arXiv subjects

Toru Kojo

Publications and source records attributed to Toru Kojo.

At least 55 records · Page 3Linked to original sources

arXiv2019

Delineating the properties of neutron star matter in cold, dense QCD

The properties of dense QCD matter are delineated through the construction of equations of state which should be consistent with the low and high density limits of QCD, nuclear laboratory experiments, and the neutron star observations. These constraints, together with the causality condition of the sound velocity, are used to develop the picture of hadron-quark continuity in which hadronic matter continuously transforms into quark matter (modulo small 1st order phase transitions). The resultant unified equation of state at zero temperature and $β$-equilibrium, which we call Quark-Hadron-Crossover (QHC19), is consistent with the measured properties of neutron stars as well as the microphysics known for the hadron phenomenology. In particular to $\sim 10n_0$ ($n_0$: saturation density) the gluons remain as non-perturbative as in vacuum and the strangeness can be as abundant as up- and down-quarks at the core of two-solar mass neutron stars. Within our modeling the maximum mass is found less than $\simeq 2.35$ times solar mass and the baryon density at the core ranges in $\sim 5$-8$n_0$.

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arXiv2019

Quark fluctuations and anisotropic confinement in magnetic fields

We study the string tension $σ$ of quantum chromodynamics (QCD) in external magnetic fields $B$ by combining the quasi-particle treatments for quarks with the collective treatments for gluons. We utilize the 1/Nc-expansion (Nc: number of colors) and the framework of Wilson's strong coupling expansion at long distance, and compare the resulting string tensions with the lattice data. The effects of magnetic fields are taken into account through the dielectric functions, which are evaluated from the one-loop polarization due to light flavor quarks with $B$-dependent effective masses $M_{\rm f}(B)\ ({\rm f}=u,d,s)$. All Landau levels are adopted in the calculations so that we can explore the string tensions from weak to strong magnetic fields. For the effective quark masses, we use a simple parameterization: $M_{\rm f}(B) = M_{\rm f}(0) + C_B |q_{\rm f}B|^{1/2}$ with $q_{\rm f}$ the electric charge of a given flavor and $C_B$ an adaptive parameter. We find that the parameter $C_B$ needs to be small, $C_B \lesssim 0.05$, to qualitatively reproduce the trends of lattice QCD results for $0 \leq |eB| \lesssim 1.5\, {\rm GeV}^2$. The quantitative agreement is found for $C_B \simeq 0$ and the strong coupling $α_S \simeq 5$ in the infrared.

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arXiv2019

New Neutron Star Equation of State with Quark-Hadron Crossover

We present a much improved equation of state for neutron star matter, QHC19, with a smooth crossover from the hadronic regime at lower densities to the quark regime at higher densities. We now use the Togashi et al.~equation of state (Togashi:2017), a generalization of the Akmal-Pandharipande-Ravenhall equation of state of uniform nuclear matter, in the entire hadronic regime; the Togashi equation of state consistently describes non-uniform as well as uniform matter, and matter at beta equilibrium without the need for an interpolation between pure neutron and symmetric nuclear matter. We describe the quark matter regime at higher densities with the Nambu--Jona--Lasinio model, now identifying tight constraints on the phenomenological universal vector repulsion between quarks and the pairing interaction between quarks arising from the requirements of thermodynamic stability and causal propagation of sound. The resultant neutron star properties agree very well with the inferences of the LIGO/Virgo collaboration, from GW170817, of the pressure vs. baryon density, neutron star radii, and tidal deformabilities. The maximum neutron star mass allowed by QHC19 is 2.35 $M_\odot$, consistent with all neutron star mass determinations.

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arXiv2019

Gluon propagator in two-color dense QCD: Massive Yang-Mills approach at one-loop

We study the Landau gauge gluon propagators in dense two-color QCD at quark chemical potential, $μ_q$, in the range from 0.5 to 1.0 GeV not reachable by the perturbative method at weak coupling. In order to take into account the non-perturbative effects, at tree level we use a massive Yang-Mills model for the Yang-Mills theory (or the Curci-Ferrari model) which has successfully described the lattice results of the gluon and ghost propagators in the Landau gauge. We couple quarks to this theory and compute the one-loop polarization effects in medium. The presence of the gluon mass significantly tempers the medium effects and uncertainties associated with the strong coupling constant $α_s$. The diquark condensate in two-color QCD is color-singlet, for which neither electric nor magnetic screening masses should appear at the scale less than the diquark gap. The presence of the gap helps to explain the lattice results which are not very sensitive to the quark density. Meanwhile we also found the limitation of the one-loop estimate as well as the lack of some physics in perturbative medium corrections.

