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 review the important features of Little Higgs models, illuminating the mechanisms that generate a naturally light Higgs field while avoiding excessive fine-tuning. The full spectrum of the Littlest Higgs model is analyzed in light of the recent discovery of the Higgs boson mass. We find viable regions in parameter space that are consistent with the standard model. / text

The Standard Model of particle physics which attempts to describe all matter and all forces in the universe (except gravity),has been in agreement with most of the experiments till date. However theoretically and phenomenologically many questions remain unanswered in the SM. The present and future colliders will help the physicists learn more about the nature of matter and all forces in the universe. In this thesis work we have mainly focused on the physics case of the future linear collider which will be a succession of the presently running Large Hadron Collider in CERN Geneva. As an introduction to the thesis work in Chapter 1 we have discussed in detail about the most planned future collider the International Linear Collider. This collider apart from being a high luminosity machine will have the advantage of beam polarization. Chapter 2 discusses about the basis structure of the Standard Model, along with its many unanswered questions. Some of the theories proposed to take care of these deficiencies are also discussed. These theories apart from explaining the shortcomings of the SM, also predicts many new particles and are thus phenomenologically rich. Exploration of these new physics scenarios can be done many ways. A detailed investigation of the direct production of particles which are not present in the SM spectrum, is one of the techniques provided the particles are within the collider reach. The other is an indirect way, where deviations from SM is studied by a through scrutinization of the SM processes. Provided new physics is observed in either of the way, in the present or future colliders it becomes necessary to pin point them. The main objective of this thesis work has been to look for various scenarios, both in a direct and indirect way and identify them. The different cases of beam polarization is also explored. Overall we find that the full potential of the linear collider can be realized only with the availability of the electron and positron beam polarization, both transverse and longitudinal. We give an overview of the importance of beam polarization and its inclusion in the calculation of e+e- collisions in Chapter 3. In Chapter 4 we have considered the possibility of finger printing the presence of heavy additional Z′bosons that arise naturally in extensions of the Standard Model such as E6 models and left-right symmetric models, through their mixing with the standard model Z boson. They are probed using W pair production and leptonic decay of one of the W’s. The Littlest Higgs Model which addresses the hierarchy problem and where the Z′arises naturally is also considered. By considering a class of observables including total cross sections, energy distributions and angular distributions of decay leptons we find significant deviation from the Standard Model predictions for these quantities with right-handed electrons and left-handed positrons at √s=800 GeV. This process complements the study of fermion pair production processes that have been considered before for discrimination between these models. We have then studied the possibility of identifying a strongly interacting Wboson sector inChapter5 which is consistent with present day Large Hadron Collider searches, at the International Linear Collider with longitudinal as well as transversely polarized electron and positron beams. We account for the final state interaction using a suitable Omnes formalism in terms of a plausible resonance description, and carry out thorough analyses of cross sections, asymmetries and angular distributions of the Ws. In order to have a fully comprehensive study we also carry out a comparison with other extensions of the Standard Model, where an s channel resonance like heavy additional Z′bosons arise naturally. We also consider the effect of the strong final state interaction on a correlation that depends on(φ- - φ+), where the φ∓are the azimuthal angles of decay leptons, and find that it is a useful discriminant. The importance of top polarization in the process e+e−→ tt with transverse beam polarization to probe interactions of the scalar and tensor type beyond the Standard Model and the way to disentangle their individual contributions is discussed in Chapter 6. 90% confidence level limits on the interactions with realistic integrated luminosity are presented and are found to improve by an order of magnitude compared to the case when the spin of the top quark is not measured. Sensitivities of the order of a few times 10−3 TeV−2 for real and imaginary parts of both scalar and tensor couplings at √s=500 and 800 GeV with an integrated luminosity of 500 fb−1 and completely polarized beams is shown to be possible. We next consider the process e+e- → γ Z with transverse beam polarization in the presence of anomalous CP-violating γZZ coupling λ1 and γγZ coupling λ2 in Chapter 7. We point out that similar to the approach in Chapter 6 if the final-state spins are resolved, then it becomes possible to fingerprint the anomalous coupling Reλ1. 90% confidence level limit on Reλ1 achievable with center-of-mass energy of 500 GeV or 800 GeV with realistic initial beam polarization and integrated luminosity is of the order of few times of 10−2 when the helicity of Zis used and 10−3 when the helicity of γis used. The resulting corrections at quadratic order to the cross section and its influence on these limits are also evaluated and are shown to be small. In Chapter 8 the production of the lightest neutralinos in the radiative process e+e−→ χ˜10χ˜10γ in supersymmetric models with grand unification is considered. We consider models wherein the standard model gauge group SU(3)c x SU(2)L x U(1)Y is unified in to the grand unified gauge groups SU(5),or SO(10). We compare and contrast the dependence of the signal cross section on the grand unified gauge group, and different representations of the grand unified gauge group, into which the standard model gauge group is unified. We carry out a comprehensive study of the radiative production process which includes higher order QED corrections in our calculations. In addition we carry out a detailed study of the background to the signal process coming from the Standard Model radiative neutrino production e+e−→ νv*γ, as well as from the radiative production of the scalar partners of the neutrinos (sneutrinos) e+e ν˜ν˜γ. The latter can be a major supersymmetric background to the radiative production of neutralinos when the sneutrinos decay invisibly. Finally in Chapter 9, we conclude and present the summary of the thesis.