arXiv subjects
Publications and source records attributed to Teiji Kunihiro.
We explore whether "f$_{0}$(600) or $σ$" exists as a pole in QCD, by a full lattice QCD simulation on the $8^{3} \times 16$ lattice using the plaquette action and Wilson fermions. It is shown that a low-mass $σ$ pole exists owing to the disconnected diagram of the meson propagator. A discussion is given on the physical content of the $σ$.
We report a project to study scalar particles by lattice QCD simulations. After a brief introduction of the current situation of lattice study of the sigma meson, we describe our numerical simulations of scalar mesons, $σ$ and $κ$. We observe a low sigma mass, $m_π<m_σ\le m_ρ$, for which the disconnected diagram plays an important role. For the kappa meson, we obtain higher mass than the experimental value, i.e., $m_κ\sim 2m_{K^*}$.
We review recent developments in exploring possible precursory phenomena of partial restoration of chiral symmetry in nuclear medium by examining the spectral function in the scalar channel. We emphasize that the wave function renormalization of the pion in the medium plays an essential role to induce the decrease of the pion decay constant as the order parameter of chiral transition. We also show that the $σ$ meson pole in the complex energy plane moves toward the origin as chiral symmetry is restored in hot and/or dense nuclear matter.
First, it is pointed out that hadron/nuclear physics based on QCD should be regarded as ``condensed matter physics'' of the QCD vacuum. We indicate that phase shift analyses which respect chiral symmetry (ChS), analyticity and crossing symmetry of the scattering amplitude show the $σ$ meson pole in the s-channel in the low mass region as well as the $ρ$ meson pole in the $t$-channel in the \pipi scattering in the scalar channel. We review recent developments in exploring possible precursory phenomena of partial restoration of \chis in nuclear medium by examining the spectral function in the scalar and the vector channels. We emphasize that the wave function renormalization of the pion in the medium plays an essential role to induce the decrease of the pion decay constant as the order parameter of chiral transition. An emphasis is also put on the importance to examine the scalar and vector channels simultaneously for exploring the possible restoration of chiral symmetry.
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.
We investigate the propagator of "f$_{0}$(600) or the $σ$" by the full-QCD simulation with Wilson fermions. We calculate the mesonic correlator in the I=0, $J^P=0^{+}$ channel on the $8^{3} \times 16$ lattice. Plaquet action and Wilson fermion action are adopted. A coupling constant $β$ is set to 4.8 and three kinds of hopping parameter, $κ$=0.1846, 0.1874 and 0.1891 are assayed. The disconnected diagram in the propagator is evaluated through taking average over 500 or 1000 Z2 noise. Simulations with the larger hopping parameter provide us with less noisy results. Though the statistics is not yet enough, our results indicate the existence of a pole with a mass in almost the same order as that of the $ρ$.
It is pointed out that the hadron spectroscopy should be a study of the structure of the QCD vacuum, low-energy elementary excitations on top of which are hadrons. Concentrating on the dynamical breaking of the chiral symmetry in the QCD vacuum, we emphasize the importance to clarify what is going on with mesons in the $I=J=0$-channel, i.e., the sigma meson channel, because it is connected to the quantum fluctuations of the chiral order parameter. After summarizing the significance of the sigma meson in QCD and low-energy hadron phenomenology, we give a review on some theoretical and experimental effort to try to reveal the possible restoration of chiral symmetry in hot and dense nuclear matter including heavy nuclei.
The properties of the scalar and vector correlations in the hot and/or dense hadronic matter close to chiral transition are discussed. Presuming that the linear realization of chiral symmetry will become appropriate at least near the critical point, we argue that the strength function in the $I=J=0$ channel will soften near the critical point, and the sigma meson will accordingly become a clearer resonance in hot and/or dense medium than in the free space. It is shown that the steep rise of the baryon-number susceptibility $χ_B$ around the critical point seen in the lattice simulations may suggest that the interactions between quarks in the vector channel become week near the critical point; this implies that the peculiar behavior of the $χ_B$ does not necessarily imply a proliferation of baryons and antibaryons (Skyrmions) which is though a natural scenario of chiral transition in the non-linear realization of chiral symmetry.
After giving brief discussions on the chiral condensate in hot and/or dense hadronic matter and the significance of the $σ$ meson in QCD, we discuss the importance of experiments using nuclear targets including ones with electro-magnetic probes for obtaining clearer confirmation of the existence of the $σ$ meson and for exploring the possible restoration of chiral symmetry in nuclear medium.