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arXiv2019

Delineating the properties of matter in cold, dense QCD

The properties of dense QCD matter are delineated through the construction of equations of state which should be consistent with QCD calculations in the low and high density limits, nuclear laboratory experiments, and the neutron star observations. These constraints, together with the causality condition of the sound velocity, are used to develop the picture of hadron-quark continuity in which hadronic matter continuously transforms into quark matter (modulo small 1st order phase transitions). For hadronic matter (at baryon density nB > ~2n0 with n0 ~ 0.16 fm^(-3) being the nuclear saturation density) we use equations of state by Togashi et al. based on microscopic variational many-body calculations, and for quark matter (nB > ~5n0) we construct equations of state using a schematic quark model (with strangeness) whose interactions are motivated by the hadron phenomenology. The region between hadronic and quark matters (~2n0 < nB < ~5n0), which is most difficult to calculate, is treated by highly constrained interpolation between nuclear and quark matter equations of state. The resultant unified equation of state at zero temperature and beta-equilibrium, which we call Quark-Hadron-Crossover (QHC18 and QHC19), is consistent with the measured properties of neutron stars and in addition gives us microscopic insights into the properties of dense QCD matter. In particular to ~10n0 the gluons can remain as non-perturbative as in vacuum and the strangeness can be as abundant as up- and down-quarks at the core of two-solar mass neutron stars. Within our modeling the maximum mass is found less than ~2.35 times solar mass and the baryon density at the core ranges in ~5-8n0.

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arXiv2019

Effective repulsion in dense quark matter from non-perturbative gluon exchange

A moderately strong vector repulsion between quarks in dense quark matter is needed to explain how a quark core can support neutron stars heavier than two solar masses. We study this repulsion, parametrized by a four-fermion interaction with coupling g_V, in terms of non-perturbative gluon exchange in QCD in the Landau gauge. Matching the energy of quark matter, g_V n_q^2 (where n_q is the number density of quarks) with the quark exchange energy calculated in QCD with a gluon propagator parametrized by a finite gluon mass m_g and a frozen coupling alpha_s, at moderate quark densities, we find that gluon masses m_g in the range 200 - 600 MeV and alpha_s = 2 - 4 lead to a g_V consistent with neutron star phenomenology. Estimating the effects of quark masses and a color-flavor-locked (CFL) pairing gap, we find that g_V can be well approximated by a flavor-symmetric, decreasing function of density. We briefly discuss similar matchings for the isovector repulsion and for the pairing attraction.

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arXiv2018

Renormalizing the zero point energy in dense QCD

We analyze the zero point energy in a dense matter of quarks or hadrons with particular attention on the renormalization of the UV divergences. Besides divergences removable by the vacuum subtraction and counter terms, there are also UV divergences associated with non-perturbative modifications of quark bases appearing in the in-medium propagators. The latter would remain after the self-energies and vertices are renormalized, unless a proper set of medium contributions is included at a given truncation. We use the formalism of the two particle irreducible action to clarify how the UV divergences are assembled to cancel. An example is given for the thermodynamic potentials with mesons as composite particles whose zero point energies apparently diverge but can be cancelled by the quark self-energy contributions. Important applications of this work are quark matter with hadronic correlations which may be realized at the core of neutron stars.

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arXiv2017

Functional renormalization group study of the Quark-Meson model with $ω$ meson

We study the phase diagram of two-flavor massless QCD at finite baryon density by applying the functional renormalization group (FRG) for a quark-meson model with $σ, π$, and $ω$ mesons. The dynamical fluctuations of quarks, $σ$, and $π$ are included into the flow equations, while the amplitudes of $ω$-fields are also allowed to fluctuate. At high temperature the effects of the $ω$-field on the phase boundary are qualitatively similar to the mean-field calculations; the phase boundary is shifted to the higher chemical potential region. As the temperature is lowered, however, the transition line bends back to the lower chemical potential region, irrespective to the strength of the vector coupling. In our FRG calculations, the driving force of the low temperature first order line is the fluctuations rather the quark density, and the effects of $ω$-fields have little impact. At low temperature, the effective potential at small $σ$ field is very sensitive to the infrared cutoff scale, and this significantly affects our determination of the phase boundaries. The critical chemical potential at the tricritical point is affected by the $ω$-field effects but its critical temperature stays around the similar value. Some caveats are given in interpreting our model results.

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arXiv2017

Phenomenological QCD equations of state for neutron star mergers, a talk presented at CPOD17

We delineate the properties of dense QCD matter through equations of state constrained by the neutron star observations. The two solar mass constraint, the radius constraint of 11-13 km, and the causality constraint on the speed of sound, are used to develop the picture of hadron-quark continuity in which hadronic matter continuously transforms into quark matter. A unified equation of state at zero temperature and beta-equilibrium is constructed by a phenomenological interpolation between nuclear and quark matter equations of state. For applications to supernovae and neutron star mergers, the unified equation of state is perturbed by temperature corrections.

