We present in this thesis a detailed analysis of Higgs boson interactions at future colliders. In particular we examine, in a model independent way, the sensitivity of an Linear Collider in probing the interaction of Higgs boson with a pair of vector bosons with/without the use of polarized initial beams and/or the information on final state fermion polarization. We devise several observables which have definite transformation properties under discrete symmetry operations to constrain the different anomalous parts of the Higgs boson interactions having the same transformation properties. We also investigate effects of initial state radiation (ISR) and beamstrahlung on probes of anomalous Higgs boson couplings at higher center of mass energies. We begin the first chapter with an introduction of the Standard Model (SM) of particle physics. We mainly focus on the Higgs sector of the SM. In this chapter we review the electroweak (EW) symmetry breaking mechanism, viz. the Higgs mechanism, responsible for generating masses of all the particles in the SM. We briefly summarize the high precision tests of the SM. We discuss constraints on the mass of the SM Higgs boson derived from theoretical considerations such as stability of the electroweak vacuum, unitarity in scattering amplitudes, perturbativity of the Higgs self-coupling and no fine-tuning in the radiative corrections in the Higgs sector. Next we present the experimental bounds on the mass of the SM Higgs boson obtained from the direct searches of the Higgs boson at LEP and from the electroweak high precision measurements. We then discuss the importance of a general model independent approach to study properties of the Higgs boson and to verify the uniqueness of the SM. In the context of low energy effective theory, this analysis can be made by using the effective Lagrangian that contains higher dimensional operators. We conclude this chapter giving examples of dimension-6 operators which can contribute to the anomalous Higgs boson interactions that we analyze in this thesis. Second chapter contains the dominant Higgs boson production processes at an collider.In a model independent analysis we consider the effects of the most general ¯ (V = W Z) vertex, consistent with Lorentz invariance, for the process where f is any light fermion. This vertex also includes the possibility of CP violation and can be written as: where ki denote the momenta of the two W’s (Z’s), ǫναβis the antisymmetric tensor with ǫ0123 = 1. Previous studies showed that the squared matrix element of the process e+e−ZH does not include all the anomalous parts of a general ZZH vertex. Also it is obvious that one cannot analyse anomalous WWH couplings using this process. Hence we consider the full process e+e−ffH to probe all the anomalous parts of the VVH vertex. We devise a general and very elegant procedure to probe these couplings at an e+e−collider. We construct various combinations by taking dot and scalar triple product of momenta of initial and final state particles. These combinations have definite transformation properties under CP and naive time reversal (T˜)transformations. Hence the corresponding observables constructed using expectation value of sign of these combinations can probe a specific part of the anomalous VVH couplings whose coefficient in the effective Lagrangian has same transformation properties. We investigate the possible sensitivity to which the anomalous VVH couplings can be probed at a Linear Collider using these observables in the process e+e−ffH for unpolarized beams [1, 2]. We consider the case of a Linear Collider, operating at center of mass energy of 500 GeV, with an integrated luminosityof 500 fb−1 and assume a Higgs boson of mass 120 GeV. We impose various kinematical cuts on different final state particles to reduce backgrounds ¯and consider the events where H decays into bb with branching ratio 0.68. We can enhance or suppress the effect of the s-channel, Z-exchange diagram by imposing cut on the ¯invariant mass of the ff system. We use b-tagging efficiency to be 70%; a value expected to be possible in the collider environment. We first consider asymmetries involving either the polar or azimuthal angular distributions. Then we combine these informations to construct combined polar-azimuthal asymmetries in order to enhance the sensitivity. We obtain strong constraints on most of the anomalous parts of the ZZH vertex using cross section and these asymmetries. The process e+eν¯ −νH has two missing ν’s in the final state. Hence their momenta are not available to construct any observables. Therefore, direct probes for T˜-odd WWH couplings viz. ℑ(bW), ℜ(˜bW), cannot be constructed and only weak, indirect bounds are possible. Further, without using polarized beams the contamination from the ZZH vertex cannot be eliminated in the determination of WWH couplings. In the third chapter we analyze use of linearly polarized e+/e−beams and/or information on final state lepton polarization in probingthe interaction of the Higgs boson with a pair of vector bosons[3, 4]. We make several combinations of different particle momenta and spins. We then define observables as expectation values of signs of these combinations for longitudinally polarized beams and/or for production of final state τ’s with a definite helicity state. Use of polarization allows us to devise more observables as compared to the unpolarized case. We list the observables for which use of polarization affords a distinct gain in sensitivity. In our analysis we divide the total luminosity of 500 fb−1 equally among different polarization states of initial state e−/e+ and take the values 80% and 60% for e−/e+ respectively, foreseen at the ILC. We construct numerical combinations of various linearly polarized cross sections to enhance the contribution of ℜ(bZ) while getting rid of ΔaZand vice versa. It is necessary to construct such combinations of cross section as ℜ(bZ), ΔaZhave same CP and T˜transformation properties and hence there are no asymmetries that can be constructed to probe them individually. With these combinations it is possible to probe both these CP-and T˜-even couplings cleanly, using