabilities within unified frameworks.

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arXiv2026

A quark-diquark model for parity doublet structure of baryons

The chiral invariant mass of baryons is a phenomenological input of parity doublet models, and its microscopic origin remains an open question. We propose that the chiral invariant mass and the parity doublet structure originate from the diquarks: the scalar ($0^+$) and pseudoscalar ($0^-$) diquarks form a parity doublet whose invariant mass is generated by gluon dynamics rather than by the quark condensate. We construct a three-flavor chiral quark--diquark model in which a quark and a diquark are bounded into a baryon through a chiral-invariant four-body interaction whose structure is reduced from one-gluon exchange. It is shown that the quark--diquark structure automatically yields the two chiral representations and the mirror assignment of the parity doublet model, and the composite baryons acquire chiral invariant masses even for massless quarks. We find that the octet baryon spectrum and the nucleon sigma terms are reproduced very well with a minimal set of parameters. Furthermore, after chiral symmetry restoration, the model predicts a distinctive inverted mass hierarchy: the nucleon remains relatively heavy, whereas the $Σ$ and $Ξ$ baryon become lighter than the nucleon. This inverse mass ordering may therefore provide a novel, experimentally testable signature towards chiral symmetry restoration.

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arXiv2026

The stability of color-flavor-locked quark matter and massive CFL quark stars

Owing to the emergence of attractive interactions between quarks, color superconductivity is expected to occur, with the color-flavor-locked (CFL) phase favored at high densities. This work investigates the absolute stability of beta-equilibrated CFL quark matter in bulk within the modified Nambu-Jona-Lasinio model, under color and electric charge neutrality conditions relevant to compact stars. Motivated by the possible existence of an ultra-low-mass central compact object in the supernova remnant HESS J1731-347 and the "mass-gap" secondary component in the GW190814 event, we systematically explore how vector repulsion, attractive diquark pairing, and nonperturbative vacuum effects influence the stiffness of CFL quark matter and its stability. Our findings suggest the existence of a physically viable region of parameter space in which the CFL phase is the true ground state of strongly interacting matter, thereby theoretically supporting the scenario of self-bound quark stars. This configuration is not only consistent with current astrophysical constraints from NICER and LIGO/Virgo observations, but also provides a possible explanation for both the $~2.6\ M_{\odot}$ secondary component in GW190814 and the ultra-low-mass compact object with $M = 0.77^{+0.20}_{-0.17}\ M_{\odot}$in HESS J1731-347.

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arXiv2026

Gravitational wave spectrum from first-order QCD phase transitions based on a parity doublet model

We investigate the gravitational wave spectrum from first-order QCD phase transitions using the parity doublet model at finite baryon chemical potential. The model incorporates the chiral invariant mass $m_0$, representing the portion of nucleon mass that persists even when chiral symmetry is restored. Within the model, we identify two first-order phase transition regions: the nuclear liquid--gas transition and the chiral phase transition. By solving the bounce equation and computing the Euclidean action $S_3/T$, we obtain the gravitational wave spectra from both transitions. The liquid--gas transition yields $α\sim \mathcal{O}(1)$ and $β/H \sim \mathcal{O}(10)$--$\mathcal{O}(100)$ near the endpoint of the first-order line, producing signals with peak frequencies from the millihertz to the nanohertz band that can fit the existing data. In contrast, the chiral transition produces signals suppressed by approximately five orders of magnitude, well below the sensitivity of all current and planned detectors. These results connect the chiral invariant mass to the gravitational wave spectrum, offering a novel probe of the origin of nucleon mass through gravitational wave astronomy.

