This thesis concerns the study of extended Higgs sectors at future colliders. Such studies are well motivated since enlarged Higgs models are a necessity in many extensions of the Standard Model (SM), although these structures may be considered purely in the context of the SM, to be called the 'non-minimal SM'. The continuous theme of the thesis is the task of distinguishing between the (many) theoretically sound non-minimal Higgs sectors at forthcoming colliders. If a Higgs boson is found it is imperative to know from which model it originates. In particular, the possible differences between the Higgs sectors of the Minimal Supersymmetric Standard Model (MSSM) and the non-minimal SM are highlighted. Considered first are the detection prospects of light charged Higgs scalars (H(^±)) at e(^+)e(^-) colliders. The discovery of a H(^±) would provide unambiguous evidence for a non- minimal Higgs sector. We show that in certain (but not all)non-minimal models a light H(^±) may exist i.e. be within the mass range accessible at LEP2 (M(_H)(_ ±) ≤ Mw). In particular the MSSM requires M(_H±) ≥ Mw, and thus detection of a at LEP2 is strong evidence against the MSSM. We discuss ways of distinguishing between the models which may contain a light H(^±) by exploiting differences in the decay channels. Attention is then given to the neutral Higgs bosons of the non-minimal SM. It is possible that these particles may possess a greatly different phenomenology to that of the mammal SM and MSSM, and we explore the feasibility of observing these differences at LEP2 and the LHC It is found that distinct, sometimes spectacular signatures are possible. The thesis next considers a more exotic Higgs representation, namely that of Higgs triplets, and compares its phenomenology at LEP2 with that of the non-minimal models covered thus far The phenomenon of Higgs bosons decoupling from the fermions(fermiophobia) arises naturally in the above triplet model, and this concept is studied in more depth in the final chapter. It is emphasized that such particles are not possible in the MSSM.

The littlest Higgs model is one of the most economical solution to the hierarchy problem of the standard model. It predicts existence of new gauge vectors and also new scalars, neutral and charged. The littlest Higgs model predicts the existence of new scalars beside a scalar that can be assigned as Higgs scalar of the standard model. In this thesis, the production of scalars in $e^+e^-$ colliders is studied. The scalar productions associated with standard model Higgs boson are also analyzed. The effects of the parameters of the littlest Higgs model to these processes are examined in detail. The collider phenomenology of the littlest Higgs model is strongly dependant on the free parameters of the model, which are the mixing angles $s,s&#039 / $ and the symmetry breaking scale $f$. The parameters of the model are strongly restricted when the fermions are charged under only one $U(1)$ subgroup. In this thesis, by charging fermions under two $U(1)$ subgroups, the constraints on the symmetry braking scale and the mixing angles are relaxed. In the littlest Higgs model, the existence of charged heavy scalars also displays an interesting feature. By writing a Majorano like term in the Yukawa Lagrangian, these heavy charged scalars are allowed to decay in to lepton pairs, violating lepton number and flavor. In this thesis, the leptonic final states and also the lepton flavor and number violating final signals are also analyzed. As a result of these thesis, it is predicted that the scalar production will be in the reach for a $sqrt{S}=2TeV$ $e^+ e^-$ collider, giving significant number of lepton flavor violating signals depending on the Yukawa couplings of the flavor violating term.

We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a pollutant). Here the unknown is a vector field that is specified by large or infinite number of degrees of freedom. We show that the inverse problem is ill-posed, i.e., there may be many or no background flows that match a given set of observations. We therefore adopt a Bayesian approach, incorporating prior knowledge of background flows and models of the observation error to develop probabilistic estimates of the fluid flow. In doing so, we leverage frameworks developed in recent years for infinite-dimensional Bayesian inference. We provide conditions under which the inference is consistent, i.e., the posterior measure converges to a Dirac measure on the true background flow as the number of observations of the solute concentration grows large. We also define several computationally-efficient algorithms adapted to the problem. One is an adjoint method for computation of the gradient of the log likelihood, a key ingredient in many numerical methods. A second is a particle method that allows direct computation of point observations of the solute concentration, leveraging the structure of the inverse problem to avoid approximation of the full infinite-dimensional scalar field. Finally, we identify two interesting example problems with very different posterior structures, which we use to conduct a large-scale benchmark of the convergence of several Markov Chain Monte Carlo methods that have been developed in recent years for infinite-dimensional settings. / Ph. D. / We consider the problem of estimating a fluid flow (e.g., of air or water) from partial and noisy observations of the concentration of a solute (e.g., a pollutant) dissolved in the fluid. Because of observational noise, and because there are cases where the fluid flow will not affect the movement of the pollutant, the fluid flow cannot be uniquely determined from the observations. We therefore adopt a statistical (Bayesian) approach, developing probabilistic estimates of the fluid flow using models of observation error and our understanding of the flow before measurements are taken. We provide conditions under which, as the number of observations grows large, the approach is able to identify the fluid flow that generated the observations. We define several efficient algorithms for computing statistics of the fluid flow, one of which involves approximating the movement of individual solute particles to estimate concentrations only where required by the inverse problem. We identify two interesting example problems for which the statistics of the fluid flow are very different. The first case produces an approximately normal distribution. The second example exhibits highly nonGaussian structure, where several different classes of fluid flows match the data very well. We use these examples to test the functionality and efficiency of several numerical (Markov Chain Monte Carlo) methods developed in recent years to compute the solution to similar problems.

