Title:

Higgs production via weak Boson fusion in the Standard Model and the MSSM

Higgs production via weak boson fusion (WBF) is an interesting and important process at both the LHC and a future linear collider. Not only is it a possible Higgs discovery channel, but it also allows us to study the properties of the Higgs boson and the mechanism of electroweak symmetry breaking. In this thesis this process is studied in detail for both the LHC and a future linear collider. Results for light Higgs production via vector boson fusion at a linear collider, taking the Higgsstrahlung contribution into account, are obtained in the (s)fermion sector of the Standard Model and the MSSM. Complete one loop results for weak boson fusion at the LHC in the Standard Model are presented. These include the effects of photon radiation and the full virtual electroweak corrections, as well as the QCD corrections (the latter are well known in the literature and have been taken from the code \tt VBFNLO \rm in this work). The electroweak corrections are found to be as important as the QCD corrections after the application of appropriate cuts  they are $\sim \mathcal{O}(5 \%)$ in the Higgs mass range of 100200 GeV. We present the dominant supersymmetric one loop corrections to neutral Higgs production, in the general case where the MSSM includes complex phases. These results are supplemented by all one loop corrections of Standard Model type and by the propagator type corrections from the Higgs sector of the MSSM, taking the dominant two loop contributions into account. In this way the most complete available result for weak boson fusion Higgs production in the MSSM is achieved. In the decoupling region, $M_A \gg M_Z$, where the light MSSM Higgs boson becomes Standard Model like, the difference between the MSSM loop corrections and those in the Standard Model (for an equivalent Higgs mass) are, as expected, relatively small  generally $\mathcal{O}(0.5 \%)$. Larger SUSY loop corrections occur for the light Higgs in the nondecoupling regime  in the $M_{h}^{max}$ scenario we see differences of $\sim \mathcal{O}(5\%)$ between the total SM and MSSM loop corrections, and in the CPX scenario, differences of $\mathcal{O}(5\%)$ are seen in the (s)fermion sector. In some regions of parameter space, production of the heavy MSSM Higgs boson is dominant, and in these regions loop corrections range between $\sim \pm 5\%$. Our results have been implemented into the public Monte Carlo program \tt VBFNLO\rm, which should serve as a useful tool for performing experimental analyses. We make use of an effective Higgs coupling as a simple (and computationally efficient) method of including the Higgs vertex corrections, while the Standard Model type box and pentagon diagrams are incorporated in the standard way using squared matrix elements. Finally, we also present parton level studies of (s)fermion corrections to Z boson production via weak boson fusion, in both the Standard Model and the MSSM. This process has the potential to be used in order to ``calibrate'' WBF Higgs production. Corrections to Z production are generally smaller than those to Higgs production, and are typically $\sim 0.8\%$.