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arXiv2026

Linear realization of SU(3) parity doublet model for octet baryons with bad diquark

We construct a linear $SU(3)_L \times SU(3)_R$ parity doublet model for octet baryons. Our model employs the $(3,\bar{3}) + (\bar{3},3)$ and $(3,6) + (6,3)$ chiral representations while excluding the $(8,1) + (1,8)$ representation. Through systematic analysis, we demonstrate that the $(3,6) + (6,3)$ representation containing symmetric ``bad'' diquarks, despite being energetically disfavored, is essential for reproducing the correct baryon mass hierarchy, particularly the $Σ$$Ξ$ mass ordering. The model incorporates both spontaneous and explicit chiral symmetry breaking, with the latter implemented through bare quark mass terms that properly account for $SU(3)$ flavor breaking effects. Our numerical analysis successfully reproduces the ground-state octet baryon masses and predicts the spectrum of excited states up to 2.5 GeV. For the experimentally challenging $Ξ$ sector, we provide specific predictions for spin-parity assignments: identifying $Ξ(1950)$ as the first positive-parity excitation. The analysis reveals that ground states are dominated by the $(3,\bar{3}) + (\bar{3},3)$ representation, consistent with the preference for ``good'' diquark configurations, while the $(3,6) + (6,3)$ contribution remains crucial for the mass spectrum.

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arXiv2026

Chiral symmetry restoration and hyperon suppression in neutron stars

The ``hyperon puzzle'' remains a fundamental challenge in nuclear astrophysics. We investigate hyperon emergence in neutron star matter using the $SU(3)$ parity doublet model with chiral representation $(3,\bar{3}) + (\bar{3},3)$. This framework naturally incorporates chiral symmetry restoration and provides a systematic description of baryon masses in dense matter through the interplay between the chiral condensate and the chiral invariant mass $m_0$. We find that the hyperon onset density exhibits strong sensitivity to $m_0$: for $m_0 = 500$ MeV, hyperons first appear at $1.9n_0$ while for $m_0 \gtrsim 750$ MeV, hyperons emerge only above $5n_0$. This delayed onset arises from the weakened density dependence of baryon masses at larger $m_0$ values. When the hyperon onset density exceeds the expected quark-hadron transition range ($2$--$5n_0$), matter undergoes deconfinement before hyperons populate, avoiding the EoS softening while maintaining consistency with massive neutron star observations. Our results demonstrate that chiral dynamics provides a natural resolution to the hyperon puzzle without requiring ad hoc repulsive hyperon interactions.

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arXiv2025

Constraining the competition between the deconfinement and chiral phase transitions in light of the multimessenger era

We extend the parity doublet model for hadronic matter and study the possible presence of quark matter inside the cores of neutron stars with the Nambu-Jona-Lasinio (NJL) model. Considering the uncertainties of the QCD phase diagram and the location of the critical endpoint, we aim to explore the competition between the chiral phase transition and the deconfinement phase transition systematically, regulated by the vacuum pressure $-B$ in the NJL model. Employing a Maxwell construction, a sharp first-order deconfinement phase transition is implemented combining the parity doublet model for the hadronic phase and the NJL model for the high-energy quark phase. The position of the chiral phase transition is obtained from the NJL model self-consistently. We find stable neutron stars with a quark core within a specific parameter space that satisfies current astronomical observations. The observations suggest a relatively large chiral invariant mass $m_0=600$ MeV in the parity doublet model and a larger split between the chiral and deconfinement phase transitions while assuming the first-order deconfinement phase transition. The maximum mass of the hybrid star that we obtain is $\sim 2.2 M_{\odot}$.

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arXiv2025

Hybrid stars with large quark cores within the parity doublet model and modified NJL model

Using the parity doublet model (PDM) for hadronic matter and a modified Nambu-Jona-Lasinio (NJL) model for quark matter, we investigate the potential existence of two- and three-flavor quark matter in neutron star cores. Both models respect chiral symmetry, and a sharp first-order phase transition is implemented via Maxwell construction. We find stable neutron stars with quark cores within a specific parameter space that satisfies current astronomical observations. Typical neutron stars with masses around $1.4 \ M_\odot$ may possess deconfined quark matter in their centers. The hybrid star scenario with a two-flavor quark core offers enough parameter space to allow the neutron stars with large quark cores exceeding $\sim 1\ M_\odot$, and allow the early deconfinement position before $2\ ρ_0$, where $ρ_0$ is the nuclear saturation density. The observations of gravitational wave event GW170817 suggest a relatively large chiral invariant mass $m_0=600\ \rm MeV$ in the PDM for scenarios involving three-flavor quark matter cores. The maximum mass of the hybrid star with a quark core is found to be approximately $2.2\ M_\odot$ for both two- or three-flavor quark matter in their centers.

