Yoshiaki Koma

Nonperturbative Determination of the QCD Potential at O(1/m)

The relativistic correction to the QCD static interquark potential at O(1/m) is investigated nonperturbatively for the first time by using lattice Monte Carlo QCD simulations. The correction is found to be comparable with the Coulombic term of the static potential when applied to charmonium, and amounts to one-fourth of the Coulombic term for bottomonium.

Spin-dependent potentials from lattice QCD

Abstract The spin-dependent corrections to the static inter-quark potential are phenomenologically relevant to describing the fine and hyperfine spin splitting of the heavy quarkonium spectra. We investigate these corrections, which are represented as the field strength correlators on the quark–antiquark source, in SU ( 3 ) lattice gauge theory. We use the Polyakov loop correlation function as the quark–antiquark source, and by employing the multi-level algorithm, we obtain remarkably clean signals for these corrections up to intermediate distances of around 0.6 fm. Our observation suggests several new features of the corrections.

Exploring the structure of the quenched QCD vacuum with overlap fermions

Overlap fermions have an exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum. We study various chiral and topological aspects of quenched gauge field configurations. This includes the localization and chiral properties of the eigenmodes, the local structure of the ultraviolet-filtered field strength tensor, as well as the structure of topological charge fluctuations. We conclude that the vacuum has a multifractal structure.

Static potential, force, and flux-tube profile in 4D compact U(1) lattice gauge theory with the multi-level algorithm

Abstract The long range properties of four-dimensional compact U(1) lattice gauge theory with the Wilson action in the confinement phase is studied by using the multi-level algorithm. The static potential, force and flux-tube profile between two static charges are successfully measured from the correlation function involving the Polyakov loop. The universality of the coefficient of the 1/ r correction to the static potential, known as the Luscher term, and the transversal width of the flux-tube profile as a function of its length are investigated. While the result supports the presence of the 1/ r correction, the width of the flux tube shows an almost constant behavior at a large distance.

Detailed study of the Abelian-projected SU(2) flux tube and its dual Ginzburg-Landau analysis

The color-electric flux tube of Abelian-projected (AP) SU(2) lattice gauge theory in the maximally Abelian gauge (MAG) is revisited. It is shown that the lattice Gribov copy effect in the MAG is crucial for the monopole-related parts of the flux-tube profiles. Taking into account both the gauge fixing procedure and the effect of finite quark-antiquark distance properly, the scaling property of the flux-tube profile is confirmed. The quantitative relation between the measured AP flux tube and the flux-tube solution of the U(1) dual Abelian Higgs (DAH) model is also discussed. The fitting of the AP flux tube in terms of the DAH flux tube indicates that the vacuum can be classified as weakly type-I dual superconductor.

Duality of gauge field singularities and the structure of the flux tube in Abelian-projected SU(2) gauge theory and the dual Abelian Higgs model

The structure of the flux-tube profile in Abelian-projected ~AP! SU~2! gauge theory in the maximally Abelian gauge is studied. The connection between the AP flux tube and the classical flux-tube solution of the U~1! dual Abelian Higgs model is clarified in terms of the path-integral duality transformation. This connection suggests that the electric photon and the magnetic monopole parts of the Abelian Wilson loop can act as separate sources creating the Coulombic and the solenoidal electric field inside a flux tube. The conjecture is confirmed by a lattice simulation which shows that the AP flux tube is composed of these two contributions.

Relativistic corrections to the static potential at

We investigate the relativistic corrections to the static potential, i.e. the O(1/m) potential and the O(1/m^2) velocity-dependent potentials, in SU(3) lattice gauge theory. They are important ingredients of potential nonrelativistic QCD for heavy quarkonium. Utilizing the multi-level algorithm, we obtain remarkably clean signals of these potentials up to r=0.9 fm. We observe long range nonperturbative contributions to these corrections.

O(1/m)

Abstract Luschers finite size mass shift formula in a periodic finite volume, involving forward scattering amplitudes in the infinite volume, is revisited for the two stable distinguishable particle system. The generalized mass shift formulae for the boson and fermion are derived in the boson–boson and fermion–boson systems, respectively. The nucleon mass shift formula is given in the nucleon–pion system and the relation to the computation within chiral perturbation theory is discussed.

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Abstract We take a new look at plaquette–plaquette correlators in 4d compact U(1) lattice gauge theory which are separated in time, both in the confined and the deconfined phases. From the behaviour of these correlators we extract glueball masses in the scalar as well as the axial-vector channels. Also in the deconfined phase, the non-zero momentum axial-vector correlator gives us information about the photon which appears as a massless particle in the spectrum. Using the Luscher–Weisz multi-level algorithm, we are able to go to large time separations which were not possible previously.

O(1/m^2)

Abstract The effective string action of the color-electric flux tube in the U(1)×U(1) dual Ginzburg–Landau (DGL) theory is studied by performing a path-integral analysis by taking into account the finite thickness of the flux tube. The DGL theory, corresponding to the low-energy effective theory of Abelian-projected SU(3) gluodynamics, can be expressed as a [U(1)] 3 dual Abelian Higgs (DAH) model with a certain constraint in the Weyl symmetric formulation. This formulation allows us to adopt quite similar path-integral techniques as in the U(1) DAH model, and therefore, the resulting effective string action in the U(1)×U(1) DGL theory has also quite a similar structure except the number of color degrees of freedom. A modified Yukawa interaction appears as a boundary contribution, which is completely due to the finite thickness of the flux tube, and is reduced into the ordinary Yukawa interaction in the deep type-II (London) limit.