Though the predictions of the Standard Model (SM) are in excellent agreement with experiments there are still several theoretical problems, such as fine-tuning and the hierarchy problem. These problems are associated with the Higgs sector of the SM, where it is widely believed that some {it ``new physics} will take over at the TeV scale. One beyond the SM theory which resolves these problems is the Little Higgs (LH) model. In this work we shall investigate the effects of the LH model on $gggg$ scattering; where the process $gggg$ at high energies occurs in the SM through diagrams involving $W$, charged quark and lepton loops (and is, therefore, particularly sensitive to any new physics
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