  In this thesis, we have studied certain gluon fusion processes which proceed
via quark loop diagrams at the leading order. The fact that these gluon-gluon
channel processes are independent processes, their contributions towards the
total/differential hadronic cross sections can be calculated separately. We
have considered the production of a pair of electroweak vector bosons in
association with a jet via gluon fusion within the standard model. These
processes were not accessible at earlier hadron colliders such as the Tevatron.
Therefore, observation of these rare processes at the LHC will be a test of the
standard model itself. Like the di-vector boson production via gluon fusion
processes, these processes are also important backgrounds for many new physics
signals, and the standard model Higgs boson signal at the LHC. These leading
order gluon fusion processes contribute to the corresponding hadronic processes
at the next-to-next-to-leading order in {\alpha}_s. We have taken a model of
extra-dimensions, the ADD (Arkani-Hamed, Dimopoulos and Dvali) model, as the
possible candidate of new physics at the LHC. This model tries to solve the
hierarchy problem of the standard model by proposing large extra space
dimensions which may be accessible at TeV scale. We have considered the direct
production of KK-gravitons (GKK) in association with an electroweak boson
(H/{\gamma}/Z) via gluon fusion. These processes contribute to the
corresponding hadronic processes at the next-to-leading order in {\alpha}_s.
Many interesting issues related to the fermion loop amplitudes have also been
discussed.
