Complete bounded λ\lambda-hypersurfaces in the weighted volume-preserving mean curvature flow

In this paper, we study the complete bounded $\lambda$-hypersurfaces in weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded $\lambda$-hypersurfaces with $|A|\leq\alpha$ and get some applications of the volume comparison theorem. Secondly, we consider the relation among $\lambda$, extrinsic radius $k$, intrinsic diameter $d$, and dimension $n$ of the complete $\lambda$-hypersurface, and we obtain some estimates for the intrinsic diameter and the extrinsic radius. At last, we get some topological properties of the bounded $\lambda$-hypersurface with some natural and general restrictions

Invisible Higgs Decay at the LHeC

The possibility that the 125 GeV Higgs boson may decay into invisible non-standard-model (non-SM) particles is theoretically and phenomenologically intriguing. In this letter we investigate the sensitivity of the Large Hadron Electron Collider (LHeC) to an invisibly decaying Higgs, in its proposed high luminosity running mode. We focus on the neutral current Higgs production channel which offers more kinematical handles than its charged current counterpart. The signal contains one electron, one jet and large missing energy. With a cut-based parton level analysis, we estimate that if the $hZZ$ coupling is at its standard model (SM) value, then assuming an integrated luminosity of 1\,\mbox{ab}^{-1} the LHeC with the proposed 60 GeV electron beam (with $-0.9$ polarization) and 7 TeV proton beam is capable of probing $\mathrm{Br}(h\rightarrow E\!\!\!\!/_T)=6\%$ at $2\sigma$ level. Good lepton veto performance (especially hadronic $\tau$ veto) in the forward region is crucial to the suppression of the dominant $Wje$ background. We also explicitly point out the important role that may be played by the LHeC in probing a wide class of exotic Higgs decay processes and emphasize the general function of lepton-hadron colliders in precision study of new resonances after their discovery in hadron-hadron collisions.Comment: 6 pages, 3 figures. Description of the backgrounds, analysis and results is simplified. Results unchanged with respect to v2. References update

A unified approach to exact solutions of time-dependent Lie-algebraic quantum systems

By using the Lewis-Riesenfeld theory and the invariant-related unitary transformation formulation, the exact solutions of the {\it time-dependent} Schr\"{o}dinger equations which govern the various Lie-algebraic quantum systems in atomic physics, quantum optics, nuclear physics and laser physics are obtained. It is shown that the {\it explicit} solutions may also be obtained by working in a sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator ({\it i. e.}, the {\it time-independent} invariant) for some quantum systems without quasi-algebraic structures. The global and topological properties of geometric phases and their adiabatic limit in time-dependent quantum systems/models are briefly discussed.Comment: 11 pages, Latex. accepted by Euro. Phys. J.