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Toru Kojo

Publications and source records attributed to Toru Kojo.

At least 73 records · Page 4Linked to original sources
arXiv2014

Chiral Spirals from Noncontinuous Chiral Symmetry: The Gross-Neveu model results

It is shown that the inhomogeneous chiral condensate in the Gross-Neveu (GN) model takes the chiral spiral form, even though the thermodynamic functional depends only on the chiral scalar density. It is the inhomogeneity of the chiral scalar condensate that drives the spatial modulations of the pseudoscalar one. The result has broader implications once we start to think of fundamental theories behind the effective models. In particular, some effective interactions---which may be omitted for descriptions of the homogeneous phases---can be dynamically enhanced due to the spatial modulations of the large mean fields. Implications for the four-dimensional counterparts of the GN model are discussed. In a quark matter context, proper forms of the effective models for the inhomogeneous phases are speculated, through considerations on the Fermi-Dirac sea coupling.

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arXiv2014

The quark mass gap in strong magnetic fields

Quarks in strong magnetic fields (|eB|>>Lambda_QCD^2 ~ 0.04 GeV^2) acquire enhanced infrared phase space proportional to |eB|. Accordingly they provide larger chiral condensates and stronger backreactions to the gluon dynamics. Confronting theories with lattice data at various values of |eB|, one can test theoretical ideas as well as validity of various approximations, domain of applicability of the effective models, and so on. The particularly interesting findings on the lattice are inverse magnetic catalysis and linear growth of the chiral condensate as a function of |eB|, which pose theoretical challenges. In this talk we propose a scenario to explain both phenomena, claiming that the quark mass gap should stay at around ~ Lambda_QCD, instead of ~|eB|^{1/2} which has been supposed from dimensional arguments and/or effective model calculations. The contrast between infrared and ultraviolet behaviors of the interaction is a key ingredient to obtain the mass gap of ~Lambda_QCD.

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arXiv2014

Color screening in cold quark matter

We compute---at finite quark chemical potentials---the color screening of cold quark matter at the one-loop level, comparing the normal, BCS-paired U(1)em (or Higgs) phase and a singlet phase with color-singlet condensate near the Fermi surface. The latter phase is computed using the example of two-color QCD with a color-singlet diquark condensate. In contrast to the normal and Higgs phases, neither electric nor magnetic screening masses appear in the singlet phase. The absence of a magnetic mass, within a perturbative framework, is a consequence of the proper treatment of gauge invariance. While at large momenta the gluon self-energies approach those in the normal phase, the medium contributions to the infrared region below a scale of the mass gap are substantially suppressed. Infrared gluons at low quark density in the singlet phase appear protected from medium effects, unless the quark-gluon vertices are significantly enhanced in the infrared.

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arXiv2013

A renormalization group approach for QCD in a strong magnetic field

A Wilsonian renormalization group approach is applied, in order to include effects of the higher Landau levels for quarks into a set of renormalized parameters for the lowest Landau level (LLL), plus a set of operators made of the LLL fields. Most of the calculations can be done in a model-independent way with perturbation theory for hard gluons, thanks to form factors of quark-gluon vertices that arise from the Ritus bases for quark fields. As a part of such renormalization program, we compute the renormalized quark self-energy at 1-loop, including effects from all higher orbital levels. The result indicates that the higher orbital levels cease to strongly affect the LLL at a rather small magnetic field of (0.1 - 0.3) GeV^2.

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arXiv2013

The quark mass gap in a magnetic field

A magnetic field and the resulting Landau degeneracy enhance the infrared contributions to the quark mass gap. The gap does not grow arbitrarily, however, for models of asymptotic free interactions. For B -> infinity, the magnetic field decouples from the dimensionally reduced self-consistent equations, so that the gap behaves as ~ Lambda_QCD (or less), instead of ~ |eB|^{1/2}. On the other hand, the number of participants to the chiral condensate keeps increasing as ~ |eB| so that |<\barψ ψ>| ~ |eB| Lambda_QCD. After the mass gap stops developing, nothing tempers the growth of screening effects as B -> infinity. These features are utilized to interpret the reduction of critical temperatures for the chiral and deconfinement at finite B, recently found on the lattice. The structures of mesons are analyzed and light mesons are identified. Applications for cold, dense quark matter are also briefly discussed.

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arXiv2013

Can the nucleon axial charge be O(Nc^0)?

The nucleon self-energy and its relation to the nucleon axial charge gA are discussed at large Nc. The energy is compared for the hedgehog, conventional, and recently proposed dichotomous nucleon wavefunctions which give different values for gA. We consider their energies at both perturbative and non-perturbative levels. In perturbative estimates, we take into account the pion exchanges among quarks up to the third orders of axial charge vertices, including the many-body forces such as the Wess-Zumino terms. It turns out that the perturbative pion exchanges among valence quarks give the same leading Nc contributions for three wavefunctions, while their mass differences are O(Lamba_qcd). The signs of splittings flip for different orders of the axial charge vertices, so it is hard to conclude which one is the most energetically favored. For non-perturbative estimates involving the modification of quark bases, we use the chiral quark soliton model as an illustration. With the hedgehog quark wavefunctions with gA of O(Nc), we investigate whether solutions with coherent pions are energetically favored. Again it is hard to give decisive conclusions, but it is likely that adding the confining effects disfavors the solution with the coherent pions, making a pion cloud around a nucleon quantum rather than coherent. The nuclear matter at large Nc is also discussed in light of the value of gA.