While the dark matter has so far only revealed itself through the gravitational influence it exerts on its surroundings, there are good reasons to believe it is made up by WIMPs – a hypothetical class of heavy elementary particles not encompassed by the Standard Model of particle physics. The Inert Doublet Model constitutes a simple extension of the Standard Model Higgs sector. The model provides a new set of scalar particles, denoted inert scalars because of their lack of direct coupling to matter, of which the lightest is a WIMP dark matter candidate. Another popular Standard Model extension is that of supersymmetry. In the most minimal scenario the particle content is roughly doubled, and the lightest of the new supersymmetric particles, which typically is a neutralino, is a WIMP dark matter candidate. In this thesis the phenomenology of inert scalar and supersymmetric dark matter is studied. Relic density calculations are performed, and experimental signatures in indirect detection experiments and accelerator searches are derived. The Inert Doublet Model shows promising prospects for indirect detection of dark matter annihilations into monochromatic photons. It is also constrained by the old LEP II accelerator data. Some phenomenological differences between the Minimal Supersymmetric Standard Model and a slight extension, the Beyond the Minimal Supersymmetric Standard Model, can be found. Also, supersymmetric dark matter models can be detected already within the early LHC accelerator data.

A numerical study of fundamental aspects of turbulent mixing has been performed,with emphasis on the behavior of passive scalars of low molecular diffusivity (high Schmidt number Sc). Direct Numerical Simulation is used to simulate incompressible, stationary and isotropic turbulence carried out at high grid resolution. Data analyses are carried out by separate parallel codes using up to 1024^3 grid points for Taylor-scale Reynolds number (R_lambda) up to 390 and Sc up to 1024.Schmidt number of order 1000 is simulated using a double-precision parallel code in a turbulent flow at a low Reynolds number of R_lambda 8 to reduce computational cost to achievable level. The results on the scalar spectrum at high Schmidt numbers appear to have a k^{-1} scaling range. In the presence of a uniform mean scalar gradient, statistics of scalar gradients are observed to deviate substantially from Kolmogorov's hypothesis of local isotropy, with a skewness factor remaining at order unity as the Reynolds number increases. However, this skewness decreases with Schmidt number suggesting that local isotropy for scalars at high Schmidt number is a better approximation. Intermittency exponents manifested by three types of two-point statistics of energy and scalar dissipation, i.e., the two-point correlator (chi(x)chi(x+r)), the second-order moment of local scalar dissipation (chi_r^2) and the variance of the logarithmic local scalar dissipation sigma^2_{lnchi_r} are discussed. Several basic issues in differential diffusion between two scalars of different molecular diffusivities transported by the same turbule nt flow, the physical process of scalar spectral transfer and subgrid-scale transfer are also briefly addressed.

In this thesis, we review the basics of phenomenology in particle physics at neutrino beam dump experiments and hadron colliders. We then consider the phenomenology of various new particles, with masses between 1 MeV and 1 TeV, at the intensity and energy frontiers. We perform sensitivity analyses for physics beyond the standard model at particle colliders (LEP and LHC) and a number of past and future neutrino beam dump experiments (SHiP, DUNE, LSND, MicroBooNE, MiniBooNE and SBND). In particular, we motivate searches for new heavy neutral leptons in single photon events at neutrino and collider experiments (and also via supernova cooling), millicharged particles in single electron events at neutrino experiments, lepton flavor violating scalars via standard model induced mixed flavor neutrino trident production at neutrino experiments, and colored scalar doublets at colliders in events with many jets, soft leptons and low missing energy. In the process, we set novel new bounds on the parameters of these theories and propose powerful new searches that can be performed. We also motivate the construction of a new detector at the LHC called milliQan, and perform a full Geant4 simulation to calculate its projected sensitivity for millicharged particles. The milliQan experiment has since been approved and is currently undergoing construction. / Thesis / Doctor of Philosophy (PhD) / In this thesis, we review the basics of particle physics at neutrino experiments and particle colliders. We then motivate and develop key searches that can be performed to look for new particles at a series of existing and future experiments. We focus on new particles with masses between the electron mass and 1000 times the proton mass. The many searches we consider involve looking for processes that produce a single ray of light, a single electron, a pair of oppositely charged "electron-like" events, new collider signatures, and/or modifications of star explosions. In the process, we set novel new bounds on many theories. We also motivate the construction of a new detector at the Large Hadron Collider called milliQan, and perform a full simulation to assess its future performance. The milliQan experiment has since been approved and is currently undergoing construction.