Tetsuo Hatsuda

The phase diagram of dense QCD

The current status of theoretical studies on the quantum chromodynamics (QCD) phase diagram at finite temperature and baryon chemical potential is reviewed with special emphasis on the origin of various phases and their symmetry breaking patterns. Topics include quark deconfinement, chiral symmetry restoration, order of the phase transitions, QCD critical point(s), colour superconductivity, various inhomogeneous states and implications from QCD-like theories.

Nuclear force from lattice QCD.

Nucleon-nucleon (NN) potential is studied by lattice QCD simulations in the quenched approximation, using the plaquette gauge action and the Wilson quark action on a 32^4 (\simeq (4.4 fm)^4) lattice. A NN potential V_{NN}(r) is defined from the equal-time Bethe-Salpeter amplitude with a local interpolating operator for the nucleon. By studying the NN interaction in the ^1S_0 and ^3S_1 channels, we show that the central part of V_{NN}(r) has a strong repulsive core of a few hundred MeV at short distances (r \alt 0.5 fm) surrounded by an attractive well at medium and long distances. These features are consistent with the known phenomenological features of the nuclear force.

Bound H dibaryon in flavor SU(3) limit of lattice QCD.

The flavor-singlet H dibaryon, which has strangeness -2 and baryon number 2, is studied by the approach recently developed for the baryon-baryon interactions in lattice QCD. The flavor-singlet central potential is derived from the spatial and imaginary-time dependence of the Nambu-Bethe-Salpeter wave function measured in N(f)=3 full QCD simulations with the lattice size of L≃2,3,4  fm. The potential is found to be insensitive to the volume, and it leads to a bound H dibaryon with the binding energy of 30-40 MeV for the pseudoscalar meson mass of 673-1015 MeV.

Hadron–hadron interactions from imaginary-time Nambu–Bethe–Salpeter wave function on the lattice

Abstract Imaginary-time Nambu–Bethe–Salpeter (NBS) wave function is introduced to extend our previous approach for hadron–hadron interactions on the lattice. Scattering states of hadrons with different energies encoded in the NBS wave function are utilized to extract non-local hadron–hadron potential. “The ground state saturation”, which is commonly used in lattice QCD but is hard to be achieved for multi-baryons, is not required. We demonstrate that the present method works efficiently for the nucleon–nucleon interaction (the potential and the phase shift) in the S 0 1 channel.

Two-baryon potentials and H-dibaryon from 3-flavor lattice QCD simulations

Abstract Baryon–baryon potentials are obtained from 3-flavor QCD simulations with the lattice volume L ≃ 4 fm , the lattice spacing a ≃ 0.12 fm , and the pseudo-scalar-meson mass M ps = 469 – 1171 MeV . The NN scattering phase-shifts and the mass of H-dibaryon in the flavor SU ( 3 ) limit are extracted from the resultant potentials by solving the Schrodinger equation. The NN phase-shifts in the SU ( 3 ) limit is shown to have qualitatively similar behavior as the experimental data. A bound H-dibaryon in the SU ( 3 ) limit is found to exist in the flavor-singlet J P = 0 + channel with the binding energy of about 26 MeV for the lightest quark mass M ps = 469 MeV . Effect of flavor SU ( 3 ) symmetry breaking on the H-dibaryon is estimated by solving the coupled-channel Schrodinger equation for Λ Λ – N Ξ – Σ Σ with the physical baryon masses and the potential matrix obtained in the SU ( 3 ) limit: a resonant H-dibaryon is found between ΛΛ and NΞ thresholds in this treatment.

Hyperon-Nucleon Force from Lattice QCD

Abstract We calculate potentials between a proton and a Ξ 0 (hyperon with strangeness −2) through the equal-time Bethe–Salpeter wave function, employing quenched lattice QCD simulations with the plaquette gauge action and the Wilson quark action on (4.5 fm)4 lattice at the lattice spacing a ≃ 0.14 fm . The ud quark mass in our study corresponds to m π ≃ 0.37 and 0.51 GeV, while the s quark mass corresponds to the physical value of m K . The central p Ξ 0 potential has a strong (weak) repulsive core in the S 0 1 ( S 1 3 ) channel for r ≲ 0.6 fm , while the potential has attractive well at medium and long distances ( 0.6 fm ≲ r ≲ 1.2 fm ) in both channels. The sign of the p Ξ 0 scattering length and its quark mass dependence indicate a net attraction in both channels at low energies.

Baryon-Baryon Interactions in the Flavor SU(3) Limit from Full QCD Simulations on the Lattice

We investigate baryon-baryon (BB) interactions in the 3-flavor full QCD simulations with degenerate quark masses for all flavors. The BB potentials in the orbital S-wave are extracted from the Nambu-Bethe-Salpeter wave functions measured on the lattice. We observe strong flavor-spin dependences of the BB potentials at short distances. In particular, a strong repulsive core exists in the flavor-octet and spin-singlet channel (the 8s representation), while an attractive core appears in the flavor singlet channel (the 1 representation). We discuss the relation of such flavor-spin dependence with the Pauli exclusion principle at the quark level. The possible existence of an H-dibaryon resonance above the ΛΛ threshold is also discussed. Subject Index: 164, 234

HADRON-QUARK CROSSOVER AND MASSIVE HYBRID STARS WITH STRANGENESS

Using the idea of smooth crossover from hadronic matter with hyperons to quark matter with strangeness, we show that the maximum mass (M max) of neutron stars with quark matter cores can be larger than those without quark matter cores. This is in contrast to the conventional softening of the equation of state due to exotic components at high density. The essential conditions for reaching our conclusion are that (1) the crossover takes place at relatively low densities, around three times the normal nuclear density and (2) the quark matter is strongly interacting in the crossover region. From these, the pressure of the system can be greater than that of purely hadronic matter at a given baryon density in the crossover density region and leads to M max greater than 2 solar mass. This conclusion is insensitive to the different choice of the hadronic equation of state with hyperons. We remark upon several implications of this result to the nuclear incompressibility, the hyperon mixing, and the neutrino cooling.

New critical point induced by the axial anomaly in dense QCD

We study the interplay between chiral and diquark condensates within the framework of the Ginzburg-Landau free energy, and classify possible phase structures of two and three-flavor massless QCD. The QCD axial anomaly acts as an external field applied to the chiral condensate in a color superconductor and leads to a crossover between the broken chiral symmetry and the color superconducting phase, and, in particular, to a new critical point in the QCD phase diagram.

Exploring Three-Nucleon Forces in Lattice QCD

Three-nucleon forces (3NF) are investigated from two-flavor lattice QCD simulations. We utilize the Nambu-Bethe-Salpeter (NBS) wave function to determine two-nucleon forces (2NF) and 3NF in the same framework. As a first exploratory study, we extract 3NF in which three nucleons are aligned linearly with an equal spacing. This is the simplest geometrical configuration which reduces the huge computational cost of calculating the NBS wave function. Quantum numbers of the three-nucleon system are chosen to be (I, J^P)=(1/2,1/2^+) (the triton channel). Lattice QCD simulations are performed using N_f=2 dynamical clover fermion configurations at the lattice spacing of a = 0.156 fm on a 16^3 x 32 lattice with a large quark mass corresponding to m_\pi= 1.13 GeV. We find repulsive 3NF at short distance in the triton channel. Several sources of systematic errors are also discussed.