We first review the recent accumulating evidences of the existence of a scalar-isoscalar meson with the mass 500 to 800 MeV which may be identified with the sigma meson as the quantum fluctuation of the amplitude of the chiral order parameter. We indicate that phase shift analyses which respect chiral symmetry (ChS), analyticity and crossing symmetry of the scattering amplitude show the sigma meson pole in the $s$-channel as well as the $ρ$ meson pole in the $t$-channel in the pi-pi scattering in the $I=J=0$ channel. We emphasize that the existence of the $σ$ resonance does not contradict with the success of the chiral perturbation theory; phenomenological difficulties with the renormalizable linear sigma model do not necessarily deny the validity of the linear representation of ChS of QCD as given by the NJL-like models which not only admit the $σ$ resonance but also reproduce the coupling constants $L_i$ and $H_i$ appearing the nonlinear chiral lagrangian. We give some examples of the hadronic phenomena which are naturally accounted for with the $σ$ meson. We show that the the $σ$ meson as the amplitude fluctuation of the chiral order parameter may be more clearly identified than in free space in hot and/or dense matter, even in finite nuclei where partial restoration of ChS may be realized.
The sigma-meson, which is at best a broad resonance in the vacuum, may suffer a substantial red-shift and appear as a soft and narrow collective mode at finite temperature and baryon densities. The physics behind this softening phenomena and its relation to the partial restoration of chiral symmetry are discussed. Possible experiments in laboratory to test the idea are also summarized.
We discuss the baryon-number susceptibility $χ_B$ and related topics which include the density fluctuations around the critical point of the chiral transition at finite temperature $T$ and baryon density $ρ_B$. Phenomenological implications of the density fluctuations near the first-order chiral transition at finite density are also discussed.
After showing the characteristic features of the chiral transition in QCD at finite temperature $T$, we note the significance of the sigma-mesonic mode in the chiral transition : Sigma meson may be regarded as the "Higgs particle" in QCD, though the existence of such a mode in the real world is still unclear. We show the properties of the sigma meson in hot and/or hadronic matter, from which we propose experiments to reveal the existence the sigma meson clearly; the experiments include relativistic heavy-ion collisions to create hot hadronic matter, and electro-production in heavy nuclei.
We first discuss the theoretical and phenomenological significance of the sigma meson ($σ$) in QCD. It is indicated that if the collective modes with the mass 500-600 MeV exists in the $I=J=0$ channel, various empirical facts in hadron physics can be naturally accounted for, which otherwise would remain mysterious. We propose several experiments to produce and detect the $σ$ in nuclei using nuclear and electro-magnetic projectiles. The recent CHAOS data which show a spectral enhancement near the 2 $m_π$ threshold in the $σ$ channel from the reactions A$(π, 2π)$A' where A and A' denotes nuclei is interpreted as a possible evidence of a partial restoration of chiral symmetry in nuclei.
The perturbative renormalization group(RG) equation is applied to resum divergent series of perturbative wave functions of quantum anharmonic oscillator. It is found that the resummed series gives the cumulant of the naive perturbation series. It is shown that a reorganization of the resummed series reproduce the correct asymptotic form of the wave function at $x\to \infty$ when the perturbation expansion is stopped at the fourth order. A brief comment is given on the relation between the present method and the delta-expansion method, which is based on a kind of a nonperturbative RG equation.
The renormalization group method is applied for obtaining the asymptotic form of the wave function of the quantum anharmonic oscillator by resumming the perturbation series. It is shown that the resumed series is the cumulant of the naive perturbation series. Working out up to the sixth order and performing a further resummation proposed by Bender and Bettencourt, we find that the agreement with the WKB result becomes worse in the higher orders than the fourth at which the agreement is the best.
On the basis of the NJL model as an effective theory of QCD and analogies with condensed matter physics, we extract simple physical pictures of the chiral phase transition at finite temperature $T$ and/or chemical potential $μ$ and predict interesting phenomena associated with the phase transition which may be seen in relativistic heavy-ion collisions to be performed in RHIC or LHC. We indicate that the macroscopic equation describing non-equilibrium phenomena of the chiral transition like DCC might be given by a diffusion-like equation rather than a wave equation especially when the baryon density is present.
We give a comprehensive review of the renormalization group method for global and asymptotic analysis, putting an emphasis on the relevance to the classical theory of envelopes and the existence of invariant manifolds of the dynamics under consideration. We clarify that an essential point of the method is to convert the problem from solving differential equations to obtaining suitable initial (or boundary) conditions. We mention that the notion of envelopes is also useful for constructing global and asymptotic behavior of wave functions of quantum systems such as the ones with the quartic potential or double-well potential.