arXiv subjects

Hiroaki Kouno

Publications and source records attributed to Hiroaki Kouno.

At least 19 recordsLinked to original sources

arXiv2026

The canonical approach at high temperature revisited

This paper discusses a paradox encountered when employing the canonical approach, particularly in the high-temperature region where the Roberge-Weiss transition exists at finite imaginary chemical potential. The paradox is that the results obtained using the canonical approach cannot match the correct results in that region. We show that the paradox originates from the Roberge-Weiss transition in the infinite-size system, which is linked to the non-trivial Polyakov-loop sectors. Furthermore, it is shown that this paradox disappears in finite-size systems because of the smearing effect for the Roberge-Weiss transition, which validates the use of the canonical approach in lattice QCD simulations.

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arXiv2026

Effective degrees of freedom, trace anomaly and c-theorem like condition in the hadron resonance gas model

The relation between the effective degrees of freedom (EDOF) and the trace anomaly is studied in the hadron resonance gas (HRG) model. If we regard the thermodynamical relation as the evolution equation and define the EDOF as P/T^4, where P and T are the pressure and the temperature, respectively, we obtain the equation which relates to the trace anomaly. The structure of the equation resembles that of the so-called c-theorem, which asserts that the EDOF should not increase as the energy scale parameter decreases, in the two dimensional conformal field theory. There is a stationary point where the trace anomaly (modified trace anomaly) vanishes, and the scale symmetry is restored. To investigate the limiting temperature of the HRG model with the excluded volume effects, we consider two types of the c-theorem like conditions for the EDOF. The first condition requires that the EDOF should not decrease when T increases. This condition is equivalent to the condition that the trace anomaly (modified trace anomaly) should not be negative. The second condition requires that the EDOF should be convex downwards as a function of T. It is found that the first condition gives the limiting temperature of the HRG model with the excluded volume effect which is much higher than the crossover transition temperature obtained by the lattice QCD calculation and, at zero baryon number density, is close to the transition temperature in the pure gluonic theory, while the second one gives the limiting temperature which almost coincides with the one obtained by using the normalized baryon number fluctuation in the previous study and is consistent with the critical point predicted by the lattice QCD calculation.

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arXiv2026

Thermodynamic geometry in hadron resonance gas model at real and imaginary baryon chemical potential and a simple sufficient condition for quark deconfinement

The thermodynamic geometry of the hadron resonance gas model with (without) excluded volume effects (EVE) of baryons is investigated. The case with imaginary mu, where mu is the baryon chemical potential, is investigated as well as the one with real mu. We calculate the scalar curvature R and use the R=0 criterion to investigate the phase structure in the mu^2-T plane where T is the temperature. The curve on which R=0 continues analytically from the imaginary mu region, where the lattice QCD is feasible, to the real mu one. In the presence of EVE, there are rich phase structures in the large real mu region as well as the Roberge-Weiss like region where mu is imaginary and a singularity appears, while there is no phase structure in the large real $μ$ region in the absence of EVE. The limitation temperature of the baryon gas is also obtained by using the baryon number fluctuation. The LQCD predicted critical point locates almost on the curve of the limitation temperature we determined. A simple empiric sufficient condition, n_B>1/(2v_B)$, is obtained for the quark deconfinement in the large real mu region, where n_B and v_B are the net baryon number density and the volume of a baryon, respectively.

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arXiv2025

Polyakov-loop phase, Roberge-Weiss periodicity and thermodynamics

In this paper, we discuss the role of Roberge-Weiss periodicity in the thermodynamics of quantum chromodynamics at moderately high temperature, where the semi-quark-gluon plasma is expected. From the construction of the grand canonical partition function at zero and also at finite density via the canonical approach, we are able to discuss the relation between contributions of the Polyakov-loop phase and Roberge-Weiss periodicity. Then, we can conclude that the existence of Roberge-Weiss periodicity is a necessary condition to reproduce exact results at moderately high temperature.