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arXiv2012

Interweaving Chiral Spirals

We elaborate how to construct interweaving chiral spirals in (2+1) dimensions, defined as a superposition of chiral spirals oriented in different directions. We divide a two-dimensional Fermi sea into distinct wedges, characterized by the opening angle 2Theta and depth Q ~ pF, where pF is the Fermi momentum. In each wedge, the energy is lowered by forming a single chiral spiral. The optimal values for Theta and Q are chosen by balancing this gain in energy versus the cost of deforming the Fermi surface (which dominates at large Theta) and patch-patch interactions (dominant at small Theta). Using a non-local four-Fermi interaction model, we estimate the gain and cost in energy by expanding in terms of 1/Nc (where Nc is the number of colors), lqcd/Q, and Theta. Due to a form factor in our non-local model, at small 1/Nc the mass gap (chiral condensate) is large, and the interaction among quarks and the condensate local in momentum space. Consequently, interactions between different patches are localized near their boundaries, and it is simple to embed many chiral spirals. We identify the dominant and subdominant terms at high density and categorize formulate an expansion in terms of lqcd/Q or Theta. The kinetic term in the transverse directions is subdominant, so that techniques from (1+1)-dimensional systems can be utilized. To leading order in 1/Nc and lqcd/Q, the total gain in energy is ~ pF lqcd^2 with Theta ~ (lqcd/pF)^{3/5}. Since Theta decreases with increasing pF, there should be phase transitions associated with the change in the wedge number. We also argue the effects of subdominant terms at lower density where the large-Nc approximation is more reliable.

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arXiv2012

A (1+1) dimensional example of Quarkyonic matter

We analyze the (1+1) dimensional QCD (QCD_2) at finite density to consider a number of qualitative issues: confinement in dense quark matter, the chiral symmetry breaking near the Fermi surface, the relation between chiral spirals and quark number density, and a possibility of the spontaneous flavor symmetry breaking. We argue that while the free energy is dominated by perturbative quarks, confined excitations at zero density can persist up to high density. So quark matter in QCD$_2$ is an example of Quarkyonic matter. The non-Abelian bosonization and associated charge-flavor-color separation are mainly used in order to clarify basic structures of QCD_2 at finite density.

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arXiv2011

Interweaving Chiral Spirals at finite quark density

The interweaving chiral spirals (ICS), that is defined as superposition of differently oriented chiral spirals, is important for qualitative understandings of the intermediate quark density region as well as quantitative estimates of the Quarkyonic region. We discuss how to construct the ICS, taking the (2+1) dimensional Fermi system as an example. We postulate that the presence of the ICS would delay the occurrence of the chiral restoration as well as deconfinement phase transition, by tempering the growth of quark fluctuations.

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arXiv2011

The Dichotomous Nucleon: Some Radical Conjectures for the Large Nc Limit

We discuss some problems with the large Nc approximation for nucleons which arise if the axial coupling of the nucleon to pions is large, g_A \sim Nc. While g_A \sim Nc in non-relativistic quark and Skyrme models, it has been suggested that Skyrmions may collapse to a small size, r \sim 1/f_pi \sim Lambda_QCD^{-1}/sqrt(Nc). (This is also the typical scale over which the string vertex moves in a string vertex model of the baryon.) We concentrate on the case of two flavors, where we suggest that to construct a nucleon with a small axial coupling, that most quarks are bound into colored diquark pairs, which have zero spin and isospin. For odd Nc, this leaves one unpaired quark, which carries the spin and isospin of the nucleon. If the unpaired quark is in a spatial wavefunction orthogonal to the wavefunctions of the scalar diquarks, then up to logarithms of Nc, the unpaired quark only costs an energy \sim Lambda_QCD. This naturally gives g_A \sim 1 and has other attractive features. In nature, the wavefunctions of the paired and unpaired quarks might only be approximately orthogonal; then g_A depends weakly upon Nc. This dichotomy in wave functions could arise if the unpaired quark orbits at a size which is parametrically large in comparison to that of the diquarks. We discuss possible tests of these ideas from numerical simulations on the lattice, for two flavors and three and five colors; the extension of our ideas to more than three or more flavors is not obvious, though.

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arXiv2010

Quarkyonic Matter and Chiral Spirals

The nuclear matter, deconfined quark matter, and Quarkyonic matter in low temperature region are classified based on the 1/Nc expansion. The chiral symmetry in the Quarkyonic matter is investigated by taking into account condensations of chiral particle-hole pairs. It is argued that the chiral symmetry and parity are locally violated by the formation of chiral spirals, < psibar exp(2 i mu z gamma^0 gamma^z) psi >. An extension to multiple chiral spirals is also briefly discussed.

