Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory

We present the first nucleon-nucleon potential at next-to-next-to-next-to-leading order (fourth order) of chiral perturbation theory. Charge-dependence is included up to next-to-leading order of the isospin-violation scheme. The accuracy for the reproduction of the NN data below 290 MeV lab. energy is comparable to the one of phenomenological high-precision potentials. Since NN potentials of order three and less are known to be deficient in quantitative terms, the present work shows that the fourth order is necessary and sufficient for a reliable NN potential derived from chiral effective Lagrangians. The new potential provides a promising starting point for exact few-body calculations and microscopic nuclear structure theory (including chiral many-body forces derived on the same footing).Comment: 4 pages Revtex including one figur

Towards a Relativistic Description of Exotic Meson Decays

This work analyses hadronic decays of exotic mesons, with a focus on the lightest one, the $J^{PC}=1^{-+}$ $\pi_{1}$, in a fully relativistic formalism, and makes comparisons with non-relativistic results. We also discuss Coulomb gauge decays of normal mesons that proceed through their hybrid components. The relativistic spin wave functions of mesons and hybrids are constructed based on unitary representations of the Lorentz group. The radial wave functions are obtained from phenomenological considerations of the mass operator. Fully relativistic results (with Wigner rotations) differ significantly from non-relativistic ones. We also find that the decay channels $\pi_{1}\to\pi b_{1}, \pi f_{1}, KK_{1}$ are favored, in agreement with results obtained using other models.Comment: 14 pages, 7 figure

Do attractive bosons condense?

Motivated by experiments on bose atoms in traps which have attractive interactions (e.g. ^7Li), we consider two models which may be solved exactly. We construct the ground states subject to the constraint that the system is rotating with angular momentum proportional to the number of atoms. In a conventional system this would lead to quantised vortices; here, for attractive interactions, we find that the angular momentum is absorbed by the centre of mass motion. Moreover, the state is uncondensed and is an example of a `fragmented' condensate discussed by Nozi\`eres and Saint James. The same models with repulsive interactions are fully condensed in the thermodynamic limit.Comment: 4 pages, Latex, RevTe

Modelling nucleon-nucleon scattering above 1 GeV

Motivated by the recent measurement of proton-proton spin-correlation parameters up to 2.5 GeV laboratory energy, we investigate models for nucleon-nucleon (NN) scattering above 1 GeV. Signatures for a gradual failure of the traditional meson model with increasing energy can be clearly identified. Since spin effects are large up to tens of GeV, perturbative QCD cannot be invoked to fix the problems. We discuss various theoretical scenarios and come to the conclusion that we do not have a clear phenomenological understanding of the spin-dependence of the NN interaction above 1 GeV.Comment: 36 pages, 8 figure

Ground-State of Charged Bosons Confined in a Harmonic Trap

We study a system composed of N identical charged bosons confined in a harmonic trap. Upper and lower energy bounds are given. It is shown in the large N limit that the ground-state energy is determined within an accuracy of $\pm 8$ and that the mean field theory provides a reasonable result with relative error of less than 16% for the binding energy .Comment: 15 page

Shell Model Monte Carlo studies of neutron-rich nuclei in the 1s-0d-1p-0f shells

We demonstrate the feasibility of realistic Shell-Model Monte Carlo (SMMC) calculations spanning multiple major shells, using a realistic interaction whose bad saturation and shell properties have been corrected by a newly developed general prescription. Particular attention is paid to the approximate restoration of translational invariance. The model space consists of the full sd-pf shells. We include in the study some well-known T=0 nuclei and several unstable neutron-rich ones around N=20,28. The results indicate that SMMC can reproduce binding energies, B(E2) transitions, and other observables with an interaction that is practically parameter free. Some interesting insight is gained on the nature of deep correlations. The validity of previous studies is confirmed.Comment: 22 pages + 7 postscript figure

Nucleon-Nucleon Interaction: A Typical/Concise Review

Nearly a recent century of work is divided to Nucleon-Nucleon (NN) interaction issue. We review some overall perspectives of NN interaction with a brief discussion about deuteron, general structure and symmetries of NN Lagrangian as well as equations of motion and solutions. Meanwhile, the main NN interaction models, as frameworks to build NN potentials, are reviewed concisely. We try to include and study almost all well-known potentials in a similar way, discuss more on various commonly used plain forms for two-nucleon interaction with an emphasis on the phenomenological and meson-exchange potentials as well as the constituent-quark potentials and new ones based on chiral effective field theory and working in coordinate-space mostly. The potentials are constructed in a way that fit NN scattering data, phase shifts, and are also compared in this way usually. An extra goal of this study is to start comparing various potentials forms in a unified manner. So, we also comment on the advantages and disadvantages of the models and potentials partly with reference to some relevant works and probable future studies.Comment: 85 pages, 5 figures, than the previous v3 edition, minor changes, and typos fixe

