arXiv subjects

Toru Kojo

Publications and source records attributed to Toru Kojo.

At least 19 recordsLinked to original sources

arXiv2026

Studying the QCD Matter produced in Heavy-Ion Collisions using the MUSES Calculation Engine

The equation of state of hot and dense matter is essential for describing heavy-ion collisions at all collision energies. Here, we explore the capabilities of the latest version of the MUSES Calculation Engine, $\textit{Calliope}$, focusing on software modules and workflows that compute the equation of state and observable properties of the matter produced in heavy-ion collisions. These include several equations of state, ranging from first-principles lattice QCD to phenomenological approaches, with or without a critical point, and with phase-space dimensionality ranging from two dimensions defined by temperature $T$ and baryon chemical potential $\mu_B$, to four dimensions after the addition of strangeness and electric-charge chemical potentials $\mu_S$ and $\mu_Q$. We also discuss modules that provide additional thermodynamic quantities and observables relevant for heavy-ion modeling, including elements of the pressure Hessian matrix and transport coefficients. Workflow examples are constructed that merge two equations of state thermodynamically consistently to extend phase-diagram coverage, and feed the results into an equation of state inverter to produce inputs suitable for hydrodynamic simulations. Finally, we apply this framework to perform a relativistic viscous hydrodynamic simulation with equations of state with an extended $T$ and $\mu_B$ coverage and a movable critical point, including effects from transport coefficients that phenomenologically encode critical scaling, at collision energies $\sqrt{s_{NN}}=7.7, 19.6$, and $39$ GeV.

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arXiv2026

Meson molecules in strong magnetic fields: non-monotonic evolution of the charged pion and kaon energies

In strong magnetic fields, charged quarks occupy the lowest Landau level, leading to an effective dimensional reduction of hadronic dynamics. This dimensional reduction naturally generates a hierarchy of scales, separating fast intra-meson quark dynamics from slow collective meson motion; this motivates a Born-Oppenheimer description of meson-meson systems. Our Born-Oppenheimer analysis shows that the infrared behavior is controlled by the interplay between dimensional reduction and the structure of the meson-meson interaction, leading to three distinct regimes: scattering-dominated, molecular, and compact multiquark states. Charged pseudoscalar mesons such as $\pi_+$ and $K_+$ provide a particularly interesting realization of this framework, as their lattice spectra at large magnetic fields suggest the emergence of loosely bound states near the boundary between scattering and molecular regimes. Our results suggest that strong magnetic fields provide a useful laboratory for exploring the emergence and classification of hadronic bound states.

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arXiv2026

A quarkyonic matter model

Quarkyonic matter is a state of matter in dense QCD whose bulk thermodynamics is dominated by quarks, while low-energy excitations remain confined. This picture leads to a crossover description from baryonic matter to quark matter, which is triggered by the saturation of quark states in dense matter ({\it quark saturation}). The crossover driven by the quark saturation accompanies rapid growth in pressure but moderate increase in energy density, resulting in a peak in the sound speed which has been indicated by observational constraints from neutron star physics. The quark saturation can occur at a few times nuclear saturation density, which is smaller than the density at which the baryon cores of $\sim 0.5$--$0.8$ fm spatially overlap. In this contribution we discuss an ideal model of quarkyonic matter, the IdylliQ model, and we explicitly describe how the baryon and quark occupation probabilities are related, and explain how stiffening of matter occurs. The model is further applied to charge neutral matter including hyperons, and it is shown that the statistical constraints at quark level induce effective repulsion among different baryon species, mitigating the hyperon softening problem in neutron star physics.

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arXiv2026

Delineating neutral and charged mesons in magnetic fields

We investigate the properties of neutral and charged mesons in magnetic fields, from weak-field to strong-field regimes. To develop analytic insights, we employ a non-relativistic quark model with a confining potential of the harmonic oscillator type. Short-range correlations, such as Coulomb and color-magnetic interactions, are treated as perturbations. In particular, we focus on the magnetic field dependence of the relative and the center-of-mass motions. The qualitative trends differ significantly between neutral and charged mesons: for neutral mesons, the transverse momenta are conserved and continuous, while charged mesons exhibit quantized transverse dynamics. The Zeeman effects, arising from intrinsic spins and orbital angular momenta, are carefully examined. In particular, for charged mesons with spins $s\ge 1$, we discuss how the zero-point energy in the internal quark motion cancels the Zeeman energy from the orbital angular momentum, ensuring the energetic stability of mesons with high spins. The effectively reduced dimensionality of these mesons in the strong-field limit is also discussed.

