The triangle-free graphs with rank 6

The rank of a graph G is defined to be the rank of its adjacency matrix A(G). In this paper we characterize all connected triangle-free graphs with rank 6

Statefinder diagnostic for the modified polytropic Cardassian universe

We apply the Statefinder diagnostic to the Modified Polytropic Cardassian Universe in this work. We find that the Statefinder diagnostic is quite effective to distinguish Cardassian models from a series of other cosmological models. The $s-r$ plane is used to classify the Modified Polytropic Cardassian models into six cases. The evolutionary trajectories in the $s-r$ plane for the cases with different $n$ and $\beta$ reveal different evolutionary properties of the universe. In addition, we combine the observational $H(z)$ data, the Cosmic Microwave Background (CMB) data and the Baryonic Acoustic Oscillation (BAO) data to make a joint analysis. We find that \textbf{Case 2} can be excluded at the 68.3% confidence level and any case is consistent with the observations at the 95.4% confidence level.Comment: Comments: Final version for publication in Physical Review D [minor revision to match the appear version] Journal-ref: Physical Review D 75, 083515 (2007

Conical Defects, Black Holes and Higher Spin (Super-)Symmetry

We study the (super-)symmetries of classical solutions in the higher spin (super-)gravity in AdS$_3$. We show that the symmetries of the solutions are encoded in the holonomy around the spatial circle. When the spatial holonomies of the solutions are trivial, they preserve maximal symmetries of the theory, and are actually the smooth conical defects. We find all the smooth conical defects in the $sl(N), so(2N+1),sp(2N), so(2N), g_2$, as well as in $sl(N|N-1)$ and $osp(2N+1|2N)$ Chern-Simons gravity theories. In the bosonic higher spin cases, there are one-to-one correspondences between the smooth conical defects and the highest weight representations of Lie group. Furthermore we investigate the higher spin black holes in $osp(3|2)$ and $sl(3|2)$ higher spin (super-)gravity and find that they are only partially symmetric. In general, the black holes break all the supersymmetries, but in some cases they preserve part of the supersymmetries.Comment: 48 pages; more clarifications on conical defects in supersymmetric cas

LHC Phenomenology of Type II Seesaw: Nondegenerate Case

In this paper, we thoroughly investigate the LHC phenomenology of the type II seesaw mechanism for neutrino masses in the nondegenerate case where the triplet scalars of various charge ($H^{\pm\pm}, H^\pm, H^0, A^0$) have different masses. Compared with the degenerate case, the cascade decays of scalars lead to many new, interesting signal channels. In the positive scenario where $M_{H^{\pm\pm}}<M_{H^\pm}<M_{H^0/A^0}$, the four-lepton signal is still the most promising discovery channel for the doubly-charged scalars $H^{\pm\pm}$. The five-lepton signal is crucial to probe the mass spectrum of the scalars, for which, for example, a $5\sigma$ reach at 14 TeV LHC for $M_{H^{\pm}}=430 GeV$ with $M_{H^{\pm\pm}}=400 GeV$ requires an integrated luminosity of 76/fb. And the six-lepton signal can be used to probe the neutral scalars $H^0/A^0$, which are usually hard to detect in the degenerate case. In the negative scenario where $M_{H^{\pm\pm}}>M_{H^\pm}>M_{H^0/A^0}$, the detection of $H^{\pm\pm}$ is more challenging, when the cascade decay $H^{\pm\pm}\to H^{\pm}W^{\pm*}$ is dominant. The most important channel is the associated $H^{\pm}H^0/A^0$ production in the final state $\ell^\pm\cancel{E}_Tb\bar{b}b\bar{b}$, which requires a luminosity of 109/fb for a $5\sigma$ discovery, while the final state $\ell^\pm\cancel{E}_Tb\bar{b}\tau^+\tau^-$ is less promising. Moreover, the associated $H^0A^0$ production can give same signals as the standard model Higgs pair production. With a much larger cross section, the $H^0A^0$ production in the final state $b\bar{b}\tau^+\tau^-$ could reach $3\sigma$ significance at 14 TeV LHC with a luminosity of 300/fb. In summary, with an integrated luminosity of order 500/fb, the triplet scalars can be fully reconstructed at 14 TeV LHC in the negative scenario.Comment: 41 pages, 20 figures, 7 tables. Version 2 accepted by PRD. 41 pages, 18 figures. Main changes are, (1) rewording in secs III and IV, removing 2 figs and quoting ref [34]; (2) a paragraph added before eq (10) to clarify constraints from electroweak precision data; (3) a paper added to ref [11]. No changes in result