Model Independent Approach to Focus Point Supersymmetry: from Dark Matter to Collider Searches

The focus point region of supersymmetric models is compelling in that it simultaneously features low fine-tuning, provides a decoupling solution to the SUSY flavor and CP problems, suppresses proton decay rates and can accommodate the WMAP measured cold dark matter (DM) relic density through a mixed bino-higgsino dark matter particle. We present the focus point region in terms of a weak scale parameterization, which allows for a relatively model independent compilation of phenomenological constraints and prospects. We present direct and indirect neutralino dark matter detection rates for two different halo density profiles, and show that prospects for direct DM detection and indirect detection via neutrino telescopes such as IceCube and anti-deuteron searches by GAPS are especially promising. We also present LHC reach prospects via gluino and squark cascade decay searches, and also via clean trilepton signatures arising from chargino-neutralino production. Both methods provide a reach out to m_{\tg}\sim 1.7 TeV. At a TeV-scale linear e^+e^- collider (LC), the maximal reach is attained in the \tz_1\tz_2 or \tz_1\tz_3 channels. In the DM allowed region of parameter space, a \sqrt{s}=0.5 TeV LC has a reach which is comparable to that of the LHC. However, the reach of a 1 TeV LC extends out to m_{\tg}\sim 3.5 TeV.Comment: 34 pages plus 36 eps figure

Supersymmetry and the relationship between a class of singular potentials in arbitrary dimensions

The eigenvalues of the potentials $V_{1}(r)=\frac{A_{1}}{r}+\frac{A_{2}}{r^{2}}+\frac{A_{3}}{r^{3}}+\frac{A_{4 }}{r^{4}}$ and $V_{2}(r)=B_{1}r^{2}+\frac{B_{2}}{r^{2}}+\frac{B_{3}}{r^{4}}+\frac{B_{4}}{r^ {6}}$, and of the special cases of these potentials such as the Kratzer and Goldman-Krivchenkov potentials, are obtained in N-dimensional space. The explicit dependence of these potentials in higher-dimensional space is discussed, which have not been previously covered.Comment: 13 pages article in LaTEX (uses standard article.sty). Please check "http://www1.gantep.edu.tr/~ozer" for other studies of Nuclear Physics Group at University of Gaziante

Reduced density matrices and entanglement entropy in free lattice models

We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a quasi-thermodynamic problem with a certain free-particle Hamiltonian. We discuss the derivation of this result, the character of the Hamiltonian and its eigenstates, the single-particle spectra and the full spectra, the resulting entanglement and in particular the entanglement entropy. This is done for various one- and two-dimensional situations, including also the evolution after global or local quenches.Comment: 33 pages, 18 figures, minor changes, references added. Review article for the special issue "Entanglement entropy in extended systems" in J. Phys.