Light scalar mesons as tetraquarks within QCD Sum Rules

We examine the interpretation of the light scalar meson nonet as tetraquark states using QCD sum rules. With the interpolating current for the tetraquark states composed of scalar diquark and scalar antidiquark, first, we construct the QCD sum rules by means of the operator product expansion up to the operators of dimension 8 and show that there is no evidence of the coupling of the tetraquark states to the light scalar meson nonet. In order to have a stable sum rule, we propose a "good" interpolating current for the tetraquarks based on chirality arguments which includes scalar and pseudoscalar diquark--antidiquarks with equal weights. In particular, for the lowest tetraquark $\sigma$--meson, we perform detail analysis of the QCD sum rule and obtain mass for the $\sigma(600)$ around 780 MeV.Comment: 4 pages, 1 figure, Talk at the Yukawa International Seminar (YKIS) 2006, "New frontiers in QCD", Kyoto, Japa

Topological triviality of smoothly knotted surfaces in 4-manifolds

Some generalizations and variations of the Fintushel-Stern rim surgery are known to produce smoothly knotted surfaces. We show that if the fundamental groups of their complements are cyclic, then these surfaces are topologically unknotted. Using a twist-spinning construction from high-dimensional knot theory, we construct examples of knotted surfaces whose complements have cyclic fundamental groups.Comment: Final version; appeared in AMS Transactions. 15 pages, 2 figure

Double point surgery and configurations of surfaces

We introduce a new operation, double point surgery, on immersed surfaces in a 4-manifold, and use it to construct knotted configurations of surfaces in many 4-manifolds. Taking branched covers, we produce smoothly exotic actions of Z/m x Z/n on simply connected 4-manifolds with complicated fixed-point sets.Comment: Final version; to appear in Journal of Topology. Removed assertion about the restriction of the Z/m x Z/n action to the Z/m and Z/n subgroup

Decaying axinolike dark matter: Discriminative solution to small-scale issues

The latest Lyman-$\alpha$ forest data severely constrain the conventional warm dark matter solution to small-scale issues in the cold dark matter paradigm. It has been also reported that unconstrained astrophysical processes may address the issues. In response to this situation, we revisit the decaying dark matter solution to the issues, discussing possible signatures to discriminate decaying dark matter from astrophysical processes as a solution to small-scale issues. We consider an axinolike particle (ALPino) decaying into an axionlike particle (ALP) and gravitino with the lifetime around the age of the Universe. The ALPino mass is sub-PeV and slightly ($\Delta m/m\sim 10^{-4}$) larger than the gravitino mass, and thus the dark matter abundance does not alter virtually after the ALPino decays. On the other hand, the gravitino produced from the ALPino decay obtains a kick velocity of $\sim 30 \,{\rm km / s}$, which is sufficiently larger than a circular velocity of dwarf galaxies to impact their dark matter distributions. The Lyman-$\alpha$ forest constraints are relieved since only a small fraction ($\sim10$%) of dark matter experiences the decay at that time. Decaying dark matter is thus promoted to a viable solution to small-scale issues. The ALPino relic abundance is determined predominantly by the decay of the lightest ordinary supersymmetric particle. The monochromatic ALP emission from the ALPino decay is converted to $\sim 50 \,{\rm GeV}$ photon under the Galactic magnetic field. The morphology of the gamma-ray flux shows a distinctive feature of the model when compared to decaying dark matter that directly decays into photons. Once detected, such distinctive signals discriminate the decaying dark matter solution to small-scale issues from unconstrained astrophysical processes.Comment: 6 pages, 3 figures; discussions improved, version accepted in PR