A Distinguished Subgroup of Compact Abelian Groups

Here “group” means additive abelian group. A compact group G contains δ–subgroups, that is, compact totally disconnected subgroups ∆ such that G/∆ is a torus. The canonical subgroup ∆(G) of G that is the sum of all δ–subgroups of G turns out to have striking properties. Lewis, Loth and Mader obtained a comprehensive description of ∆(G) when considering only finite dimensional connected groups, but even for these, new and improved results are obtained here. For a compact group G, we prove the following: ∆(G) contains tor(G), is a dense, zero-dimensional subgroup of G containing every closed totally disconnected subgroup of G, and G/∆(G) is torsion-free and divisible; ∆(G) is a functorial subgroup of G, it determines G up to topological isomorphism, and it leads to a “canonical” resolution theorem for G. The subgroup ∆(G) appeared before in the literature as td(G) motivated by completely different considerations. We survey and extend earlier results. It is shown that td, as a functor, preserves proper exactness of short sequences of compact groups

Nucleon Structure and Hyperon Form Factors from Lattice QCD.

In this work, I report the latest lattice QCD calculations of nucleon and hyperon structure from chiral fermions in 2+1-flavor dynamical simulations. All calculations are done with a chirally symmetric fermion action, domain-wall fermions, for valence quarks. I begin with the latest lattice results on the nucleon structure, focusing on results from RBC/UKQCD using 2+1-flavor chiral fermion actions. We find the chiral-extrapolated axial coupling constant at physical pion mass point. to be 1.23(5), consistent with experimental value. The renormalization constants for the structure functions are obtained from RI/MOM-scheme non-perturbative renormalization. We find first moments of the polarized and unpolarized nucleon structure functions at zero transfer momentum to be 0.133(13) and 0.203(23) respectively, using continuum chiral extrapolation. These are consistent with the experimental values, unlike previous calculations which have been 50% larger. We also have a prediction for the transversity, which we find to be 0.56(4). The twist-3 matrix element is consistent with zero which agrees with the prediction of the Wandzura-Wilczek relation. In the second half of this work, I report an indirect dynamical estimation of the strangeness proton magnetic moments using mixed actions. With the analysis of hyperon form factors and using charge symmetry, the strangeness of proton is found to be -0.066(2G), consistent with the Adelaide-JLab Collaboration's result. The hyperon {Sigma} and {Xi} axial coupling constants are also performed for the first time in a lattice calculation, g{sub {Sigma}{Sigma}} = 0.441(14) and g{sub {Xi}{Xi}} = -0.277(11)

Cross-sections for neutral channels in K P interactions between 1470 and 1560 MeV C.M. energy

The results presented in this thesis are from the preliminary data on a K P formation experiment. The experiment was carried out at the Rutherford Laboratory using the British National Hydrogen bubble chamber with a Track Sensitive Target (T.S.T.) to afford gamma-ray detection. The final states selected for the analysis are Λºπº, ϵºπº and Kºn at incident momenta between 200 and 500 MeV(_c). The T S T technique employed in this experiment is discussed in detail, in particular its limitations and how they should be handled are described. The cross-sections for Λº + neutrals, Λºπ(^+)π(^-) and Kºn channels are obtained in 20 MeV (_c) momentum intervals and the presence of the Λ (1520) is quite clear. The kaon flux is determined by using the observed tau-decays. The data is divided into 6 intervals of incident momentum between 250 and 500 MeV(_c) and fits are made to the distribution of missing mass squared to the A -hyperon, the production angular distribution and the polarisation of the A . These fits gave the Legendre expansion coefficients describing the angular distributions and the polarisations for the Λºπº and ϵºπº final states. The results are in good agreement with the previous data. Finally events fitted as Λºπº and ϵºπº hypotheses with one associated gamma-ray are chosen. Here the gamma-ray is used to resolve the Λº/ϵº ambiguity. The observed production angular distributions for these events are compared with the results from the fit above using Λº and ϵº events without gamma-rays. Also, the decay proton angular distribution of the fitted ϵºπº events is compared with the results from the fit. There is a good consistency between the two results and that of the previous data