Probing Anomalous Higgs Boson Couplings at Colliders

In this thesis, our main focus is on the $HHH$ and $VVHH$ couplings which are loosely bound. The $HHH$ coupling will determine the shape the Higgs potential and $VVHH$ couplings will tell us how the gauge bosons are coupled to the Higgs fields. We consider a few processes of Higgs boson production and decay to study these couplings. We calculate one-loop QCD and electroweak correction for these processes. In this thesis, we discuss spinor helicity formalism, which has been used in computing Feynman amplitudes for QCD and electroweak correction to these processes. We discuss one-loop Feynman integrals and one-loop electroweak renormalization and Catani-Seymour dipole subtraction scheme in this thesis. We compute all possible self-energy contributions at one-loop for electroweak renormalization. In this thesis, in the first work, we consider the process $b\bar{b}\rightarrow W^+W^-H$. Due to the non-negligible coupling of the Higgs boson with the bottom quarks, there is a dependence on the $WWHH$ coupling in this process. We find that the corrections to the final state with the longitudinally polarized $W$ bosons are large. In the second work, we study one-loop electroweak correction to $H\rightarrow \nu_e\bar{\nu_e}\nu_\mu\bar{\nu_\mu}$. We discuss $\gamma^5$-anomaly, complex mass scheme and input parameter schemes which are relevant for one-loop electroweak correction. The corrections depend on the $HHH$ and $ZZHH$ couplings. We investigate this dependence in $\kappa$-framework. In the third work, we study one-loop electroweak correction to the $H\rightarrow e^+e^-\mu^+\mu^-$ process. The corrections depend on $HHH$ and $ZZHH$ couplings. We observe the same behavior in the relative change of the decay width for this process as the process $H\rightarrow \nu_e\bar{\nu_e}\nu_\mu\bar{\nu_\mu}$ when we vary $HHH$ and $ZZHH$ couplings.