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arXiv2024

Hadron-quark hybrid model, modular transformation and Roberge-Weiss transition

In the framework of modular transformations, we reformulate the recently proposed hadron-quark hybrid model when the imaginary baryonic chemical potential is introduced. As a result, we can consider the torus, which is characterized by the complex number densities of baryons (antibaryons) and quarks (antiquarks). We apply this model to analyze the Roberge-Weiss transition. It is shown that the torus vanishes at the baryonic chemical potential where the Roberge-Weiss transition appears because the number density of baryons (antibaryons) is not linearly independent of the number density of quarks (antiquarks). When the temperature T is lower than the Roberge-Weiss transition temperature TRW, the torus shrinks smoothly to the one-dimensional object at the Roberge-Weiss transition point, but the discontinuity does not appear. On the other hand, the discontinuity of the geometrical object appears when T>TRW. We also calculate the modulus of the torus and transform it into the fundamental region. The transformed moduli are symmetric below TRW, but the symmetry is broken above TRW.

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arXiv2024

Roberge-Weiss periodicity and singularity in hadron resonance gas model with excluded volume effects

Quantum chromodynamics (QCD) with pure imaginary baryon number chemical potential mu =i theta T, where T is temperature and theta is a real number, has the Roberge-Weiss periodicity. We study the theta-dependence of the baryon number density and the pressure in the hadron resonance gas model with excluded volume effects of baryons. It is shown that the baryon number density and the pressure are smooth periodic functions of theta at low or high temperature. However, they have singular behavior at theta =(2k+1)pi where k is an integer, when T sim 211MeV. This temperature is consistent with the Roberge-Weiss transition temperature TRW obtained by lattice QCD simulations. This singularity can be explained by the dual excluded volume effects in which the roles of point-like and non point-like particles are exchanged each other in the ordinary excluded volume effects. It is also indicated that the excluded volume effect is visible just below TRW and is directly detectable by the lattice QCD simulation at finite theta. We compare the results with the one obtained by the Polyakov-loop extended Nambu-Jona-Lasinio model.

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arXiv2024

Hadron-quark transition and chiral symmetry restoration at high density

A simple phenomenological hybrid hadron-quark model with effective volume effects of baryons and chiral dynamics is investigated. The hybrid EoS naturally connects the low density baryonic matter with the high density quark matter. In the intermediate region, the phase which can not be regarded as pure hadron matter or pure quark matter appears. In this model, there is a possibility that the abrupt first -order like transition to pure quark matter induces the strong chiral symmetry restoration and the speed of sound has a large peak at considerable large density.

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arXiv2021

Multiplicity, probabilities, and canonical sectors for the cold QCD matter

At sufficiently low temperature, without requiring any numerical data at finite real chemical potential, we can clarify the canonical partition function with fixed quark number via the imaginary chemical potential region with few ansatzs. The canonical partition function relates to the multiplicity distribution which can be observed in collider experiments and thus we may access important information of the properties of the QCD matter based on the canonical method. In this paper, we estimate the multiplicity entropy, the configuration entropy, and the pointwise information which can be calculable with the canonical partition function to understand the properties of the cold QCD matter at finite density. With the large $N_\mathrm{c}$ limit where $N_\mathrm{c}$ is the number of colors, we can simply estimate the tendency of them, and then the relation to the quarkyonic phase is clarified. In addition, we discuss the nontrivial ground state degeneracy from the viewpoint of the canonical sectors.