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arXiv2017

From hadrons to quarks in neutron stars: a review

We review the equation of state of matter in neutron stars from the solid crust through the liquid nuclear matter interior to the quark regime at higher densities. We focus in detail on the question of how quark matter appears in neutron stars, and how it affects the equation of state. After discussing the crust and liquid nuclear matter in the core we briefly review aspects of microscopic quark physics relevant to neutron stars, and quark models of dense matter based on the Nambu--Jona-Lasinio framework, in which gluonic processes are replaced by effective quark interactions. We turn then to describing equations of state useful for interpretation of both electromagnetic and gravitational observations, reviewing the emerging picture of hadron-quark continuity in which hadronic matter turns relatively smoothly, with at most only a weak first order transition, into quark matter with increasing density. We review construction of unified equations of state that interpolate between the reasonably well understood nuclear matter regime at low densities and the quark matter regime at higher densities. The utility of such interpolations is driven by the present inability to calculate the dense matter equation of state in QCD from first principles. As we review, the parameters of effective quark models -- which have direct relevance to the more general structure of the QCD phase diagram of dense and hot matter -- are constrained by neutron star mass and radii measurements, in particular favoring large repulsive density-density and attractive diquark pairing interactions. We describe the structure of neutron stars constructed from the unified equations of states with crossover. Lastly we present the current equations of state -- called "QHC18" for quark-hadron crossover -- in a parametrized form practical for neutron star modeling.

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arXiv2017

Phenomenological QCD equations of state for neutron star mergers

Thermal QCD equations of state at high baryon density are sensitive to the phase structure and the resulting excitation modes. The leading contribution at low temperature can be either ~p_F^2 T^2 (pF: Fermi momentum, T: temperature) for phases with gapless quarks, or ~T^4 for phases with gapped quarks. In the latter the thermal pressure is dominated by collective modes. Starting with a schematic quark model developed for neutron star structure, we estimate the thermal contributions and zero point energy from the Nambu-Goldstone modes by building them upon the mean field background for the color-flavor-locked quark matter. Applying the phase shift representation for thermodynamic potentials, we include not only the bound state pairs but also resonating pairs. According to the Levinson's theorem, the high energy contributions tend to cancel the pole contributions to the thermodynamics, tempering the UV behaviors in the zero point energy. Our primary target in this talk is the domain with baryon density nB as large as ~ 5-10n_0 (n_0 = 0.16 fm^{-3}: nuclear saturation density), and the temperature T of the order ~30-100 MeV. The insights into this domain may be obtained through the future detection of gravitational waves from neutron star merging events.

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arXiv2017

Pseudo Nambu-Goldstone modes in neutron stars

If quarks and gluons are either gapped or confined in neutron stars (NSs), the most relevant light modes are Nambu-Goldstone (NG) modes. We study NG modes within a schematic quark model whose parameters at high density are constrained by the two-solar mass constraint. Our model has the color-flavor-locked phase at high density, with the effective couplings as strong as in hadron physics. We find that strong coupling effects make NG modes more massive than in weak coupling predictions, and would erase several phenomena caused by the stressed pairings in mismatched Fermi surfaces. For instance, we found that charged kaons, which are dominated by diquark and anti-diquark components, are not light enough to condense at strong coupling. Implications for gravitational wave signals for NS-NS mergers are also briefly discussed.

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arXiv2017

QCD in stars

We discuss cold dense QCD by examining constraints from neutron stars, nuclear experiments, and QCD calculations at low and high baryon density. The two solar mass constraint and suggestive small radii (10~13 km) of neutron stars constrain the strength of hadron-quark matter phase transitions. Assuming the adiabatic continuity from hadronic to quark matter, we use a schematic quark model for hadron physics and examine the size of medium coupling constants. We find that to baryon density nB ~ 10n0 (n0: nuclear saturation density), the model coupling constants should be as large as in the vacuum, indicating that gluons remain non- perturbative even after the quark matter formation.

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arXiv2016

Mesons in strong magnetic fields: (I) General analyses

We study properties of neutral and charged mesons in strong magnetic fields |eB|>> Lambda_QCD^2 with Lambda_QCD being the QCD renormalization scale. Assuming long-range interactions, we examine magnetic-field dependences of various quantities such as the constituent quark mass, chiral condensate, meson spectra, and meson wavefunctions by analyzing the Schwinger-Dyson and Bethe-Salpeter equations. Based on the density of states obtained from these analyses, we extend the hadron resonance gas (HRG) model to investigate thermodynamics at large B. As B increases the meson energy behaves as a slowly growing function of the meson's transverse momenta, and thus a large number of meson states is accommodated in the low energy domain; the density of states at low temperature is proportional to B^2. This extended transverse phase space in the infrared regime significantly enhances the HRG pressure at finite temperature, so that the system reaches the percolation or chiral restoration regime at lower temperature compared to the case without a magnetic field; this simple picture would offer a gauge invariant and intuitive explanation of the inverse magnetic catalysis.

