Propagation of boundary-induced discontinuity in stationary radiative transfer

We consider the boundary value problem of the stationary transport equation in the slab domain of general dimensions. In this paper, we discuss the relation between discontinuity of the incoming boundary data and that of the solution to the stationary transport equation. We introduce two conditions posed on the boundary data so that discontinuity of the boundary data propagates along positive characteristic lines as that of the solution to the stationary transport equation. Our analysis does not depend on the celebrated velocity averaging lemma, which is different from previous works. We also introduce an example in two dimensional case which shows that piecewise continuity of the boundary data is not a sufficient condition for the main result.Comment: 15 pages, no figure

On the Existence of H1H^1 solutions for Stationary Linearized Boltzmann Equations in a Small Convex Domain

In this article, we investigate the incoming boundary value problem for the stationary linearized Boltzmann equations in $\Omega \subseteq \mathbb{R}^{3}$. For a $C^2$ bounded domain with boundary of positive Gaussian curvature, the existence theory is established in $H^{1}(\Omega \times \mathbb{R}^{3})$ provided that the diameter of the domain $\Omega$ is small enough.Comment: 19 pages, 1 figur

Study of the Gauge Mediation Signal with Non-pointing Photons at the CERN LHC

In this paper we study the gauge mediation signal with the ATLAS detector at the CERN LHC. We focus on the case where the NLSP is the long-lived lightest neutralino ($\tilde{\chi}^0_1$) which decays dominantly into a photon ($\gamma$) and a gravitino ($\tilde{G}$). A non-pointing photon from the neutralino decay can be detected with good position and time resolutions by the electormagnetic calorimeter (ECAL), while the photon momentum would be precisely measured if the photon is converted inside the inner tracking detector before reaching the ECAL. A new technique is developed to determine the masses of the slepton ($\tilde{\ell}$) and the neutralino from events with a lepton and a converted non-pointing photon arising from the cascade decay $\tilde{\ell}\to \ell\tilde{\chi}^0_1\to \ell\gamma \tilde{G}$. A Monte Carlo simulation at a sample point shows that the masses would be measured with an error of 3% for $\cal{O}$(100) selected $\ell\gamma$ pairs. Once the sparticle masses are determined by this method, the decay time and momentum of the neutralino are solved using the ECAL data and the lepton momentum only, for all $\ell\gamma$ pairs without the photon conversion. We estimate the sensitivity to the neutralino lifetime for $c\tau=10$ cm to $\cal{O}$(10) m.Comment: 19 page, 7 figures, revte

A Detailed Study of the Gluino Decay into the Third Generation Squarks at the CERN LHC

In supersymmetric models a gluino can decay into tb\tilde{\chi}^{\pm}_1 through a stop or a sbottom. The decay chain produces an edge structure in the m_{tb} distribution. Monte Carlo simulation studies show that the end point and the edge height would be measured at the CERN LHC by using a sideband subtraction technique. The stop and sbottom masses as well as their decay branching ratios are constrained by the measurement. We study interpretations of the measurement in the minimal supergravity model. We also study the gluino decay into tb and \tilde{\chi}^{\pm}_2 as well as the influence of the stop left-right mixing on the m_{bb} distribution of the tagged $tb$ events.Comment: revtex, 20 pages in PRD format, 35 eps file

Measuring Invisible Particle Masses Using a Single Short Decay Chain

We consider the mass measurement at hadron colliders for a decay chain of two steps, which ends with a missing particle. Such a topology appears as a subprocess of signal events of many new physics models which contain a dark matter candidate. From the two visible particles coming from the decay chain, only one invariant mass combination can be formed and hence it is na\"ively expected that the masses of the three invisible particles in the decay chain cannot be determined from a single end point of the invariant mass distribution. We show that the event distribution in the $\log(E_{1T}/E_{2T})$ vs. invariant mass-squared plane, where $E_{1T}$, $E_{2T}$ are the transverse energies of the two visible particles, contains the information of all three invisible particle masses and allows them to be extracted individually. The experimental smearing and combinatorial issues pose challenges to the mass measurements. However, in many cases the three invisible particle masses in the decay chain can be determined with reasonable accuracies.Comment: 45 pages, 32 figure

Physics at the e+ e- Linear Collider

A comprehensive review of physics at an e+e- Linear Collider in the energy range of sqrt{s}=92 GeV--3 TeV is presented in view of recent and expected LHC results, experiments from low energy as well as astroparticle physics.The report focuses in particular on Higgs boson, Top quark and electroweak precision physics, but also discusses several models of beyond the Standard Model physics such as Supersymmetry, little Higgs models and extra gauge bosons. The connection to cosmology has been analyzed as well.Comment: 179 pages, plots and references updated, version to be published at EPJ

Wedgebox analysis of four-lepton events from neutralino pair production at the LHC

`Wedgebox' plots constructed by plotting the di-electron invariant mass versus the di-muon invariant mass from pp -> e^+e^- mu^+ mu^- + missing energy signature LHC events. Data sets of such events are obtained across the MSSM input parameter space in event-generator simulations, including cuts designed to remove SM backgrounds. Their study reveals several general features: (1)Regions in the MSSM input parameter space where a sufficient number of events are expected so as to be able to construct a clear wedgebox plot are delineated. (2)The presence of box shapes on a wedgebox plot either indicates the presence of heavy Higgs bosons decays or restricts the location to a quite small region of low \mu and M_2 values \lsim 200 GeV, a region denoted as the `lower island'. In this region, wedgebox plots can be quite complicated and change in pattern rather quickly as one moves around in the (\mu, M_2) plane. (3)Direct neutralino pair production from an intermediate Z^{0*} may only produce a wedge-shape since only \widetilde{\chi}_2^0\widetilde{\chi}_3^0 decays can contribute significantly. (4)A double-wedge or wedge-protruding-from-a-box pattern on a wedgebox plot, which results from combining a variety of MSSM production processes, yields three distinct observed endpoints, almost always attributable to \widetilde{\chi}_{2,3,4}^0 \to \widetilde{\chi}_1^0 \ell^+\ell^- decays, which can be utilized to determine a great deal of information about the neutralino and slepton mass spectra and related MSSM input parameters. Wedge and double-wedge patterns are seen in wedgebox plots in another region of higher \mu and M_2 values, denoted as the`upper island.' Here the pattern is simpler and more stable as one moves across the (\mu, M_2) input parameter space.Comment: 28 pages (LaTeX), 8 figures (encapsulated postscript

Search for Higgs bosons of the Universal Extra Dimensions at the Large Hadron Collider

The Higgs sector of the Universal Extra Dimensions (UED) has a rather involved setup. With one extra space dimension, the main ingredients to the construct are the higher Kaluza-Klein (KK) excitations of the Standard Model Higgs boson and the fifth components of the gauge fields which on compactification appear as scalar degrees of freedom and can mix with the former thus leading to physical KK-Higgs states of the scenario. In this work, we explore in detail the phenomenology of such a Higgs sector of the UED with the Large Hadron Collider (LHC) in focus. We work out relevant decay branching fractions involving the KK-Higgs excitations. Possible production modes of the KK-Higgs bosons are then discussed with an emphasis on their associated production with the third generation KK-quarks and that under the cascade decays of strongly interacting UED excitations which turn out to be the only phenomenologically significant modes. It is pointed out that the collider searches of such Higgs bosons face generic hardship due to soft end-products which result from severe degeneracies in the masses of the involved excitations in the minimal version of the UED (MUED). Generic implications of either observing some or all of the KK-Higgs bosons at the LHC are discussed.Comment: 25 pages, 9 figures and 1 tabl