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arXiv2021

Nonanalyticity, sign problem and Polyakov line in Z3-symmetric heavy quark model at low temperature: Phenomenological model analyses

The nonanalyticity and the sign problem in the Z3-symmetric heavy quark model at low temperature are studied phenomenologically. For the free heavy quarks, the nonanalyticity is analyzed in the relation to the zeros of the grand canonical partition function. The Z3-symmetric effective Polyakov-line model (EPLM) in strong coupling limit is also considered as an phenomenological model of Z3-symmetric QCD with large quark mass at low temperature. We examine how the Z3-symmetric EPLM approaches to the original one in the zero-temperature limit. The effects of the Z3-symmetry affect the structure of zeros of the microscopic probability density function at the nonanalytic point. The average value of the Polyakov line can detect the structure, while the other thermodynamic quantities are not sensible to the structure in the zero-temperature limit. The effect of the imaginary quark chemical potential is also discussed. The imaginary part of the quark number density is very sensitive to the symmetry structure at the nonanalytical point. For a particular value of the imaginary quark number chemical potential, large quark number may be induced in the vicinity of the nonanalytical point.

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arXiv2021

Anatomy of the dense QCD matter from canonical sectors

We investigate the nuclear and the quark matter at finite real chemical potential ($μ_\mathrm{R}$) and low temperature from the viewpoint of the canonical sectors constructed via the imaginary chemical potential region. Based on the large $N_\mathrm{c}$ estimation, where $N_\mathrm{c}$ is the number of color, we can discuss the confinement-deconfinement nature at finite $μ_\mathrm{R}$ from the canonical sectors. We found the expectation that the sharp change of canonical sectors at $μ_\mathrm{R} \sim M_\mathrm{B}/N_\mathrm{c}$, where $M_\mathrm{B}$ is the lowest baryon mass, is happen in the large $N_\mathrm{c}$ regime, and it is matched with the quarkyonic picture. In addition, we discussed the color superconductivity and the chiral properties from the structure of canonical sectors. Even in the present anatomy from the canonical sectors, we can have the suitable picture for the dense QCD matter.

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arXiv2021

Persistent homology analysis for dense QCD effective model with heavy quarks

The isospin chemical potential region is known as the sign-problem free region of quantum chromodynamics (QCD). In this paper, we introduce the isospin chemical potential to the three-dimensional three-state Potts model to mimic the dense QCD; e.g., the QCD effective model with heavy quarks at finite density. We call it as QCD-like Potts model. The QCD-like Potts model does not have the sign problem, but we can expect that it shares some properties with QCD. Since we can obtain the non-approximated Potts spin configuration at finite isospin chemical potential where the simple Metropolis algorithm can work, we perform the persistent homology analysis towards exploring the dense spatial structure of QCD. We show that the averaged birth-death ratio has the same information with the Polyakov loop, but the maximum birth-death ratio has additional information near the phase transition.

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arXiv2021

A model consistent with LQCD data on $ρ$-meson screening mass

Recently, state-of-art LQCD calculations were done for $π$-meson and $ρ$-meson screening mass, ${M_π^{\rm scr}}(T)$ and ${M_ρ^{\rm scr}}(T)$. We consider the two-flavor system, and focus on temperature dependence $T$ of ${M_π^{\rm scr}}(T)$ and ${M_ρ^{\rm scr}}(T)$. Our aim is to construct a model consistent with LQCD data on ${M_ρ^{\rm scr}}(T)$ and ${M_π^{\rm scr}}(T)$.

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arXiv2020

Information theoretical view of QCD effective model with heavy quarks

To understand the phase transition phenomena, information theoretical approaches can pick up some important properties of the phenomena based on the probability distribution. In this paper, we show information theoretical aspects of the 3-dimensional 3-state Potts model with the external field which is corresponding to the QCD effective model with heavy quarks. The transfer mutual information which represents the information flow of two spin variables is numerically estimated based on the Markov-chain Monte-Carlo method. The transfer mutual information has the peak near the confinement-deconfinement transition, and it may be used to detect the precursors of the transition. Since the transfer mutual information still have the peak even if the Polyakov-loop changes continuously and smoothly, we may pick up some aspects of the confinement-deconfinement nature from the information flow properties. Particularly, the transfer mutual information shows the significantly different behavior below and above the Roberge-Weiss endpoint existed in the pure imaginary chemical potential region, which may indicate the system change by the confinement-deconfinement transition.

