Hiroko Ichie

Baryonic flux in quenched and two-flavor dynamical QCD after Abelian projection

We study the distribution of color electric flux of the three-quark system in quenched and full QCD (with N{sub f}=2 flavors of dynamical quarks) at zero and finite temperature. To reduce ultraviolet fluctuations, the calculations are done in the Abelian projected theory fixed to the maximally Abelian gauge. In the confined phase we find clear evidence for a Y-shape flux tube surrounded and formed by the solenoidal monopole current, in accordance with the dual superconductor picture of confinement. In the deconfined, high temperature phase monopoles cease to condense, and the distribution of the color electric field becomes Coulomb-like.

ABELIAN DOMINANCE FOR CONFINEMENT AND RANDOM PHASE PROPERTY OF OFF-DIAGONAL GLUONS IN THE MAXIMALLY ABELIAN GAUGE

Abstract We study abelian dominance for confinement in terms of the local gluon properties in the maximally abelian (MA) gauge both in the analytical consideration and in the lattice QCD. In the MA gauge, the off-diagonal gluon amplitude | A μ ± | is strongly suppressed, which is observed as “microscopic abelian tendency” on the link variable in lattice QCD. According to the suppression of the off-diagonal gluon amplitude, the phase variable of the off-diagonal gluon tends to be random in the MA gauge, besides the residual gauge degrees of freedom. Within the random-variable approximation for the off-diagonal phase variable, we demonstrate that the off-diagonal gluon contribution to the Wilson loop obeys the perimeter law in the MA gauge, and show exact abelian dominance for the string tension, although a small deviation is brought about by the finite size effect of the Wilson loop. We numerically confirm these results using the lattice QCD simulations.We study abelian dominance for confinement in terms of the local gluon properties in the maximally abelian (MA) gauge in a semi-analytical manner with the help of the lattice QCD. The global Weyl symmetry persistently remains as the relic of SU(Nc) in the MA gauge, and provides the ambiguity on the electric and magnetic charges. We derive the criterion on the SU(Nc)gauge invariance in terms of the residual symmetry in the abelian gauge. In the lattice QCD, we find microscopic abelian dominance on the link variable for the whole region of β in the MA gauge. The off-diagonal angle variable, which is not constrained by the MA-gauge fixing condition, tends to be random besides the residual gauge degrees of freedom. Within the randomvariable approximation for the off-diagonal angle variable, we prove that off-diagonal gluon contribution to the Wilson loop obeys the perimeter law in the MA gauge, and show exact abelian dominance for the string tension, although small deviation is brought by the finite size effect of the Wilson loop in the actual lattice QCD simulation. ∗E-mail: ichie@th.phys.titech.ac.jp †E-mail: suganuma@rcnp.osaka-u.ac.jp

Dynamics of monopoles and flux tubes in two-flavor dynamical QCD

We investigate the confining properties of the QCD vacuum with N{sub f}=2 flavors of dynamical quarks, and compare the results with the properties of the quenched theory. We use nonperturbatively O(a) improved Wilson fermions to keep cutoff effects small. We focus on color magnetic monopoles. Among the quantities we study are the monopole density and the monopole screening length, the static potential and the profile of the color electric flux tube. We furthermore derive the low-energy effective monopole action. Marked differences between the quenched and dynamical vacuum are found.

Quark Confinement Physics from Quantum Chromodynamics

We show the construction of the dual superconducting theory for the confinement mechanism from QCD in the maximally abelian (MA) gauge using the lattice QCD Monte Carlo simulation. We find that essence of infrared abelian dominance is naturally understood with the off-diagonal gluon mass moff ≈- 1.2GeV induced by the MA gauge fixing. In the MA gauge, the off-diagonal gluon amplitude is forced to be small, and the off-diagonal gluon phase tends to be random. As the mathematical origin of abelian dominance for confinement, we demonstrate that the strong randomness of the off-diagonal gluon phase leads to abelian dominance for the string tension. In the MA gauge, there appears the macroscopic network of the monopole world-line covering the whole system. We investigate the monopole-current system in the MA gauge by analyzing the dual gluon field Bμ. We evaluate the dual gluon mas as mB = 0.4 ∼ 0.5GeV in the infrared region, which is the lattice-QCD evidence of the dual Higgs mechanism by monopole condensation. Owing to infrared abelian dominance and infrared monopole condensation, QCD in the MA gauge is describable with the dual Ginzburg-Landau theory.

Tetraquark and Pentaquark Systems in Lattice QCD

We study multi-quark systems in lattice QCD. First, we revisit and summarize our accurate mass measurements of low-lying 5Q states with J = 1/2 and I = 0 in both positive- and negative-parity channels in anisotropic lattice QCD. The lowest positive-parity 5Q state is found to have a large mass of about 2.24 GeV after the chiral extrapolation. To single out the compact 5Q state from NK scattering states, we use the hybrid boundary condition (HBC), and find no evidence of the compact 5Q state below 1.75 GeV in the negative-parity channel. Second, we study the multi-quark potential in lattice QCD to clarify the inter-quark interaction in multi-quark systems. The 5Q potential V5Q for the QQ- Q -QQ system is found to be well described by the “OGE Coulomb plus multi-Y Ansatz”: The sum of the one-gluon-exchange (OGE) Coulomb term and the multi-Y-type linear term based on the flux-tube picture. The 4Q potential V4Q for the QQ- QQ system is also described by the OGE Coulomb plus multi-Y Ansatz, when QQ and QQ are well separated. The 4Q system is described as a “two-meson” state with disconnected flux tubes, when the nearest quark and antiquark pair are spatially close. We observe a lattice-QCD evidence for the “flip-flop”, i.e., the fluxtube recombination between the connected 4Q state and the “two-meson” state. On the confinement mechanism, the lattice QCD results indicate the flux-tube-type linear confinement in multi-quark hadrons. Finally, we propose a proper quark-model Hamiltonian based on the lattice QCD results.

