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T. Kunihiro

Publications and source records attributed to T. Kunihiro.

36 records · Page 2Linked to original sources
arXiv2002

Precursor of Color Superconductivity

We investigate possible precursory phenomena of color superconductivity at finite temperature $T$ with an effective theory of QCD. It is found that the fluctuation of the diquark pair field exists with a prominent strength even well above the critical temperature $T_c$. We show that such a fluctuaiton forms a collective mode, the corresponding pole of which approaches the origin as $T$ is lowered to $T_c$ in the complex energy plane. We discuss the possible relevance of the precursor to the observables to be detected in heavy-ion collisions.

hep-ph↗
arXiv2002

Chiral and Color-superconducting Phase Transitions with Vector Interaction in a Simple Model

We investigate effects of the vector interaction on chiral and color superconducting (CSC) phase transitions at finite density and temperature in a simple Nambu-Jona-Lasinio model. It is shown that the repulsive density-density interaction coming from the vector term, which is present in the effective chiral models but has been omitted, enhances the competition between the chiral symmerty breaking (chiSB) and CSC phase transition, and thereby makes the thermodynamic potential have a shallow minimum over a wide range of values of the correlated chiral and CSC order parameters. We find that when the vector coupling is increased, the first order transition between the chiSB and CSC phases becomes weaker, and the coexisting phase in which both the chiral and color-gauge symmetry are dynamically broken comes to exisit over a wider range of the density and temperature. We also show that there can exist two endpoints, which are tricritical points in the chiral limit, along the critical line of the first order transition in some range of values of the vector coupling. Although our analysis is based on a simple model, the nontrivial interplay between the chiSB and CSC phases induced by the vector interaction is expected to be a universal phenomenon and might give a clue to understanding results obtained with two-color QCD on the lattice.

hep-ph↗
arXiv2002

Formation of sigma Mesic Nuclei in (d,t) and (d,^3He) Reactions

We explore the possibility to observe an enhanced 2pi correlation in the scalar iso-scalar (sigma) channel in nuclei by (d,t) and (d,^3He) reactions to obtain new information on the partial restoration of chiral symmetry in the nuclear medium. The sensitivity of the reaction spectra on the change of the chiral condensate in the nuclear medium is examined.

nucl-th↗
arXiv2002

Simultaneous Softening of sigma and rho Mesons associated with Chiral Restoration

Complex poles of the unitarized pi-pi scattering amplitude in nuclear matter are studied. Partial restoration of chiral symmetry is modeled by the decrease of in-medium pion decay constant f*_{pi}. For large chiral restoration (f*_{pi}/f_{pi} << 1), 2nd sheet poles in the scalar (sigma) and the vector (rho) mesons are both dictated by the Lambert W function and show universal softening as f*_{pi} decreases. In-medium pi-pi cross section receives substantial contribution from the soft mode and exhibits a large enhancement in low-energy region. Fate of this universality for small chiral restoration (f*_{pi}/f_{pi} ~ 1) is also discussed.

hep-ph↗
arXiv2002

Precursor of Color Superconductivity in Hot Quark Matter

We investigate possible precursory phenomena of color superconductivity in quark matter at finite temperature T with use of a simple Nambu-Jona-Lasinio model. It is found that the fluctuating pair field exists with a prominent strength even well above the critical temperature T_c. We show that the collective pair field has a complex energy located in the second Riemann sheet, which approaches the origin as T is lowered to T_c. We discuss the possible relevance of the precursor to the observables to be detected in heavy ion collisions.

nucl-th↗
arXiv2001

The $σ$-meson and $π$-$π$ Correlation in Hot/Dense Medium: soft modes for chiral transition in QCD

