16,133 research outputs found

### Searching for high-$K$ isomers in the proton-rich $A\sim80$ mass region

Configuration-constrained potential-energy-surface calculations have been
performed to investigate the $K$ isomerism in the proton-rich $A\sim80$ mass
region. An abundance of high-$K$ states are predicted. These high-$K$ states
arise from two and four-quasi-particle excitations, with $K^{\pi}=8^{+}$ and
$K^{\pi}=16^{+}$, 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-$K$ states may indicate a combination of $K$ isomerism
and shape isomerism

### Testing linear hypotheses in high-dimensional regressions

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 $p\le 20$.
On the other hand, assuming that the data dimension $p$ as well as the number
$q$ of regression variables are fixed while the sample size $n$ 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 $p$ and a large sample size $n$.
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 $p$ and
large $n$ context, but also for moderately large data dimensions like $p=30$ or
$p=50$. 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

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

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

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