Abstract:
We study the coupling of two longitudinal Z-bosons to two gluons via technicolor interactions. Noticing a similarity of this process to $2 \gamma \rightarrow 2 \pi^{0}$, we calculate the amplitude in chiral perturbation theory in one-generation technicolor model. At the invariant mass of $ Z_{L}Z_{L}$ above the colored pseudo-Goldstone boson threshold, we find the signal in proton collisions at $\sqrt{s} = 14\, TeV$ is stronger than the standard model background by an order of magnitude, and is large enough to be easily observable at LHC. The cross section for $W_{L}^{+}W_{L}^{-}$ pair production is also presented.

Abstract:
We present the anomalous cross section for baryon number violation in the standard model from the perturbation of large-order behavior of forward scattering amplitudes to the order $\left(\epsilon /n\right)^{8/3} \ln\left(\epsilon /n\right)$. An improved high energy behavior of the anomalous cross section is observed. We also argue that the asymptotic form of $F(\epsilon g) \equiv -g \ln \sigma_{ano} $ is given in the form: $F(\epsilon g) \rightarrow d + c \cdot \epsilon g $ for $ \epsilon g \rightarrow \infty$ with $c, d $ constants satisfying $c, d \geq 0$, and $F(\epsilon g) >0$ for all energies. The constants are not determined.

Abstract:
Higher order renormalons beyond the chain of one-loop bubbles are discussed. A perturbation method for the infrared renormalon residue is found. The large order behavior of the current-current correlation function due to the first infrared renormalon is determined in both QED and QCD to the first three orders.

Abstract:
We point out that heavy fermion production through the fusion of the longitudinal gauge bosons might be relevant in probing the strongly interacting symmetry breaking sector of the electroweak interactions, by showing the dependence of the one loop amplititude for ($ w^{+} w^{-} \rightarrow \overline{t} t $) on the symmetry breaking mechanism. The one loop amplitude for ($ w^{+} w^{-} \rightarrow \overline{t} t $) is calculated for the standard model and extended technicolour theory. Techni-rho meson exchange is also briefly discussed. We find at $m_{t} = 150 ~GeV$ the cross section of top pair production in $ e^{+} e^{-}$ collisions is comparable in order of magnitude to that of the longitudinal gauge boson scattering.

Abstract:
We calculate the one-loop QCD correction for inclusive jet cross section and Drell-Yan process in a general low-energy effective Lagrangian for composite quarks and leptons.

Abstract:
The goldstino-matter interactions given by the Goldberger-Treiman relations can receive higher dimensional operator corrections of $ O(q^{2}/M^{2})$, where $M$ denotes the mass of the mediators through which SUSY breaking is transmitted. These corrections in the gauge mediated SUSY breaking models arise from loop diagrams, and an explicit calculation of such corrections is presented. It is emphasized that the Goldberger-Treiman vertices are valid only below the mediator scale and at higher energies goldstinos decouple from the MSSM fields. The implication of this fact on gravitino cosmology in GMSB models is mentioned.