4-Gluon Vertex Splitting Function and Jet Observables

I generalize the Altarelli-Parisi approach to finding the QCD splitting functions to the case of 4-vertex interactions. I apply the results to the 4-gluon interaction and use them to define several jet observables. I estimate the correction associated with the 4-gluon interaction compared with QCD 3-vertex interactions, and find that such a correction can be significant, especially at low energies. For instance, it is estimated that at energy scales between 100 GeV and 1 TeV, the corrections associated with the 4-g vertex could range between ~ 6% - 10%, however, the correction becomes smaller at the TeV scale and 3-vertex interactions become significantly more dominant.