16,133 research outputs found

    Searching for high-KK isomers in the proton-rich A80A\sim80 mass region

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    Configuration-constrained potential-energy-surface calculations have been performed to investigate the KK isomerism in the proton-rich A80A\sim80 mass region. An abundance of high-KK states are predicted. These high-KK states arise from two and four-quasi-particle excitations, with Kπ=8+K^{\pi}=8^{+} and Kπ=16+K^{\pi}=16^{+}, respectively. Their excitation energies are comparatively low, making them good candidates for long-lived isomers. Since most nuclei under studies are prolate spheroids in their ground states, the oblate shapes of the predicted high-KK states may indicate a combination of KK isomerism and shape isomerism

    Testing linear hypotheses in high-dimensional regressions

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    For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more importantly, these distributional approximations are feasible only for moderate dimension of the dependent variable, say p20p\le 20. On the other hand, assuming that the data dimension pp as well as the number qq of regression variables are fixed while the sample size nn grows, several asymptotic approximations are proposed in the literature for Wilk's \bLa including the widely used chi-square approximation. In this paper, we consider necessary modifications to Wilk's test in a high-dimensional context, specifically assuming a high data dimension pp and a large sample size nn. Based on recent random matrix theory, the correction we propose to Wilk's test is asymptotically Gaussian under the null and simulations demonstrate that the corrected LRT has very satisfactory size and power, surely in the large pp and large nn context, but also for moderately large data dimensions like p=30p=30 or p=50p=50. As a byproduct, we give a reason explaining why the standard chi-square approximation fails for high-dimensional data. We also introduce a new procedure for the classical multiple sample significance test in MANOVA which is valid for high-dimensional data.Comment: Accepted 02/2012 for publication in "Statistics". 20 pages, 2 pages and 2 table

    Ratio of Hadronic Decay Rates of J\psi and \psi(2S) and the \rho\pi Puzzle

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    The so-called \rho\pi puzzle of J\psi and \psi(2S) decays is examined using the experimental data available to date. Two different approaches were taken to estimate the ratio of J\psi and \psi(2S) hadronic decay rates. While one of the estimates could not yield the exact ratio of \psi(2S) to J\psi inclusive hadronic decay rates, the other, based on a computation of the inclusive ggg decay rate for \psi(2S) (J\psi) by subtracting other decay rates from the total decay rate, differs by two standard deviations from the naive prediction of perturbative QCD, even though its central value is nearly twice as large as what was naively expected. A comparison between this ratio, upon making corrections for specific exclusive two-body decay modes, and the corresponding experimental data confirms the puzzles in J\psi and \psi(2S) decays. We find from our analysis that the exclusively reconstructed hadronic decays of the \psi(2S) account for only a small fraction of its total decays, and a ratio exceeding the above estimate should be expected to occur for a considerable number of the remaining decay channels. We also show that the recent new results from the BES experiment provide crucial tests of various theoretical models proposed to explain the puzzle.Comment: 8 pages, no figure, 4 table

    Breaking Discrete Symmetries in Broken Gauge Theories

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    We study the spontaneous breaking of discrete symmetries in theories with broken gauge symmetry. The intended application is to CP breaking in theories with gauged flavor symmetries, but the analysis described here is preliminary. We dispense with matter fields and take the gauge theory to be weakly coupled and broken spontaneously by unspecified, short-distance forces. We develop an effective-field-theory description of the resultant low energy theory, and ask whether this theory by itself can describe the subsequent breaking of discrete symmetries. We conclude that this can happen depending on the parameters of the effective theory, and that the intrinsic violation is naturally of order unity.Comment: 9 pages, 1 figure, corrected typos, added a referenc