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arXiv2025

Origin of nucleon mass in the light of PSR J0614-3329 with quark-hadron crossover

The recent NICER observation of PSR J0614-3329, revealing the smallest reliably measured neutron star radius of $R = 10.29^{+1.01}_{-0.86}$ km at mass $M = 1.44^{+0.06}_{-0.07} M_\odot$, provides an unprecedented constraint on the equation of state of dense matter. We investigate the implications of this measurement for the origin of nucleon mass within the parity doublet model framework, which naturally incorporates both chiral variant and chiral invariant mass components. We construct unified equations of state by employing the parity doublet model with isovector scalar meson $a_0(980)$ for hadronic matter up to twice nuclear saturation density, smoothly connected to a Nambu-Jona-Lasinio-type quark model at higher densities through a crossover transition. By systematically varying the chiral invariant mass $m_0$ and quark matter parameters, we determine which values simultaneously satisfy all current astrophysical constraints, including gravitational wave observations from GW170817, NICER measurements of several pulsars, and the existence of two-solar-mass neutron stars. The inclusion of PSR J0614-3329 dramatically refines the allowed range of the chiral invariant mass from the previous constraint of $580~\text{MeV} \lesssim m_0 \lesssim 860~\text{MeV}$ to $800~\text{MeV} \lesssim m_0 \lesssim 860~\text{MeV}$, raising the lower bound by approximately 220 MeV. This result indicates that the chiral invariant mass must constitute at least 85\% of the nucleon mass, challenging the traditional picture of nucleon mass generation through spontaneous chiral symmetry breaking alone and highlighting the importance of gluon condensation and other non-chiral mechanisms.

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arXiv2025

Suppression of dynamical momentum-space shell by chiral symmetry

We investigate the appearance of quark degrees of freedom in dense isospin-symmetric nuclear matter. We employ the parity doublet model to incorporate chiral dynamics. Specifically, we contrast quarkyonic matter, in which quarks occupy states above the nucleon Fermi surface, with baryquark matter, in which quarks populate states inside the nucleonic Fermi sea. We find that while baryquark matter is generally energetically favored over quarkyonic matter, the self-consistent treatment of the momentum-space shell reveals that purely hadronic matter provides the lowest free energy up to densities well beyond nuclear saturation. Consequently, the contribution of quarks is not relevant within the model's domain of applicability, even though chiral symmetry becomes restored. This demonstrates that the onset of quark degrees of freedom and the restoration of chiral symmetry need not coincide.

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arXiv2025

Implication of neutron star observations to the origin of nucleon mass

We investigate the implications of neutron star observations for understanding the origin of nucleon mass using a framework that combines three complementary approaches: the equation of state based on parity doublet structure for hadronic matter below $2n_0$, the Nambu-Jona-Lasinio (NJL) model for quark matter above $5n_0$, and a model-independent analysis of the intermediate density region based on fundamental physical principles. By systematically exploring parameter spaces and comparing theoretical predictions with recent observational constraints, we establish constraints on the chiral invariant mass. Our results suggest that more than a half of the nucleon mass originates from sources beyond spontaneous chiral symmetry breaking, challenging conventional understanding of nucleon mass generation. These constraints arise solely from fundamental physical principles and observational data, independent of specific assumptions about the nature of the quark-hadron transition, providing robust insights into the microscopic origin of hadron masses.

