We classify the sets of four lattice points that all lie on a short arc of a circle which has its center at the origin; specifically on arcs of length tR on a circle of radius R, for any given t > 0. In particular we prove that any arc of length ( 40 + 40 3 √ 10 )1/3 R on a circle of radius R, with R > √ 65, contains at most three lattice points, whereas we give an explicit infinite family of 4...

We calculate the two flavor equation of state for QCD on lattices with lattice spacing a = (6T )−1 and find that cutoff effects are substantially reduced compared to an earlier ∗new address: Fakultät für Physik, Universität Bielefeld, D-33615, Bielefeld, Germany †new address: Department of Physics, Washington University, St. Louis, MO 63130, USA

In the lattice theory the tensor product A⊗B is naturally defined on (0,∨)−semilattices. In general, when restricted to lattices this construction will not yield a lattice. However, if the tensor product A ⊗ B is capped, then A⊗B is a lattice. It is stated as an open problem in [4] whether the converse is true. In the present paper we prove that it is not so, that is, there are bounded lattices...

We give a progress report of our new a −1 ≈ 3 GeV quenched calculation of kaon matrix elements with domain-wall fermion and DBW2 gauge action. Our smaller lattice spacing allows us to address the effect of charmed quark on the lattice. We show preliminary results of BK renormalized non-perturbatively and K → π matrix elements.

The masses and dispersions of light hadrons are calculated in lattice QCD using an O(a) tadpole-improved gluon action and an O(a) tadpole-improved next-nearest-neighbor fermion action originally proposed by Hamber and Wu. Two lattices of constant volume with lattice spacings of approximately 0.40 fm and 0.24 fm are considered. The results reveal some scaling violations at the coarser lattice sp...

We investigate the anisotropic lattice with O(a) improved quark action as a candidate of framework in which we can treat both the heavy and light quark region in the same manner and systematically reduce the systematic uncertainties. To examine applicability of anisotropic lattice, we calculate the charmed meson spectrum and decay constants in quenched approximation. We find consistent result w...

We consider the problem of unfolding lattice trees and polygons in hexagonal or triangular lattice in two dimensions. We show that a hexagonal/triangular lattice chain (resp. tree) can be straightened in O(n) (resp. O(n)) moves and time, and a hexagonal/triangular lattice polygon can be convexified in O(n) moves and time. We hope that the techniques we used shed some light on solving the more g...

The quark-line disconnected diagram is a potentially important ingredient in lattice QCD calculations of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. It is also a notoriously difficult one to evaluate. Here, for the first time, we give an estimate of this contribution based on lattice QCD results that have a statistically significant signal, albeit...

Exotic and higher spin (> 1) mesons are still not throughly investigated in lattice QCD. Using a set of derivative based operators we report our exploratory study of these mesons in charmonium region. We use a 123 × 48 anisotropic (ξ = 3) clover lattice with inverse temporal lattice spacing a−1 = 6.05 GeV. Techniques developed in this exploratory study will be utilized in our future comprehensi...