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arXiv2026

Quarkyonic matter and hadron-quark crossover from an ultracold atom perspective

The dense matter equation of state is of great interest due to the recent development of astrophysical observations for neutron stars. A rapid increase in pressure indicates a continuous crossover from a hadron phase to a quark phase without any phase transitions, yet its microscopic mechanism remains elusive. Recently, a peak in the speed of sound and a baryon momentum-shell structure, which are predicted from a quarkyonic matter picture, have been regarded as key features of the hadron-quark crossover. In this work, we explore a field-theoretical framework to describe the hadron-quark crossover, drawing an analogy with the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover established in ultracold atomic experiments. Strikingly, a peak in the speed of sound and the baryon momentum-shell structure can simultaneously be explained by the tripling fluctuation effect arising from a different context of quantum many-body physics. We demonstrate these properties in a simplified model and provide a microscopic derivation of the quarkyonic matter model within our field-theoretical framework.

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arXiv2026

QCD-Like Theories with Different Color Numbers

Quantum chromodynamics (QCD) with a general number of colors, $\Nc$, provides a powerful theoretical laboratory to explore the dynamics of non-Abelian gauge theories. Although $\Nc =3$ does not look a large number, the $1/\Nc$ expansion provides us with a very useful classification and book-keeping scheme for hadronic processes and sharpens conceptions otherwise obscured in real-world QCD with $\Nc = 3$. Important applications are dense QCD matter where the first principle methods for QCD are not available and many conceptual issues remain to be clarified. In this chapter we first review hadrons at large $\Nc$ from the viewpoint of quark-gluon dynamics, and then extend the discussions to hot/dense matter, focusing on confinement-deconfinement aspects. We emphasize how the large-$\Nc$ limit provides a unified organizing principle for hadronic and quark degrees of freedom in regimes where first-principle methods are limited. Two-color and isospin QCD, for which lattice simulations at finite density can be performed for a special reason, is reviewed.

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arXiv2025

Statistical repulsion on hyperons in two-color dense QCD

We investigate the onset of hyperons in baryonic (diquark) matter in two-color QCD (QC$_2$D) by introducing heavy quark doublets that emulate strange quarks. An even number of flavors is required to avoid the sign problem in lattice Monte Carlo simulations. To explore QC$_2$D matter containing both light and heavy quarks, we construct a model in which quarks interact with light-light, light-heavy (hyperonic), and heavy-heavy diquarks via Yukawa couplings. As the quark chemical potential increases, the light diquarks condense first and form baryonic matter, and this onset density can be understood in hadronic terms. In contrast, the onset density of hyperons is substantially higher than that estimated from the hadronic sector of the model. This shift reflects an effective repulsion among baryons induced by the pre-occupied light quarks. The Pauli blocking of light quarks suppresses the attractive diquark correlations responsible, in vacuum, for making hyperons lighter than the sum of the constituent light and heavy quark masses. Implications for three-color QCD are also briefly discussed.

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arXiv2025

Thermal quarks and Polyakov loops in two-color dense QCD

We study confinement and deconfinement in dense two color QCD by analyzing the dynamics of thermal quarks and gluons. The Polyakov loop is used as a probe of the relevant thermal excitations, distinguishing quark and hadron dominated regimes in dense matter. To describe the Polyakov loop, we adopt both lattice informed phenomenological models and the massive Yang Mills framework. After calibrating these models at zero density, we investigate in medium modifications of the Polyakov loops and gluon propagators at finite temperature and density. Diquark gaps control the screening at zero temperature, whereas the screening due to thermal quarks is sensitive to the Polyakov loop. Inclusion of the Polyakov loop helps to reproduce lattice data at low temperature, suggesting that thermal excitations are predominantly hadronic rather than uncorrelated quarks.

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arXiv2024

Stiffening of matter in quark-hadron continuity: a mini-review

Recent observations of neutron stars, combined with causality, thermodynamic stability, and nuclear constraints, indicate a rapid stiffening of QCD matter at densities slightly above nuclear saturation density ($n_0 \simeq 0.16\,{\rm fm}^{-3}$). The evolution of the stiffening is faster than expected from purely nucleonic models with many-body repulsion. Taking into account the quark substructure of baryons, we argue that the saturation of quark states occurs at $\sim$ 2-3$n_0$, driving quark matter formation even before baryonic cores of radius $\sim$0.5 fm spatially overlap. We describe the continuous transitions from hadronic to quark matter within a quarkyonic matter model in which gluons are assumed to remain confining at densities of interest. To obtain analytic insight into the transient regime, we construct an ideal model of quarkyonic matter, the {\it IdylliQ} model, in which one can freely switch from baryonic to quark descriptions and vice versa.

