Abstract: We describe a measurement of the time-integrated luminosity of the data collected by the BABAR experiment at the PEP-II asymmetric-energy e(+)e(-) collider at the Upsilon(4S), Upsilon(3S), and Upsilon(2S) resonances and in a continuum region below each resonance. We measure the time-integrated luminosity by counting e(+)e(-)-> e(+)e(-) and (for the Upsilon(4S) only) e(+)e(-)->mu(+)mu(-) candidate events, allowing additional photons in the final state. We use data-corrected simulation to determine the cross-sections and reconstruction efficiencies for these processes, as well as the major backgrounds. Due to the large cross-sections of e(+)e(-)-> e(+)e(-) and e(+)e(-)->mu(+)mu(-), the statistical uncertainties of the measurement are substantially smaller than the systematic uncertainties. The dominant systematic uncertainties are due to observed differences between data and simulation, as well as uncertainties on the cross-sections. For data collected on the Upsilon(3S) and Upsilon(2S) resonances, an additional uncertainty arises due to Upsilon -> e(+)e(-)X background. For data collected off the Upsilon resonances, we estimate an additional uncertainty due to time dependent efficiency variations, which can affect the short off-resonance runs. The relative uncertainties on the luminosities of the on-resonance (off-resonance) samples are 0.43% (0.43%) for the Upsilon(4S), 0.58% (0.72%) for the Upsilon(3S), and 0.68% (0.88%) for the Upsilon(2S).

Abstract: The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also means that a new physical theory can be obtained from a known one. One of the procedures that allow us to do so is called expansion of Lie algebras, and has been recently used in different physical applications-particularly in gauge theories of gravity. Here we report on further developments of this method, required to understand in a deeper way their consequences in physical theories. We have found theorems related to the preservation of some properties of the algebras under expansions that can be used as criteria and, more specifically, as necessary conditions to know if two arbitrary Lie algebras can be related by some expansion mechanism. Formal aspects, such as the Cartan decomposition of the expanded algebras, are also discussed. Finally, an instructive example that allows us to check explicitly all our theoretical results is also provided.

Abstract: We analyze the implications for the status and prospects of supersymmetry of the Higgs discovery and the last XENON data. We focus mainly, but not only, on the CMSSM and NUHM models. Using a Bayesian approach we determine the distribution of probability in the parameter space of these scenarios. This shows that, most probably, they are now beyond the LHC reach. This negative chances increase further (at more than 95% c.l.) if one includes dark matter constraints in the analysis, in particular the last XENON100 data. However, the models would be probed completely by XENON1T. The mass of the LSP neutralino gets essentially fixed around 1TeV. We do not incorporate ad hoc measures of the fine-tuning to penalize unnatural possibilities: such penalization arises automatically from the careful Bayesian analysis itself, and allows to scan the whole parameter space. In this way, we can explain and resolve the apparent discrepancies between the previous results in the literature. Although SUSY has become hard to detect at LHC, this does not necessarily mean that is very fine-tuned. We use Bayesian techniques to show the experimental Higgs mass is at similar to 2 sigma off the CMSSM or NUHM expectation. This is substantial but not dramatic. Although the CMSSM or the NUHM are unlikely to show up at the LHC, they are still interesting and plausible models after the Higgs observation; and, if they are true, the chances of discovering them in future dark matter experiments are quite high.