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arXiv2010

Covering the Fermi Surface with Patches of Quarkyonic Chiral Spirals

We argue that in cold, dense quark matter, in the limit of a large number of colors the ground state is unstable with respect to creation of a complicated Quarkyonic Chiral Spiral (QCS) state, in which both chiral and translational symmetries are spontaneously broken. The entire Fermi surface is covered with patches of QCSs, whose number increases as the quark density does. The low energy excitations are gapless, given by Wess-Zumino-Novikov-Witten model plus transverse kinetic terms localized about different patches.

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arXiv2010

Quarkyonic Chiral Spirals

We consider the formation of chiral density waves in Quarkyonic matter, which is a phase where cold, dense quarks experience confining forces. We model confinement following Gribov and Zwanziger, taking the gluon propagator, in Coulomb gauge and momentum space, as 1/(p^2)^2. We assume that the number of colors, N, is large, and that the quark chemical potential, mu, is much larger than renormalization mass scale, Lambda_QCD. To leading order in 1/N and Lambda_QCD/mu, a gauge theory with Nf flavors of massless quarks in 3+1 dimensions naturally reduces to a gauge theory in 1+1 dimensions, with an enlarged flavor symmetry of SU(2Nf). Through an anomalous chiral rotation, in two dimensions a Fermi sea of massless quarks maps directly onto the corresponding theory in vacuum. A chiral condensate forms locally, and varies with the spatial position, z, as < psibar exp(2 i mu z gamma^0 gamma^z) psi >. Following Schon and Thies, we term this two dimensional pion condensate a (Quarkyonic) chiral spiral. Massive quarks also exhibit chiral spirals, with the magnitude of the oscillations decreasing smoothly with increasing mass. The power law correlations of the Wess-Zumino-Novikov-Witten model in 1+1 dimensions then generate strong infrared effects in 3+1 dimensions.

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arXiv2008

Brane-induced Skyrmion on S^3: baryonic matter in holographic QCD

We study baryonic matter in holographic QCD with D4/D8/\bar{D8} multi-D brane system in type IIA superstring theory. The baryon is described as the "brane-induced Skyrmion", which is a topologically non-trivial chiral soliton in the four-dimensional meson effective action induced by holographic QCD. We employ the "truncated-resonance model" approach for the baryon analysis, including pion and ρmeson fields below the ultraviolet cutoff scale M_KK \sim 1GeV, to keep the holographic duality with QCD. We describe the baryonic matter in large N_c as single brane-induced Skyrmion on the three-dimensional closed manifold S^3 with finite radius R. The interactions between baryons are simulated by the curvature of the closed manifold S^3, and the decrease of the size of S^3 represents the increase of the total baryon-number density in the medium in this modeling. We investigate the energy density, the field configuration, the mass and the root-mean-square radius of single baryon on S^3 as the function of its radius R. We find a new picture of "pion dominance" near the critical density in the baryonic matter, where all the (axial) vector meson fields disappear and only the pion field survive. We also find the "swelling" phenomena of the baryons as the precursor of the deconfinement, and propose the mechanism of the swelling in general context of QCD. The properties of the deconfinement and the chiral symmetry restoration in the baryonic matter are examined by taking the proper order parameters. We also compare our truncated-resonance model with another "instanton" description of the baryon in holographic QCD, considering the role of cutoff scale M_KK.

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arXiv2008

Baryons and Baryonic Matter in Holographic QCD from Superstring

We study baryons and baryonic matter in holographic QCD using a D4/D8/$\bar{\rm D8}$ multi-D-brane system in the superstring theory. We obtain the chiral soliton solution for baryons in the four-dimensional meson theory derived from the multi-D-brane system. For the analysis of finite baryon-density matter, we investigate the chiral soliton on $S^3$ in holographic QCD, and find the delocalization of the soliton, i.e., the swelling of baryons in dense matter.

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arXiv2008

QCD Sum Rules and 1/$N_c$ expansion

The 1/$N_c$ arguments are developed to classify the hadronic states in the correlators. Arguments applied to the $σ$ meson correlator enable to separate the instanton, glueball, and, in particular, the $ππ$ scattering states by $1/N_c$ from both 2q and 4q correlators. The bare resonance pole with no mixing effects are analyzed with the QCD sum rules (QSR). The results suggest the existence of nontrivial correlation for the mass reduction of 4q system.

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arXiv2008

Dynamical study of bare $σ$ pole with $1/N_c$ classifications

Systematic $1/N_c$ counting of correlators is performed to directly relate quark-gluon dynamics to qualitatively different hadronic states order by order. Both 2q and 4q correlators of $σ$ quanta are analyzed with $1/N_c$ separation of the instanton, glueball, and in particular, two meson scattering states. The {\it bare} resonance pole with no mixing effects are studied with the QCD sum rules (QSR). The bare mass relation for large $N_c$ mesons, $m_ρ<m_{4q}^{I=J=0}<m_{2q}^{I=J=0}$, is derived. The firm theoretical ground of the QSR at the leading $1/N_{c}$ analyses is also emphasized.

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