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arXiv2025

Ferromagnetic instabilities in quarkyonic matter

We investigate the magnetic properties of quarkyonic matter, which naturally bridges nuclear and quark matter at intermediate densities relevant to neutron star cores. We extend the quarkyonic model to include spin polarization, where nucleons near the Fermi surface can be polarized while quarks in the deep Fermi sea remain unpolarized due to strong Pauli blocking. After including neutron interactions with spin-dependent terms, we find that quarkyonic matter can develop ferromagnetic instabilities at low densities, characterized by negative magnetic susceptibility. This ferromagnetic behavior occurs in pure neutron matter, independent of proton contributions, and results from the competition between attractive spin-dependent interactions and kinetic energy costs. The system returns to paramagnetic behavior at higher densities when Pauli pressure dominates. Our results demonstrate that the splitting of Fermi momenta of quarkyonic matter produces fundamentally different magnetic responses compared to conventional nuclear matter, with important implications for neutron star magnetism and magnetar physics.

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arXiv2025

Constraints on the strength of first-order phase transition and its relation to nucleon mass

We investigate the constraints on the strength of first-order phase transitions in neutron star matter and its relation to the origin of nucleon mass. By combining the parity doublet model for the hadronic phase, the Nambu-Jona-Lasinio model for quark matter, and the integral constraint framework for intermediate densities, we construct equation of states spanning the full density range relevant to neutron stars. Our approach systematically explores how the chiral invariant mass $m_0$ affects the allowable properties of first-order quark-hadron phase transitions. Through comparison with recent neutron star observations, we establish a inverse correlation between the allowed phase transition strength and the chiral invariant mass. Our results demonstrate a direct connection between fundamental questions about the microscopic origin of nucleon mass and macroscopic neutron star observables, providing a novel astrophysical probe of chiral dynamics and QCD physics under extreme conditions.

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arXiv2025

Chiral Invariant Mass Constraints from HESS J1731 347 in an Extended Parity Doublet Model with Isovector Scalar Meson

The recent discovery of a central compact object (CCO) within the supernova remnant HESS J1731-347, with mass $0.77^{+0.20}_{-0.17} \ M_\odot $ and radius $10.4^{+0.86}_{-0.78}$ km is the lightest and smallest compact object ever observed. We identify it as an ultra-light Neutron star (NS) and constrain the chiral invariant mass of nucleon $m_0$ from the observational data of NS using an extended parity doublet model with including the isovector scalar meson $a_0(980)$. We study the higher order asymmertic matter properties such as the symmetry incompressibility $K_{sym}$ and the symmetry skewness $Q_{sym}$ in the presence of $a_0$ meson. We find that $K_{sym}$ and $Q_{sym}$ is sensitive to the chiral invariant mass of nucleon $m_0$ in the presence of $a_0$ meson. We show that the equation of state in the present model satisfies all observational constraints within $2σ$ credible region including the HESS J1731-347 observation, as well as the constraint from $K_{sym}$ when $740 \,\text{ MeV} \lesssim m_0 \lesssim 860 \,\text{ MeV}$ for $L_0 = $ 57.7 MeV. Yet, the $1σ$ constraint from neutron stars appears to be not fully compatible with the constraint from $K_{sym}$ from the present model.

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arXiv2024

Quarkyonic matter with chiral symmetry restoration

We present a novel unified approach to describe the dense symmetric nuclear matter by combining the quarkyonic matter framework with the parity doublet model. This integration allows for a consistent treatment of the transition from hadronic to quark degrees of freedom while incorporating chiral symmetry restoration effects. Our model introduces a chiral invariant mass for both baryons and constituent quarks, enabling a smooth crossover between hadronic and quark matter in symmetric nuclear matter. We derive the equation of state (EOS) for this hybrid system and investigate its thermodynamic properties. The model predicts a gradual onset of quark degrees of freedom at high densities while maintaining aspects of confinement.

