Munehisa Ohtani

Sigma and hydrodynamic modes along the critical line

Assuming a tricritical point of two-flavor QCD in the space of temperature, baryon number chemical potential, and quark mass, we study the change of the associated soft mode along the critical line within the Ginzburg-Landau approach and the Nambu\char21{}Jona-Lasinio model. The ordering density along the chiral critical line is the scalar density whereas a linear combination of the scalar, baryon number, and energy densities becomes the proper ordering density along the critical line with finite quark masses. It is shown that the critical eigenmode shifts from the sigma-like fluctuation of the scalar density to a hydrodynamic mode at the tricritical point, where we have two ordering densities, the scalar density and a linear combination of the baryon number and energy densities. We argue that the appearance of the critical eigenmode with hydrodynamic character is a logical consequence of divergent susceptibilities of the conserved densities.

Renormalization group equations in a model of generalized hidden local symmetry and restoration of chiral symmetry

We study possible restoration patterns of chiral symmetry in a generalized hidden local symmetry model, which is a low energy effective theory of QCD including pseudo-scalar, vector and axial-vector mesons. We derive Wilsonian renormalization group equations and analyze the running couplings and their fixed points at the chiral restoration point. We find three types of the chiral restoration, which are classified as the standard, vector manifestation and intermediate scenarios, respectively. It turns out that the rho and A_1 meson become massless and their decay into pion is suppressed in all the restoration patterns. The each restoration scenario violates or fulfills the vector meson dominance at the critical point in a different manner, which may reflect on the contributions from the pion to the dilepton spectrum.

Hadronic structure from the lattice

In recent years the investigation of hadron structure using lattice techniques has attracted growing attention. The computation of several important quantities has become feasible. Furthermore, theoretical developments as well as progress in algorithms and an increase in computing resources have contributed to a significantly improved control of systematic errors. In this article we give an overview on the work that has been carried out in the framework of the Hadron Physics I3 (I3HP) network “Computational (lattice) hadron physics”. Here we will not restrict ourselves to spin physics but focus on results for nucleon spectrum and structure from the QCDSF collaboration. For a broader overview of developments in this field see, e.g., [1].

Quantum Hall states of gluons in dense quark matter

We have recently shown that dense quark matter possesses a color ferromagnetic phase in which a stable color magnetic field arises spontaneously. This ferromagnetic state has been known to be Savvidy vacuum in the vacuum sector. Although the Savvidy vacuum is unstable, the state is stabilized in the quark matter. The stabilization is achieved by the formation of quantum Hall states of gluons, that is, by the condensation of the gluon’s color charges transmitted from the quark matter. The phase is realized between the hadronic phase and the color superconducting phase. After a review of quantum Hall states of electrons in semiconductors, we discuss the properties of quantum Hall states of gluons in quark matter in detail. Especially, we evaluate the energy of the states as a function of the coupling constant. We also analyze solutions of vortex excitations in the states and evaluate their energies. We find that the states become unstable as the gauge coupling constant becomes large, or the chemical potential of the quarks becomes small, as expected. On the other hand, with the increase of the chemical potential, the color superconducting state arises instead of the ferromagnetic state. We also show that the quark matter produced by heavy ion collisions generates observable strong magnetic field ∼ 10 Gauss when it enters the ferromagnetic phase.

Soft modes at the critical end point in the chiral effective models

At the critical end point in QCD phase diagram, the scalar, vector and entropy susceptibilities are known to diverge. The dynamic origin of this divergence is identified within the chiral effective models as softening of a hydrodynamic mode of the particle-hole-type motion, which is a consequence of the conservation law of the baryon number and the energy.

COLOR FERROMAGNETIC QUARK MATTER IN NEUTRON STARS

We show that color ferromagnetic phase of quark matter is energetically more favored than color superconducting phases in neutron stars. Namely, increasing baryon density in neutron stars transforms nuclear matter into the quark matter of the color ferromagnetic phase. Further increase of the density makes the quark matter take the color superconducting phases. We find that a critical mass of the neutron star with such an internal structure is about

Nucleon structure with partially twisted boundary conditions

1.6M_{\odot}

UA(1) breaking and phase transition in chiral random matrix model

. We stress that analysis of gluon dynamics is crucial for exploring dense quark matter.

Color ferromagnetism of quark matter and quantum Hall states of gluons in SU(3) gauge theory

A large number of fundamental hadron structure observables are defined in the limit of vanishing momentum transfer, but at the same time cannot be directly extracted from forward matrix elements. This is a challenge for current lattice QCD simulations, where volumes and lattice spacings are such that the lowest accessible non-zero momentum transfers are ∼ 0.15 GeV 2 and larger, making in general model-dependent extrapolations to the forward limit necessary. Twisted boundary conditions for the valence quarks provide the opportunity to study hadronic matrix elements in dynamical lattice QCD calculations for almost arbitrary hadron momenta. We present preliminary results for the Dirac- and Pauli form factors and the form factors of the energy momentum tensor for the nucleon very close to the forward limit, using partially twisted boundary conditions. The calculations are based on gauge configurati ons generated with two flavors of clover-improved Wilson fermions.

Effect of the pion thermal width on the sigma spectrum

We propose a chiral random matrix model which properly incorporates the flavor-number dependence of the phase transition owing to the U{sub A}(1) anomaly term. At finite temperature, the model shows the second-order phase transition with mean-field critical exponents for two massless flavors, while in the case of three massless flavors the transition turns out to be of the first order. The topological susceptibility satisfies the anomalous U{sub A}(1) Ward identity and decreases gradually with the temperature increased.