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arXiv2024

Tripling Fluctuations and Peaked Sound Speed in Fermionic Matter

A crossover involving three-fermion clusters is relevant to the hadron-quark crossover, which, if occurring in a neutron star, could naturally reproduce the dense-matter equation of state recently deduced from simultaneous observations of neutron-star masses and radii. To understand the crossover mechanism, we examine the role of tripling fluctuations induced by the formation of three-fermion clusters. The phase-shift representation of fluctuations manifests an interplay of bound and scattering states, leading to non-monotonic momentum distributions of baryon-like clusters and peaked sound speed at finite densities. We demonstrate them by applying our approach to a nonrelativistic system of one-dimensional three-color fermions analogous to the hadron-quark matter.

hep-ph↗

arXiv2024

Evolution of strangeness and hyperons in quarkyonic matter

We study the evolution of matter composition from nuclear to quark densities in the confining regime, by extending an ideal model of Quarkyonic matter, IdylliQ model, to multi-flavor systems including strangeness. The model provides a dual description of quark and baryon occupation probabilities which are determined by minimizing the energy of the system. Saturation of low-momentum quark states drives the formation of quark matter and constrains baryon distributions, inducing statistical repulsion among baryon species. Applying the model to charge-neutral matter composed of neutrons, $\Lambda_0$, and $\Sigma_0$ hyperons, we find that, for typical size of baryons, $d$-quark saturation occurs before hyperons appear, delaying their onset and shifting the threshold density from $\sim 2$--$3n_{\rm sat}$ to $\sim 5$--$6n_{\rm sat}$ ($n_{\rm sat} \approx 0.16\,{\rm fm^{-3}}$: nuclear saturation density). After hyperons emerge, low-momentum hyperon states remain only sparsely occupied due to the quark saturation. These features mitigate the hyperon puzzle, in which the appearance of hyperons softens neutron star equations of state significantly by increasing energy density with little pressure increase. Our results highlight the key role of quark saturation in dense baryonic matter and provide new insights into the interplay between quark dynamics and hyperon physics in neutron stars.

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arXiv2024

Neutron-quark stars: Discerning viable alternatives for the higher-density part of the equation of state of compact stars

We investigate binary neutron star (BNS) mergers using general-relativistic numerical simulations with hadronic and hybrid equations of state (EOSs), incorporating the latest observations and theoretical constraints. We address two viable scenarios for the transition to quark matter: a quark-hadron crossover (QHC) or a strong first-order phase transition (1PT). To distinguish between different models, we define neutron-quark stars (NQS) as configurations where quark effects emerge at masses below the lowest observed neutron-star mass. While traditional "hybrid stars" may be distinguished by purely hadronic configurations through mass-radius measurements, the mass-radius relations of NQSs resemble those of purely hadronic models, with no sharp boundary between hadrons and quarks. The name NQS effectively captures the absence of a phase boundary between hadrons and quarks in QHC scenarios. Our results indicate that QHC models can be distinguished from hadronic ones if both the inspiral and postmerger gravitational waves (GWs) are observed. In particular, the dominant postmerger frequency ($f_2$) tends to be lower than in hadronic models with the same tidal deformability ($\Lambda$). We also present the first general-relativistic simulations of BNS mergers where the stars already contain quark matter before merging. These involve a strong first-order phase transition (1PT) at 1.8 times nuclear saturation density, followed by a stiff quark EOS. Finally, we identify a robust linear correlation between the total GW energy emitted after the merger and the $f_2$ frequency. Remarkably, this relation holds regardless of the quark presence.

astro-ph.HE↗

arXiv2024

Isospin QCD as a laboratory for dense QCD

QCD with the isospin chemical potential, $\mu_I$, is a useful laboratory to delineate the microphysics in dense QCD. To study the quark-hadron-continuity we use a quark-meson model that interpolates hadronic and quark matter physics at microscopic level. The equation of state is dominated by mesons at low density but taken over by quarks at high density. We extend our previous studies with two-flavors to the three-flavors case to study the impact of the strangeness which may be brought by kaons $(K_+, K_0) = (u\bar{s}, s\bar{d})$ and the U$_A$(1) anomaly. In the normal phase the excitation energies of kaons are reduced by $\mu_I$ in the same way as hyperons in nuclear matter at finite baryon chemical potential. Once pions condense, kaon excitation energies increases as $\mu_I$ does. Moreover, strange quarks become more massive through the U$_A$(1) coupling to the condensed pions. Hence at zero and low temperature the strange hadrons and quarks are highly suppressed. The previous findings in two-flavor models, sound speed peak, negative trace anomaly, gaps insensitve to $\mu_I$, persist in our three-flavor model and remain consistent with the lattice results to $\mu_I \sim 1$ GeV. We discuss the non-perturbative power corrections and quark saturation effects as important ingredients to understand the crossover equations of state measured on the lattice.

