Complete 2-loop quantum electrodynamic contributions to the muon lifetime in the Fermi model

The complete 2-loop QED contributions to the muon lifetime have been calculated analytically in the Fermi theory. The exact result for the effects of virtual and real photons, virtual electrons, muons and hadrons as well as e+e- pair creation is Delta Gamma^(2)=Gamma_0(alpha/pi)^2[(156815/5184)-(1036/27)zeta(2) -(895/36)zeta(3)+(67/8)zeta(4) +53zeta(2)ln(2)-(0.042+/-0.002)] where Gamma_0 is the tree-level width. This eliminates the theoretical error in the extracted value of the Fermi coupling constant, G_F, which was previously the source of the dominant uncertainty. The new value is G_F=(1.16637 +/- 0.00001) x 10^-5 GeV^-2 with the error being entirely experimental. Several experiments are planned for the next generation of muon lifetime measurements and these can proceed unhindered by theoretical uncertainties.Comment: 9 pages, LaTeX, uses sprocl.sty, amsmath.sty, amssymb.sty and axodraw.sty. To appear in the Proceedings of the IVth International Symposium on Radiative Corrections (RADCOR98), Barcelona, Spain, 8-12 September, 1998, edited by J. Sol

The limits of mean-field heterozygosity estimates under spatial extension in simulated plant populations

Computational models of evolutionary processes are increasingly required to incorporate multiple and diverse sources of data. A popular feature to include in population genetics models is spatial extension, which reflects more accurately natural populations than does a mean field approach. However, such models necessarily violate the mean field assumptions of classical population genetics, as do natural populations in the real world. Recently, it has been questioned whether classical approaches are truly applicable to the real world. Individual based models (IBM) are a powerful and versatile approach to achieve integration in models. In this study an IBM was used to examine how populations of plants deviate from classical expectations under spatial extension. Populations of plants that used three different mating strategies were placed in a range of arena sizes giving crowded to sparse occupation densities. Using a measure of population density, the pollen communication distance (Pcd), the deviation exhibited by outbreeding populations differed from classical mean field expectations by less than 5% when Pcd was less than 1, and over this threshold value the deviation significantly increased. Populations with an intermediate mating strategy did not have such a threshold and deviated directly with increasing isolation between individuals. Populations with a selfing strategy were influenced more by the mating strategy than by increased isolation. In all cases pollen dispersal was more influential than seed dispersal. The IBM model showed that mean field calculations can be reasonably applied to natural outbreeding plant populations that occur at a density in which individuals are less than the average pollen dispersal distance from their neighbors

On the Precise Determination of the Fermi Coupling Constant from the Muon Lifetime

The determination of the Fermi coupling constant, G_F, is examined in the light of recently calculated 2-loop QED corrections and planned experiments to measure the muon lifetime to a level below 1ppm. The methods used in the calculation of the QED corrections are described in detail. Sources of the dominant theoretical and experimental uncertainties are identified. Finally the incorporation of G_F into analyses using the full electroweak Standard Model is discussed.Comment: 48 pages LaTeX. 11 figures. Uses amsmath.sty, axodraw.sty, cite.st

Gauge Invariance and the Unstable Particle

It is shown how to construct exactly gauge-invariant S-matrix elements for processes involving unstable gauge particles such as the $Z^0$ boson. The results are applied to derive a physically meaningful expression for the cross-section $\sigma(e^+e^-\to Z^0Z^0)$ and thereby provide a solution to the long-standing problem of the unstable particle.Comment: 8 pages LaTeX. Uses aipproc.sty and epsfig.sty. Talk presented at 1st Latin American Symposium on High-energy Physics, SILAFAE-I, Merida, November 1--5, 199

Debranding in Fantasy Realms: Perceived Marketing Opportunities within the Virtual World

This paper discusses the application of the concept of debranding within immersive virtual environments. In particular the issue of the media richness and vividness of experience is considered in these experience realms that may not be conducive to traditional branding invasive strategies. Brand equity is generally seen to be the desired outcome of branding strategies and the authors suggest that unless the virtual domains are considered as sacred spaces then brand equity may be compromised. The application of the above concepts is applied to the differing social spaces that operate within the different experience realms. The ideas of resonance, presence and interactivity are considered here. They lead to the development of a constructed positioning by the participants. Through the process of debranding, marketers may be able to enter these sacred spaces without negative impact to the brand. Perception of these virtual spaces was found to be partially congruent with this approach to branding. It thus presents a number of challenges for the owners of such virtual spaces and also virtual worlds in increasing the commercial utilization of investment in these environments