After a brief overview of the realization of chiral symmetry in hot and/or dense medium, the implications of the existence of a light scalar-isoscalar meson (which we call $σ$ throughout this report) are discussed in the vacuum and in the medium. Special emphasis is put on its relation to the fluctuation of the chiral order parameter $<\bar{q}q>$. In the vacuum, the $σ$-meson is an elusive resonance corresponding to a pole deep in the second Riemann sheet of the $π$-$π$ scattering matrix in the $I$=$J$=0 channel. This is because the the amplitude fluctuation of $<\bar{q}q>$ (corresponding to {\rm ur}-$σ$) and the phase fluctuation of $<\bar{q}q>$ (2 pion states) mix strongly in the vacuum. As the temperature and/or density of the system increase, however, there arises a softening of this complex pole due to the partial restoration of chiral symmetry. Such soft modes play a key role to understand the QCD phase structure. We demonstrate that even a slight softening of the $σ$ mode could induce strong spectral enhancement and strong $π$-$π$ correlation near the 2$m_π$ threshold in the $I$=$J$=0 channel, which thereby can be a signature of the partial restoration of chiral symmetry. Such spectral enhancement may be seen not only in hot matter created by the relativistic heavy ion collisions but also in cold matter (heavy nuclei) probed by photons and hadrons. Relevance of the partial restoration of chiral symmetry in heavy nuclei with the recent data by the CHAOS and CB collaborations as well as with on-going and future experiments are also discussed.

nucl-th↗
arXiv2001

Renormalization Group Method Applied to Kinetic Equations: roles of initial values and time

The so-called renormalization group (RG) method is applied to derive kinetic and transport equations from the respective microscopic equations. The derived equations include Boltzmann equation in classical mechanics, Fokker-Planck equation, a rate equation in a quantum field theoretical model. Utilizing the formulation of the RG method which elucidates the important role played by the choice of the initial conditions, the general structure and the underlying assumptions in the derivation of kinetic equations in the RG method is clarified. It is shown that the present formulation naturally leads to the choice for the initial value of the microscopic distribution function at arbitrary time $t_0$ to be on the averaged distribution function to be determined. The averaged distribution function may be thought as an integral constant of the solution of microscopic evolution equation; the RG equation gives the slow dynamics of the would-be initial constant, which is actually the kinetic equation governing the averaged distribution function. It is further shown that the averaging as given above gives rise to a coarse-graining of the time-derivative which is expressed with the initial time $t_0$, thereby leads to time-irreversible equations even from a time-reversible equation. It is shown that a further reduction of Boltzmann equation to fluid dynamical equations and the adiabatic elimination of fast variables in Fokker-Planck equation are also performed in a unified way in the present method.

hep-th↗
arXiv2000

In-medium pi-pi Correlation Induced by Partial Restoration of Chiral Symmetry

We show that both the linear and the non-linear chiral models give an enhancement of the pi-pi cross section near the 2pi threshold in the scalar-iso-scalar (I=J=0) channel in nuclear matter. The reduction of the chiral condensate, i.e., the partial chiral restoration in nuclear matter, is responsible for the enhancement in both cases. We extract an effective 4pi-nucleon vertex which is responsible for the enhancement but has not been considered in the non-liear models for in-medium pi-pi interaction. Relation of this vertex and a next-to-leading order terms in the heavy-baryon chiral lagrangian, L_piN^(2), is also discussed.

hep-ph↗
arXiv1999

Chiral Symmetry Realization for Even- and Odd-parity Baryon Resonances

Baryon resonances with even and odd parity are collectively investigated from the viewpoint of chiral symmetry(ChS). We propose a quartet scheme where Delta's and N^*'s with even and odd parity form a chiral multiplet. This scheme gives parameter-free constraints on the baryon masses in the quartet, which are consistent with observed masses with spin 1/2, 3/2, 5/2. The scheme also gives selection rules in the one-pion decay: The absence of the parity non-changing decay N(1720) -> pi Delta(1232) is a typical example which should be confirmed experimentally to unravel the role of ChS in baryon resonances.

hep-ph↗
arXiv1999

Renormalization Group Flow Equation at Finite Density

For the linear sigma model with quarks we derive renormalization group flow equations for finite temperature and finite baryon density using the heat kernel cutoff. At zero temperature we evolve the effective potential to the Fermi momentum and compare the solutions of the full evolution equation with those in the mean field approximation. We find a first order phase transition either from a massive constituent quark phase to a mixed phase, where both massive and massless quarks are present, or from a metastable constituent quark phase at low density to a stable massless quark phase at high density. In the latter solution, the formation of droplets of massless quarks is realized even at low density.

nucl-th↗
arXiv1999

Renormalization-group Method for Reduction of Evolution Equations; invariant manifolds and envelopes

