Lattices of quasi-equational theories as congruence lattices of semilattices with operators, Part I

We show that for every quasivariety K of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S,+,0,F). As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found.Comment: Presented on International conference "Order, Algebra and Logics", Vanderbilt University, 12-16 June, 2007 25 pages, 2 figure

On sgoldstino interpretation of HyperCP events

We discuss possible sgoldstino interpretation of the observation, reported by HyperCP collaboration, of three $\Sigma^+\to p\mu^+\mu^-$ decay events with dimuon invariant mass 214.3 MeV within detector resolution. We find that this interpretation is consistent in models with (i) parity conservation in sgoldstino interactions, (ii) pseudoscalar sgoldstino $P$ of mass 214 MeV and heavier scalar sgoldstino, and (iii) low supersymmetry breaking scale, \sqrt{F} = 2.5-60 TeV. In these models, sgoldstino can be observed in decays $K^+\to\pi^+\pi^0 P$, $K_L\to\pi\pi P$ and $K_S\to\pi\pi P$ at the branching ratios of at least of order 10^{-12}, 10^{-8} and 10^{-11}, respectively. The model can be probed also at e^+e^- colliders in the channels $e^+e^-\to\gamma P$ and $e^+e^-\to e^+e^-P$, where the cross section is likely to be in the range 1 pb - 5 ab.Comment: 14 pages, 1 figure; v2: replaced with journal version, predictions for kaons refine

Stoponium Search at Photon Linear Collider

In some supersymmetric extensions of the Standard Model fairly light superpartner of t-quark is predicted, which may form bound states ({\it stoponiums}) under certain conditions. We study prospects of search for stoponium at the future Photon Linear Collider. It is found that this machine could be the best machine for discovery and study of these resonances at some scenarios of supersymmetric extension of the Standard Model. In particular, if the $hh$ decay channel is dominant stoponium could be observed at the beginning of PLC run with collision energy tuned at the stoponium mass. If this channel is kinematically closed stoponium could be discovered in $gg$, $\gamma\gamma$ and $ZZ$ decay channels but higher statistics are needed. Effects of the stoponium-Higgs mixing and degeneracy are briefly discussed.Comment: 11 pages, 2 figures added, corrections taken into account result in increasing of signal significanc