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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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arXiv2024

Thermal effects on sound velocity peak and conformality in isospin QCD

We study thermal effects on equations of state (EOS) in isospin QCD, utilizing a quark-meson model coupled to a Polyakov loop. The quark-meson model is analyzed at one-loop that is the minimal order to include quark substructure constraints on pions which condense at finite isospin density. In the previous study we showed that the quark-meson model at zero temperature produces the sound velocity peak and the negative trace anomaly in the domain between the chiral effective theory regime at low density and the perturbative QCD regime at high density, in reasonable agreement with lattice simulations. We now include thermal effects from quarks in the Polyakov loop background and examine EOS, especially the sound velocity and trace anomaly along isentropic trajectories. At large isospin density, there are three temperature windows; (i) the pion condensed region with almost vanishing Polyakov loops, (ii) the pion condensed region with finite Polyakov loops, and (iii) the quark gas without pion condensates. In the domain (i), the gap associated with the pion condensate strongly quenches thermal excitations. As the system approaches the domain (ii), thermal quarks, which behave as non-relativistic particles, add energy density but little pressure, substantially reducing the sound velocity to the value less than the conformal value while increasing the trace anomaly toward the positive value. Approaching the domain (iii), thermal quarks become more relativistic as pion condensates melt, increasing sound velocity toward the conformal limit. Corrections from thermal pions are also briefly discussed.

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arXiv2023

Universality in quasinormal modes of neutron stars with quark-hadron crossover

We examine the gravitational wave frequencies of the fundamental ($f$-) and 1st pressure ($p_1$-) modes excited in the neutron star models constructed with the quark-hadron crossover (QHC) type equations of state (EOS). We find that the $f$-mode frequencies with QHC EOS basically are smaller and the $p_1$-mode frequencies with QHC EOS are larger than those with hadronic EOS, focusing on the neutron star model with a fixed mass. We also find that the universality in the $f$-mode frequencies multiplied by the stellar mass as a function of the stellar compactness or as a function of the dimensionless tidal deformability, which is derived with various hadronic EOSs, can keep even with QHC EOS. That is, using these universal relations, one cannot distinguish QHC EOS from hadronic EOSs. Instead, using the relations one can extract the stellar radii whose evolution from low to high mass neutron stars can differentiate QHC from hadronic EOSs. On the other hand, we find that the $p_1$-mode frequencies multiplied by the stellar mass with QHC EOS significantly deviate in a certain mass range from the corresponding empirical relations derived with various hadronic EOSs, with which one may distinguish QHC EOS from hadronic EOSs.

astro-ph.HE↗

arXiv2023

Momentum Shell in Quarkyonic Matter from Explicit Duality: A Dual Model for Cold, Dense QCD

We present a model of cold QCD matter that bridges nuclear and quark matter through the duality relation between quarks and baryons. The baryon number and energy densities are expressed as functionals of either the baryon momentum distribution, $f_{\rm B}$, or the quark distribution, $f_{\rm Q}$, which are subject to the constraints on fermions, $0 \le f_{\rm B,Q} \le 1$. The theory is ideal in the sense that the confinement of quarks into baryons is reflected in the duality relation between $f_{\rm Q}$ and $f_{\rm B}$, while other possible interactions among quarks and baryons are all neglected. The variational problem with the duality constraints is formulated and we explicitly construct analytic solutions, finding two distinct regimes: A nuclear matter regime at low density and a Quarkyonic regime at high density. In the Quarkyonic regime, baryons underoccupy states at low momenta but form a momentum shell with $f_{\rm B}=1$ on top of a quark Fermi sea. Such a theory describes a rapid transition from a soft nuclear equation of state to a stiff Quarkyonic equation of state. At this transition, there is a rapid increase in the pressure.

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arXiv2023

Sound velocity peak and conformality in isospin QCD

We study zero temperature equations of state (EOS) in isospin QCD within a quark-meson model which is renormalizable and hence eliminates high density artifacts in models with the ultraviolet cutoff (e.g., NJL models). The model exhibits a crossover transition of pion condensations from the Bose-Einstein-Condensation regime at low density to the Bardeen-Cooper-Schrieffer regime at high density. The EOS stiffens quickly and approaches the quark matter regime at density significantly less than the density for pions to spatially overlap. The sound velocity develops a peak in the crossover region, and then gradually relaxes to the conformal value $1/3$ from above, in contrast to the perturbative QCD results which predicts the approach from below. In the context of QCD computations, this opposite trend is in part due to the lack of gluon exchanges in our model, and also due to the non-perturbative power corrections arising from the condensates. We argue that with large power corrections the trace anomaly can be negative. In quantitative level, our EOS is consistent with the lattice results in the BEC regime but begins to get stiffer at higher density. The sound velocity peak also appears at higher density. The BCS gap in our model is $\Delta \simeq 300$ MeV in the quark matter domain, and naive application of the BCS relation for the critical temperature $T_c \simeq 0.57\Delta$ yields the estimate $T_c \simeq 170$ MeV, in good agreement with the lattice data.

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