Scaling Laws and Effective Dimension in Lattice SU(2) Yang-Mills Theory with a Compactified Extra Dimension

Monte Carlo simulations are performed in a five-dimensional lattice SU(2) Yang-Mills theory with a compactified extra dimension, and scaling laws are studied. Our simulations indicate that as the compactification radius $R$ decreases, the confining phase spreads more and more to the weak coupling regime, and the effective dimension of the theory changes gradually from five to four. Our simulations also indicate that the limit $a_4 to 0$ with $R/a_4$ kept fixed exists both in the confining and deconfining phases if $R/a_4$ is small enough, where $a_4$ is the lattice spacing in the four-dimensional direction. We argue that the color degrees of freedom in QCD are confined only for $R < R_{\rm max}$, where a rough estimate shows that $1/R_{\rm max}$ lies in the TeV range. Comments on deconstructing extra dimensions are given.Comment: 15 pages, TeX, 5 figure

A lattice computation of the first moment of the kaon's distribution amplitude

We present a lattice computation of the first moment of the kaon's leading-twist distribution amplitude. The results were computed using ensembles with 2+1 dynamical flavours with the domain wall fermion action and Iwasaki gauge action from the RBC and UKQCD joint dataset. The first moment is non-zero because of SU(3)-breaking effects, and we find that we are able to measure these effects very clearly. We observe the expected chiral behaviour and finally obtain , which agrees very well with results obtained using sum-rules, but with a significantly smaller error. We discuss the systematic uncertainties in detail and explain the prospects for their further reduction. In particular, we are implementing a programme of non-perturbative renormalization to improve the precision on the normalization of the lattice operators (currently performed perturbatively) and are repeating the calculation on a large lattice (243×64 as compared to the present 163×32 lattice).<br/