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arXiv2024

Exploring the first-order phase transition in neutron stars using the parity doublet model and NJL-type quark model

We investigate the possibility and impacts of a first-order phase transition from hadronic matter to quark matter in neutron stars (NSs) using two specific models: the parity doublet model (PDM) for the hadronic phase and the Nambu-Jona-Lasinio (NJL) type model for the quark phase. By combining these models, we construct hybrid equations of state (EOSs) that capture the transition between the two phases. We explore the parameter space of both models to identify the conditions under which a first-order phase transition can occur and study its effects on NS properties. We identify the suitable parameter space and constrain the onset density of the first-order phase transition. For $m_0$ = 500 MeV -- the chiral invariant mass in PDM, the phase transition occurs between 1.9$n_0$ and 2.95$n_0$ and ends between 2.1$n_0$ and 3.6$n_0$. Increasing $m_0$ to 600 MeV shifts the phase transition to higher densities, occurring between 2.9$n_0$ and 4.1$n_0$ and ending between 3.4$n_0$ and 4.6$n_0$.

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arXiv2024

Reconciling the HESS J1731-347 constraints with Parity doublet model

The recent discovery of a central compact object (CCO) within the supernova remnant HESS J1731-347, characterized by a mass of approximately $0.77^{+0.20}_{-0.17} M_{\odot}$ and a radius of about $10.4^{+0.86}_{-0.78}$ km, has opened up a new window for the study of compact objects. This CCO is particularly intriguing because it is the lightest and smallest compact object ever observed, raising questions and challenging the existing theories. To account for this light compact star, a mean-field model within the framework of parity doublet structure is applied to describe the hadron matter. Inside the model, part of the nucleon mass is associated with the chiral symmetry breaking while the other part is from the chiral invariant mass $m_0$ which is insensitive to the temperature/density. The value of $m_0$ affects the nuclear equation of state for uniform nuclear matter at low density and exhibits strong correlations with the radii of neutron stars. We point out that HESS J1731-347 can be explained as the lightest neutron star for $m_0 \simeq 850$\,MeV.

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arXiv2024

Parity doublet model for baryon octets: ground states saturated by good diquarks and the role of bad diquarks for excited states

Parity doublet model is an effective chiral model that includes the chiral variant and invariant masses of baryons. The chiral invariant mass has large impacts on the density dependence of models which can be constrained by neutron star observations. In the previous work, models of two-flavors have been considered up to a few times nuclear saturation density, but in such dense region it is also necessary to consider hyperons. With the chiral invariant masses baryons can stay massive in extreme environments (e.g., neutron stars) where the chiral symmetry restoration takes place. In this work, we generalize the previous $\mbox{SU(2)}_L \times \mbox{SU(2)}_R$ parity models of nucleons to $\mbox{SU(3)}_L \times \mbox{SU(3)}_R$ models of the baryon octet, within the linear realization of the chiral symmetry. The major problem in constructing such models has been too many candidates for the chiral representations of baryons. Motivated by the concepts of diquarks and the mended symmetry, we choose the $(3_L, \bar{3}_R) + (\bar{3}_L, 3_R)$, $(3_L, 6_R) + (6_L, 3_R)$ and $(1_L, 8_R) + (8_L, 1_R)$ representations and use quark diagrams to constrain the possible types of Yukawa interactions. The masses of the baryon octets for positive and negative baryons up to the first excitations are successfully reproduced. As expected from the diquark considerations, the ground state baryons are well dominated by $(3_L, \bar{3}_R) + (\bar{3}_L, 3_R)$ and $(1_L, 8_R) + (8_L, 1_R)$ representations, while the excited states require $(3_L, 6_R) + (6_L, 3_R)$ representations. Important applications of our model are the chiral restoration for strange quarks at large density and the continuity of diquarks from hadronic to quark matter. We also address the problem of large Yukawa couplings which are enhanced in three-flavor construction.

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