linearly polarized beams. We find that longitudinal beam polarization can improve the sensitivity to CP-odd ZZH couplings viz. ℜ(˜bZ), ℑ(˜bZ), by a factor of about 6 −7. We also construct observables for final state τ’s with definite helicity. We make a plausible assumption that it should be possible to isolate events with τ’s in definite helicity state with an efficiency of 40%. With this assumption we demonstrate that the use of final state τ polarization can improve the sensitivity to the CP-even and T˜-odd ZZH coupling (ℑ(bZ)) by a factor of about 3. Moreover use of final state τ-polarization measurement along with linearly polarized beams can improve the sensitivity for one of the CP-odd ZZH couplings (ℜ(˜bZ))bya factor of about 2.Use of longitudinally polarized beams can also help to reduce the contamination in the measurement of the WWH couplings coming from the ZZH vertex contribution. We also perform χ2-analysis using the observables for different polarizations. The cross section of the t–channel diagram increases with increasing center of mass energy. Therefore, off hand it may look like that going to higher energy can increase the sensitivity to WWH couplings. Hence in this chapter we further investigate possible gain in sensitivity going to higher center of mass energies[3, 4]. We use the same observables constructed with unpolarized beams and consider various center of mass energies ranging from 300 GeV to 3 TeV. We find that it is possible to increase the bZ)byabouta factor 2 1 TeVas compared to the case of 500 GeV. In this analysis we include the effects of initial state radiation (ISR) and beamstrahlung. Both the ISR and beamstrahlung =500 GeV, the ISR can affect cross sections for s–channel processes by 10−15%.However, we observe that the effects of ISR and beamstrahlung change both the SM and anomalous contributions more beneficial for the study of anomalous V V H couplings. In the last chapter we investigate the role of transversely polarized beams to constrain the anomalous V V H couplings[5]. Using transverse spin direction of e±it is possible to devise observables which are nonzero only for transversely polarized beams. Use of transverse beam polarization allows construction of completely independent probes of both the CP-and T˜-even anomalous ZZH couplings (ΔaZ, ℜ(bZ)), leading to independent determination of all the anomalous parts of the ZZH vertex. In addition the use of transverse beam polarization can also add to the sensitivity for one of the CP-odd ZZH couplings viz. ℜ(˜bZ). Measurement of final state τ-polarization with transversely polarized beams can in fact also offer improvement on the sensitivity for ℑ(bZ) which is even under CP-and odd under T˜-transformation. Use of transverse beam polarization cannot improve the bounds on the anomalous WWH couplings as the squared matrix element of the t– channel WW–fusion diagram does not have any transverse beam polarization dependent term. A summary of the results obtained in this thesis is follows. We have developed a general procedure to construct observables with specific CP and T˜transformation properties to probe various anomalous couplings of the Higgs boson to a pair of vector bosons (V = W/Z) at an e+/e−Linear Collider. We investigate probes of these couplings in the process e+e−ffH. This process gives access to those anomalous couplings which cannot be probed using angular distribution of the Z boson in the process e+eZH. We showed that it would be possible to obtain stringent bounds on some of the parts of the anomalous ZZH vertex even without using polarized beams and/or information on polarization of final state particles. Use of longitudinal beam polarization and/or final state τ polarization can significantly enhance the sensitivity in probing most of the anomalous parts of a general ZZH vertex. Use of longitudinal beam polarization also reduces the contamination from the ZZH couplings in the determination of the ˜T-even anomalous WWH couplings (ℜ(bW), ℑ(˜bW)). However, two missing neutrinos in the final state do not allow any direct probe of the T˜-odd WWH couplings (ℑ(bW), ℜ(˜bW)).We find that use of transverse polarization of the beams is essential to construct independent probes of the two anomalous ZZH couplings, which are even under CP and T˜transformations, viz.ΔaZand ℜ(bZ).We observed that there will be no significant gain 500 GeV), but with polarized beams is preferable from the point of view of studying anomalous V V H coupling. (For mathematical equations pl see the pdf file.)

The International Linear Collider (ILC), a high precision electron-positron machine with centre of mass energy extending up to the TeV scale, is curently being proposed and designed. With unprecedented small beam size and high intensity the ILC aims at luminosities of the order of $10^(34)$~cm$^(-2)$s$^(-1)$. Careful monitoring of the beam parameters that affect the luminosity will be mandatory if these ambitious goals are to be achieved.<br /><br />One of the key parameters is beam emittance, the optimisation of which requires beam size monitors with micron resolution.<br />With this aim, a non-invasive laser-wire monitor prototype was designed, installed and run at the PETRA ring. Prior to its installation, background simulations and measurements were performed to verify that they would be low enough to allow<br /> the laser-wire programme to proceed. A lead-tungstate crystal calorimeter for the laser-wire was commissioned, including a study of temperature dependance, geometrical acceptance and energy response. The first laser-wire measurements of the PETRA positron beam size were then performed. The system, calibration and results are reported here.<br /><br />At the ILC, beam energy spread and beamstrahlung effects modify the luminosity spectrum. Determination of these effects is crucial in order to extract precision physics from threshold scans. In order to provide a run-time diagnostic scheme to address this, a fast luminosity spectrum measurement technique employing forward calorimetry and statistical unfolding was devised, using the Bhabha process at low angles. The scheme is described and first results are presented.