Study of quark confinement in baryons with lattice QCD

In SU(3) lattice QCD, we perform the detailed study for the ground-state three-quark (3Q) potential V 3 Q g.s. and the 1st excited-state 3Q potential V 3 Q e.s. , i.e., the energies of the ground state and the 1st excited state of the gluon field in the presence of the static three quarks. From the accurate calculation for more than 300 different patterns of 3Q systems, the static ground-state 3Q potential V 3 Q g.s. is found to be well described by the Coulomb plus Y-type linear potential (Y-Ansatz) within 1%-level deviation. As a clear evidence for Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in maximally-Abelian projected QCD. For about 100 patterns of 3Q systems, we calculate the 1st excited-state 3Q potential V 3 Q e.s. , and find a large gluonic-excitation energy Δ E 3 Q ≡ V 3 Q e.s. − V 3 Q g.s. of about 1 GeV, which gives a physical reason of the success of the quark model even without gluonic excitations. We present also the first study for the penta-quark potential V5Q in lattice QCD, and find that V5Q is well described by the sum of the OGE Coulomb plus multi-Y type linear potential.

Role of Large Gluonic Excitation Energy for Narrow Width of Penta-Quark Baryons in QCD String Theory

We study the narrow decay width of low-lying penta-quark baryons in the QCD string theory in terms of gluonic excitations. In the QCD string theory, penta-quark baryons decay via a gluonic-excited state of a baryon and meson system, where a pair of Y-shaped junction and anti-junction is created. Since lattice QCD shows that the lowest gluonic-excitation energy takes a large value of about 1 GeV, the decay of penta-quark baryons near the threshold is considered as a quantum tunneling process via a highly-excited state (a gluonic-excited state) in the QCD string theory. This mechanism strongly suppresses the low-lying penta-quark decay and leads to an extremely narrow decay width.

Multi-flux-tube system in the dual Ginzburg-Landau theory

We study the system of multi color-flux-tubes in terms of the dual Ginzburg-Landau theory. We consider two ideal cases, where the directions of all the color-flux-tubes are the same in one case and alternative in the other case for neighboring flux-tubes. We formulate the system of multi color-flux-tubes by regarding it as the system of two color-flux-tubes penetrating through a two dimensional sphere surface. We find the multi flux-tube configuration becomes uniform above some critical flux-tube number density ρ c = 1.3 ∼ 1.7fm −2. On the other hand, the inhomogeneity on the color electric distribution appears when the flux-tube density is smaller than ρ c. We discuss the relation between the inhomogeneity in the color-electric distribution and the flux-tube number density in the multi-flux-tube system created during the QGP formation process in the ultra-relativistic heavy-ion collision.

QCD phase transition at finite temperature in the dual Ginzburg-Landau theory.

We study the pure-gauge QCD phase transition at finite temperatures in the dual Ginzburg-Landau theory, an effective theory of QCD based on the dual Higgs mechanism. We formulate the effective potential at various temperatures by introducing the quadratic source term, which is a new useful method to obtain the effective potential in the negative-curvature region. Thermal effects reduce the QCD-monopole condensate and bring a first-order deconfinement phase transition. We find a large reduction of the self-interaction among QCD monopoles and the glueball masses near the critical temperature by considering the temperature dependence of the self-interaction. We also calculate the string tension at finite temperatures.

Behind the success of the quark model

Abstract The ground-state three-quark (3Q) potential V 3Q g.s. and the excited-state 3Q potential V 3Q e.s. are studied using SU(3) lattice QCD at the quenched level. For more than 300 patterns of the 3Q systems, the ground-state potential V 3Q g.s. is investigated in detail in lattice QCD with 12 3 × 24 at β = 5.7 and with 16 3 × 32 at β = 5.8, 6.0. As a result, the ground-state potential V 3Q g.s. is found to be well described with Y-ansatz within the 1%-level deviation. From the comparison with the Q- Q potential, we find the universality of the string tension as σ 3 Q ≅ σ Q Q and the one-gluon-exchange result as A 3 Q ≅ 1 2 A Q Q . The excited-state potential V 3Q e.s. is also studied in lattice QCD with 16 3 × 32 at β = 5.8 for 24 patterns of the 3Q systems. The energy gap between V 3Q g.s. and V 3Q e.s. , which physically means the gluonic excitation energy, is found to be about 1GeV in the typical hadronic scale, which is relatively large compared with the excitation energy of the quark origin. This large gluonic excitation energy justifies the great success of the simple quark model.The ground-state three-quark (3Q) potential