Extension to order β23\beta^{23} of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices

Using a renormalized linked-cluster-expansion method, we have extended to order $\beta^{23}$ the high-temperature series for the susceptibility $\chi$ and the second-moment correlation length $\xi$ of the spin-1/2 Ising models on the sc and the bcc lattices. A study of these expansions yields updated direct estimates of universal parameters, such as exponents and amplitude ratios, which characterize the critical behavior of $\chi$ and $\xi$. Our best estimates for the inverse critical temperatures are $\beta^{sc}_c=0.221654(1)$ and $\beta^{bcc}_c=0.1573725(6)$. For the susceptibility exponent we get $\gamma=1.2375(6)$ and for the correlation length exponent we get $\nu=0.6302(4)$. The ratio of the critical amplitudes of $\chi$ above and below the critical temperature is estimated to be $C_+/C_-=4.762(8)$. The analogous ratio for $\xi$ is estimated to be $f_+/f_-=1.963(8)$. For the correction-to-scaling amplitude ratio we obtain $a^+_{\xi}/a^+_{\chi}=0.87(6)$.Comment: Misprints corrected, 8 pages, latex, no figure

Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems

High-temperature series are computed for a generalized $3d$ Ising model with arbitrary potential. Two specific ``improved'' potentials (suppressing leading scaling corrections) are selected by Monte Carlo computation. Critical exponents are extracted from high-temperature series specialized to improved potentials, achieving high accuracy; our best estimates are: $\gamma=1.2371(4)$, $\nu=0.63002(23)$, $\alpha=0.1099(7)$, $\eta=0.0364(4)$, $\beta=0.32648(18)$. By the same technique, the coefficients of the small-field expansion for the effective potential (Helmholtz free energy) are computed. These results are applied to the construction of parametric representations of the critical equation of state. A systematic approximation scheme, based on a global stationarity condition, is introduced (the lowest-order approximation reproduces the linear parametric model). This scheme is used for an accurate determination of universal ratios of amplitudes. A comparison with other theoretical and experimental determinations of universal quantities is presented.Comment: 65 pages, 1 figure, revtex. New Monte Carlo data by Hasenbusch enabled us to improve the determination of the critical exponents and of the equation of state. The discussion of several topics was improved and the bibliography was update

Kernel based methods for accelerated failure time model with ultra-high dimensional data

<p>Abstract</p> <p>Background</p> <p>Most genomic data have ultra-high dimensions with more than 10,000 genes (probes). Regularization methods with <it>L</it>₁and <it>L_p</it>penalty have been extensively studied in survival analysis with high-dimensional genomic data. However, when the sample size <it>n </it>≪ <it>m </it>(the number of genes), directly identifying a small subset of genes from ultra-high (<it>m </it>> 10, 000) dimensional data is time-consuming and not computationally efficient. In current microarray analysis, what people really do is select a couple of thousands (or hundreds) of genes using univariate analysis or statistical tests, and then apply the LASSO-type penalty to further reduce the number of disease associated genes. This two-step procedure may introduce bias and inaccuracy and lead us to miss biologically important genes.</p> <p>Results</p> <p>The accelerated failure time (AFT) model is a linear regression model and a useful alternative to the Cox model for survival analysis. In this paper, we propose a nonlinear kernel based AFT model and an efficient variable selection method with adaptive kernel ridge regression. Our proposed variable selection method is based on the kernel matrix and dual problem with a much smaller <it>n </it>× <it>n </it>matrix. It is very efficient when the number of unknown variables (genes) is much larger than the number of samples. Moreover, the primal variables are explicitly updated and the sparsity in the solution is exploited.</p> <p>Conclusions</p> <p>Our proposed methods can simultaneously identify survival associated prognostic factors and predict survival outcomes with ultra-high dimensional genomic data. We have demonstrated the performance of our methods with both simulation and real data. The proposed method performs superbly with limited computational studies.</p