We compute the masses of the π and of the ρ mesons in the quenched approximation on a lattice with fixed lattice spacing a ≃ 0.145 fm for SU(N) gauge theory with N = 2, 3, 4, 6. We find that a simple linear expression in 1/N correctly captures the features of the lowest-lying meson states at those values of N . This enables us to extrapolate to N = ∞ the behaviour of mπ as a function of the qua...

From an accurate determination of the inter-quark potential, one can study the running coupling constant for a range of R-values and hence estimate the scale Λ MS. Detailed results are presented for SU (3) pure gauge theory.

In this paper, we will define a signed Lattice measure on σ-algebras, as well as give the definition of positive and negative Lattice. Herein, we will show that the Hahn Decomposition Theorem decomposes any space X into a positive lattice A and a negative Lattice B such that A∨B =X and the signed Lattice measure of A ∧ B is 0.

Let L be a lattice in Rd, d ≥ 2, and let A ⊂ Rd be a Lipschitz domain which satisfies some additional weak technical regularity assumption. In the first part of the paper we consider certain lattice sums over points which are close to ∂A. The main result is that these lattice sums approximate corresponding surface integrals for small lattice spacing. This is not obvious since the thickness of t...

In this talk I discuss the problems and virtues of SUSY GUTs in four dimensions. I then show how to solve some of these problems, without foregoing the virtues, by considering an SO(10) SUSY GUT in five dimensions. I discuss gauge coupling unification and neutrino masses. In particular, it is shown that the 5D compactification scale and cutoff scale are determined by fitting the low energy valu...

Scale setting for QCD with two flavors of staggered quarks is examined using Wilson flow over a factor of four change in both the lattice spacing and the pion mass. The statistics needed to keep the errors in the flow scale fixed is found to increase approximately as the inverse square of the lattice spacing. Tree level improvement of the scales t0 and w0 is found to be useful in most of the ra...

We review lattice evidence for existence of thin vortices in the vacuum state of SU(2) gluodynamics. On the average, the non-Abelian action density per unit area is ultraviolet divergent as a−2 where a is the lattice spacing. At small scales, the surface looks very crumpled so that the corresponding entropy factor appears also ultraviolet divergent. The total area, however, scales in physical u...

This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton–Cabrera–Frank-type model following the Xiang’s work (Xiang in SIAM J Appl Math 63(1):241–258, 2002). We prove that as the lattice parameter goes to zero, for a finite time interval, a modified discrete model converges to the strong solution of the limiting PDE with first-order conver...

Recent results from lattice QCD calculations relevant to particle physics phenomenology are reviewed. They include the calculations of strong coupling constant, quark masses, kaon matrix elements, and D and B meson matrix elements. Special emphasis is on the recent progress in the simulations including dynamical quarks.

The effect of lattice mismatch on the chemical ordering of epitaxial FePt films was studied. The results showed that the lattice constant scd of the FePt films decreased with increasing lattice mismatch « from about 2.23% to 6.33%. Upon further increase of « to about 8.8%, c increased. On the other hand, the variation of the lattice constant sad of the FePt films showed a reversal behavior to t...