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arXiv2020

A hadron-quark hybrid model reliable for the EoS in $μ_{B} \leq 400$ MeV

We present a simple version of hadron-quark hybrid (HQH) model in the $μ_B$--$T$ plain, where $T$ is temperature and $μ_{B}$ is the baryon-number chemical potential. The model is composed of the independent-quark model for quark-gluon states and an improved version of excluded-volume hadron resonance gas (EV-HRG) model for hadronic states. In the improved version of EV-HRG, the pressure has charge conjugation and is obtained by a simple analytic form. The switching function from hadron states to quark-gluon states in the present model has no chemical potential dependence. The simple HQH model is successful in reproducing LQCD results on the transition region of chiral crossover and the EoS in $μ_{B} \leq 400$ MeV. We then predict the chiral-crossover region in $400 \leq μ_{B} \leq 800$ MeV. We also predict a transition line derived from isentropic trajectories in $0 \leq μ_{B} \leq 800$ MeV and find that the effect of strangeness neutrality is small there.

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arXiv2020

Persistent homology analysis of deconfinement transition in effective Polyakov-line model

The persistent homology analysis is applied to the effective Polyakov-line model on a rectangular lattice to investigate the confinement-deconfinement nature. The lattice data are mapped onto the complex Polyakov-line plane without taking the spatial average and then the plane is divided into three domains. This study is based on previous studies for the clusters and the percolation properties in lattice QCD, but the mathematical method of the analyses are different. The spatial distribution of the data in the individual domain is analyzed by using the persistent homology to obtain information of the multiscale structure of center clusters. In the confined phase, the data in the three domains show the same topological tendency characterized by the birth and death times of the holes which are estimated via the filtration of the alpha complexes in the data space, but do not in the deconfined phase. By considering the configuration averaged ratio of the birth and death times of holes, we can construct the nonlocal order-parameter of the confinement-deconfinement transition from the multiscale topological properties of center clusters.

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arXiv2019

Roberge-Weiss periodicity, canonical sector and modified Polyakov-loop

To obtain deeper understanding of QCD properties at finite temperature, we consider the Fourier decomposition of the grand-canonical partition function based on the canonical ensemble method via the imaginary chemical potential. Expectation values are, then, represented by summation over each canonical sector. We point out that the modified Polyakov-loop can play an important role in the canonical ensemble; for example, the Polyakov-loop paradox which is known in the canonical ensemble method can be evaded by considering the quantity. In addition, based on the periodicity issue of the modified Polyakov-loop at finite imaginary chemical potential, we can construct the systematic way to compute the dual quark condensate which has strong unclearness in its foundation in the presence of dynamical quarks so far.

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arXiv2019

Themodynamics for pure SU($2$) gauge theory using gradient flow

We study the equation of state of pure SU($2$) gauge theory using Monte Carlo simulations. The scale-setting of lattice parameters has been carried by using the gradient flow. We propose a reference scale $t_0$ for the SU($2$) gauge theory satisfying $t^2 \langle E \rangle|_{t=t_0} =0.1$, which is fixed by a natural scaling-down of the standard $t_0$-scale for the SU($3$) case based on perturbative analyses. We also show the thermodynamic quantities as a function of $T/T_c$, which are derived by the energy-momentum tensor using the small flow-time expansion of the gradient flow.

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arXiv2018

Thermodynamics for SU(2) pure gauge theory using gradient flow

We present the scale-setting function and the equation of state of the pure SU(2) gauge theory using the gradient flow method. We propose a reference scale t0 for the SU(2) gauge theory satisfying $t^2\langle E \rangle|_{t=t_0} = 0.1$. This reference value is fixed by a natural scaling-down of the standard t0-scale for the SU(3) gauge theory based on the perturbative analyses. We also show the thermodynamic quantities as a function of $T/T_c$, which are derived by the energy-momentum tensor using the small flow time expansion of the gradient flow.

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