Shin Muroya

Lattice QCD at Finite Density An Introductory Review

This is a pedagogical review of the lattice study of finite density QCD. It is intended to provide the minimum necessary content, so that it may be used as an introduction for newcomers to the field and also for those working in nonlattice areas. After a brief introduction in which we discuss the reasons that finite density QCD is an active and important subject, we present the fundamental formulae that are necessary for the treatment given in the following sections. Next, we survey lattice QCD simulational studies of system with small chemical potentials, of which there have been several prominent works reported recently. Then, two-color QCD calculations are discussed, where we are free from the notorious phase problem and have a chance to consider many new features of finite density QCD. Of special note is the result of recent simulations indicating quark pair condensation and the in-medium effect. Tables of SU(3) and SU(2) lattice simulations at finite baryon density are given. In the next section, we survey several related works that may represent a starting point of future development, although some of these works have not attracted much attention yet. This material is described in a pedagogical manner. Starting from a simple 2-d model, we briefly discuss a lattice analysis of the NJL model. We describe a non-perturbative analytic approach, i.e., the strong coupling approximation method and some results. The canonical ensemble approach, instead of the usual grand canonical ensemble may be another route to reach high density. We examine the density of state method and show that this old idea includes the recently proposed factorization method. An alternative method, the complex Langevin equation, and an interesting model, the finite isospin model, are also discussed. We give brief comments on a partial sum with respect to Z3 symmetry and the meron-cluster algorithm, which might solve the sign problem partially or completely. In the Appendix, we discuss several technical points that are useful in practical calculations.

Scalar mesons in lattice QCD

Recently there has been renewed and growing interestin scalarmesons[1, 2]. Oneofthe mostnoteworthydevel-opments in this field is the re-identification of the σ(600)after some twenty years. The results of re-analyses of theπ-π scattering phase shift of the scattering (S) matrixstrongly suggest the existence of the pole of the σ mesonwith I = 0 and J

Behavior of hadrons at finite density.: Lattice study of color SU(2) QCD

Abstract Using two-color lattice QCD with Wilson fermions, we report a study of the finite baryon number density system with two-flavors. First we investigate the Polyakov line and thermodynamical quantities in the ( κ , μ ) plane, where κ and μ are the hopping parameter and chemical potential in the fermion action, respectively. Then we calculate propagators of meson ( q Γq ) and baryon ( qΓq ) states. We find that the vector meson propagators are strongly modified in large μ regions, indicating the reduction of the mass. This anomalous behavior of the vector meson is observed for the first time in lattice QCD.

Hydrodynamical analysis of hadronic spectra in the 130 GeV/nucleon Au + Au collisions

We study one-particle spectra and a two-particle correlation function in the 130 GeV/nucleon

(3+1)-dimensional relativistic hydrodynamical expansion of hot and dense matter in ultra-relativistic nuclear collision

mathrm{Au}+mathrm{Au}

Charge diffusion constant in hot and dense hadronic matter: A hadro-molecular-dynamics calculation

collisions at the Relativistic Heavy Ion Collider by making use of a hydrodynamical model. We calculate the one-particle hadronic spectra and present an analysis of Bose-Einstein correlation functions based on a numerical solution of the hydrodynamical equations which takes both longitudinal and transverse expansion into account appropriately. The hydrodynamical model provides excellent agreement with the experimental data in the pseudorapidity and the transverse momentum spectra of charged hadrons, the rapidity dependence of the antiproton-to-proton ratio, and almost consistent results for the pion Bose-Einstein correlation functions. Our numerical solution with a simple freeze-out picture suggests the formation of a quark-gluon plasma with large volume and low net-baryon density.

Lattice study of Λp scattering length

Abstract. A full (3+1)-dimensional calculation using Lagrangian hydrodynamics is proposed for relativistic nuclear collisions. This calculation enables us to evaluate the anisotropic flow of the hadronic matter which appears in non-central and/or asymmetrical relativistic nuclear collisions. Applying hydrodynamical calculations to the deformed uranium collisions in the AGS energy region, we discuss the nature of the space-time structure and particle distributions in detail.

Lattice Lattice study of “f0 (600) or σ”

We evaluate the charge diffusion constant of dense and hot hadronic matter based on the molecular dynamical method by using a hadronic collision generator which describes nuclear collisions at energies 101 − 2 GeV/A and satisfies detailed balance at low temperatures (T ≤ 200 MeV). For the hot and dense hadronic matter in the temperature range T = 80–200 MeV and with baryon number density, nB, from 0.16fm−3 to 0.32fm−3, the charge diffusion constant D gradually increases from 0.5 fmc to 2 fmc with temperature and is almost independent of baryon number density. Based on the obtained diffusion constant, we make simple discussions on the diffusion of charge fluctuation in ultrarelativistic nuclear collisions.

Monte Carlo study of two-color QCD with finite chemical potential: Status report of Wilson fermion simulation

Abstract A lattice QCD calculation of S-wave scattering length in the channel of Λp is carried out in the quenched approximation at β = 5.6, on a 43 × 8 lattice. Preliminary results show an attractive interaction with small value of scattering length.

Numerical analysis of a two-pion correlation function based on a hydrodynamical model

We investigate the propagator of f