Physics beyond the Standard Model and Collider Phenomenology

We briefly review the Standard Model of the particle physics focussing on the gauge hierachy problem and the naturalness problem regarding the stabilization of the light Higgs mass. We list the alternative models which address the hierachy problem in addition to conventional Supersymmetric models and Composite models. They include extra dimensional models and Little Higgs models. We investigate the production of heavy $W_{H}$ at the linear $e^{+}e^{-}$ collider at high centre-of-mass energies at 3 and 5 TeV using the Littlest Higgs model where the global group is $SU(5)/SO(5)$. In certain region of the parameter space, the heavy boson induced signals could be distinguishable from the Standard Model background. Based on tree-level open-string scattering amplitudes in the low string-scale scenario, we derive the massless fermion scattering amplitudes. The amplitudes are required to reproduce those of the Standard Model at tree level in the low energy limit. We then obtain four-fermion contact interactions by expanding in inverse powers of the string scale and explore the constraints on the string scale from low energy data. The Chan-Paton factors and the string scale are treated as free parameters. We find that data from the neutral and charged current processes at HERA, Drell-Yan process at the Tevatron, and from LEP-II put lower bounds on the string scale $M_S$, for typical values of the Chan-Paton factors, in the range $M_S \geq 0.9-1.3$ TeV, comparable to Tevatron bounds on $Z^\prime$ and $W^\prime$ masses. We consider the low-energy stringy corrections to the 4-fermion scattering at the linear $e^{+}e^{-}$ collider at the 500-GeV centre-of-mass energy. The signals look similar to the contributions from the Kaluza-Klein (KK) graviton exchange but could be distinguishable if there is sufficient number of events. Theoretically, the stringy signals contain both spin 1 and 2 corrections while the KK contains only spin 2. We calculate the tree-level open-string amplitudes for the scattering of four massless particles with diphoton final states. These amplitudes are required to reproduce those of standard model at the tree level in the low energy limit. After low energy stringy corrections, we found that they have similar form to the same processes induced by exchange of the Kaluza-Klein (KK) excitations of graviton in ADD scenario. Using this similarity, we apply constraints on the KK mass scale $M_D$ to the string scale $M_S$. The results are consistent with constraints from the 4-fermion scattering, about $0.6-0.9$ TeV. We construct tree-level four-particle open-string amplitudes relevant to dilepton and diphoton production at hadron colliders. We expand the amplitudes into string resonance (SR) contributions and compare the total cross-section through the first SR with the $Z^{\prime}$ search at the Tevatron. We establish a current lower bound based on the CDF Run I results on the string scale to be about $1.1-2.1$ TeV, and it can be improved to about $1.5-3$ TeV with 2 fb$^{-1}$. At the LHC, we investigate the properties of signals induced by string resonances in dilepton and diphoton processes. We demonstrate the unique aspects of SR-induced signals distinguishable from other new physics, such as the angular distributions and forward-backward asymmetry. A $95\%$ C.L. lower bound can be reached at the LHC for $M_S>8.2-10$ TeV with an integrated luminosity of $300$ fb$^{-1}$. We emphasize the generic features and profound implications of the amplitude construction. We discuss the stringy gauge ``singlet'' interaction induced by stringy dynamics for scattering of $n>3$ particles. Existence of this stringy interaction could lead to stringent bound on the string scale in the braneworld scenario when it is subject to experimental constraints on proton decay. We discuss IR limit of four-fermion scattering amplitudes in braneworld models including intersecting-branes and SUSY $SU(5)$ GUT version of it. With certain compactification where instanton effect is negligible, grand unification condition in D6-D6 intersecting-branes scenario subject to experimental constraint on proton decay provides possibility for upper limit on the string scale, $M_S$, through relationship between the string coupling, $g_s$, and the string scale. We discuss how IR divergence is related to number of twisted fields we have to introduce into intersection region and how it can change IR behaviour of tree-level amplitudes in various intersecting-branes models. Using number of twisted fields, we identify some intersecting-branes models whose tree-level amplitudes are purely stringy in nature and automatically proportional to $g_s/M^2_{S}$ at low energy. They are consequently suppressed by the string scale. For comparison, we also derive limit on the lower bound of the string scale from experimental constraint on proton decay induced from purely stringy contribution in the coincident-branes model, the limit is about $10^5$ TeV.