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arXiv2016

Phenomenological neutron star equations of state: 3-window modeling of QCD matter

We discuss the 3-window modeling of cold, dense QCD matter equations of state at density relevant to neutron star properties. At low baryon density, n_B < ~ 2n_s (n_s: nuclear saturation density), we utilize purely hadronic equations of state that are constrained by empirical observations at density n_B ~ n_s and neutron star radii. At high density, n_B > ~ 5n_s, we use the percolated quark matter equations of state which must be very stiff to pass the two-solar mass constraints. The intermediate domain at 2 < n_B/n_s < 5 is described as neither purely hadronic nor percolated quark matter, and the equations of state are inferred by interpolating hadronic and percolated quark matter equations of state. Possible forms of the interpolation are severely restricted by the condition on the (square of) speed of sound, 0 < c_s^2 < 1. The characteristics of the 3-window equation of state are compared with those of conventional hybrid and self-bound quark matters. Using a schematic quark model for the percolated domain, it is argued that the two-solar mass constraint requires the model parameters to be as large as their vacuum values, indicating that the gluon dynamics remains strongly non-perturbative to n_B ~ 10n_s. The hyperon puzzle is also briefly discussed in light of quark descriptions.

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arXiv2015

Phenomenological QCD equations of state for neutron stars

We delineate the properties of QCD matter at baryon density n_B=1-10n_0 (n_0: nuclear saturation density), through the construction of neutron star equations of state that satisfy the neutron star mass-radius constraints as well as physical conditions on the speed of sound. The QCD matter is described in the 3-window modeling: at n_B < 2n_0 purely nuclear matter; at n_B > 5n_0 percolated quark matter; and at 2n_0 < n_B < 5n_0 matter intermediate between these two which are constructed by interpolation. Using a schematic quark model with effective interactions inspired from hadron and nuclear physics, we analyze the strength of interactions necessary to describe observed neutron star properties. Our finding is that the interactions should remain as strong as in the QCD vacuum, indicating that gluons at n_B =1-10 n_0 remain non-perturbative even after quark matter formation.

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arXiv2015

The Quarkyonic Star

We discuss theoretical scenarios on crossover between nuclear matter (NM) and quark matter (QM). We classify various possibilities into three major scenarios according to the onset of diquark degrees of freedom that characterizes color-superconducting (CSC) states. In the conventional scenario NM occurs at the liquid-gas (or liquid-vacuum at zero temperature) phase transition and QM occurs next, after which CSC eventually appears. With the effect of strong correlation, the BEC-BCS scenario implies that CSC occurs next to NM and QM comes last in the BCS regime. We adopt the quarkyonic scenario in which NM, QM, and CSC are theoretically indistinguishable and thus these names refer to not distinct states but relevant descriptions of the same physical system. Based on this idea we propose a natural scheme to interpolate NM near normal nuclear density and CSC with vector coupling at high baryon density. We finally discuss the mass-radius relation of the neutron star and constraints on parameters in the proposed scheme.

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arXiv2015

Phenomenological QCD equation of state for massive neutron stars

We construct an equation of state for massive neutron stars based on quantum chromodynamics phenomenology. Our primary purpose is to delineate the relevant ingredients of equations of state that simultaneously have the required stiffness and satisfy constraints from thermodynamics and causality. These ingredients are: (i) a repulsive density-density interaction, universal for all flavors; (ii) the color-magnetic interaction active from low to high densities; (iii) confining effects, which become increasingly important as the baryon density decreases; (iv) non-perturbative gluons, which are not very sensitive to changes of the quark density. We use the following "3-window" description: At baryon densities below about twice normal nuclear density, 2n_0, we use the Akmal-Pandharipande-Ravenhall (APR) equation of state, and at high densities, > (4-7)n_0, we use the three-flavor Nambu-Jona-Lasinio (NJL) model supplemented by vector and diquark interactions. In the transition density region, we smoothly interpolate the hadronic and quark equations of state in the chemical potential-pressure plane. Requiring that the equation of state approach APR at low densities, we find that the quark pressure in non-confining models can be larger than the hadronic pressure, unlike in conventional equations of state. We show that consistent equations of state of stiffness sufficient to allow massive neutron stars are reasonably tightly constrained, suggesting that gluon dynamics remains non-perturbative even at baryon densities ~10n_0.

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