The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian RG equations in statistical physics and quantum field theory. It is clarified that the perturbative RG method constructs invariant manifolds successively as the initial value of evolution equations, thereby the meaning to set $t_0=t$ is naturally understood where $t_0$ is the arbitrary initial time. We show that the integral constants in the unperturbative solution constitutes natural coordinates of the invariant manifold when the linear operator $A$ in the evolution equation has no Jordan cell; when $A$ has a Jordan cell, a slight modification is necessary because the dimension of the invariant manifold is increased by the perturbation. The RG equation determines the slow motion of the would-be integral constants in the unperturbative solution on the invariant manifold. We present the mechanical procedure to construct the perturbative solutions hence the initial values with which the RG equation gives meaningful results. The underlying structure of the reduction by the RG method as formulated in the present work turns out to completely fit to the universal one elucidated by Kuramoto some years ago. We indicate that the reduction procedure of evolution equations has a good correspondence with the renormalization procedure in quantum field theory; the counter part of the universal structure of reduction elucidated by Kuramoto may be the Polchinski's theorem for renormalizable field theories. We apply the method to interface dynamics such as kink-anti-kink and soliton-soliton interactions in the latter of which a linear operator having a Jordan-cell structure appears.

hep-th↗
arXiv1999

A Precursor of Chiral Symmetry Restoration in the Nuclear Medium

Spectral enhancement near the 2m_π threshold in the I=J=0 channel in nuclei is shown to be a distinct signal of the partial restoration of chiral symmetry. The relevance of this phenomenon with the possible detection of 2π^{0} and 2γin hadron-nucleus and photo-nucleus reactions is discussed.

nucl-th↗
arXiv1999

Chiral Transition in Nuclear Medium and Relevant Observables

We discuss how the possible changes of hadron properties can be tested, associated with the chiral transition in nuclear medium; the hadrons discussed are the vector mesons,the $σ$ meson and the chiral partner of the nucleon. We emphasize that the proper quantity is the spectral function which describes the nuclear medium having a hadron; the analysis of electro-quasielastic reactions, for instance, has a relevance to the physics of CERES. The similarity is indicated between the physics discussed here with that of giant resonances. Experiments using nuclear targets are proposed to observe the $σ$ meson and to explore how the partial chiral restoration in nuclear medium manifests itself.

nucl-th↗
arXiv1999

Precritical Chiral Fluctuations in Nuclei

Spectral enhancement near 2 m_π threshold in the I=J=0 channel in nuclei is shown to be a distinct signal of the partial restoration of chiral symmetry. The relevance of this phenomenon with possible detection of 2π^{0} and 2γin hadron-nucleus and photo-nucleus reactions is discussed.

nucl-th↗
arXiv1997

Dynamical Reduction of Discrete Systems Based on the Renormalization Group Method

The renormalization group (RG) method is extended for global asymptotic analysis of discrete systems. We show that the RG equation in the discretized form leads to difference equations corresponding to the Stuart-Landau or Ginzburg-Landau equations. We propose a discretization scheme which leads to a faithful discretization of the reduced dynamics of the original differential equations.

patt-sol↗
arXiv1996

Optimized Perturbation Theory for Wave Functions of Quantum Systems

The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings.

hep-th↗
arXiv1994

QCD Phenomenology based on a Chiral Effective Lagrangian

We review the Nambu-Jona-Lasinio (NJL) approach to the dynamical breaking of chiral symmetry in Quantum Chromodynamics (QCD). The subjects treated in Part I include the vacuum structure of QCD, mass spectra and coupling constants of hadrons, flavor mixing in mesons, the violation of the OZI rule in baryons, and the validity of the chiral perturbation in QCD. A subtle interplay between the axial anomaly and the current-quark masses is shown to play important roles, and a realistic evaluation of the strangeness and heavy quark contents of hadrons is given. In Part II, the NJL model is applied to the system at finite temperature ($T$) and density ($ρ$) relevant to the early universe, interior of the neutron stars and the ultra-relativistic heavy ion collisions. The subjects treated here include the quark condensates in the medium, meson properties at finite $T$ ($ρ$) and their experimental implications. A special attention is paid to fluctuation phenomena near the critical temperature. (to be published in Physics Reports)

hep-ph↗