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In this paper, we give the general expressions for a special series of treeamplitudes of the Yang-Mills theory. This series of amplitudes have twoadjacent massless spin-1 particles with extra-dimensional momenta and anynumber of positive helicity gluons. With special helicity choices, we use thespinor helicity formalism to express these n-point amplitudes in compact forms,and find a clever way to use the BCFW recursion relations to prove the results.Then these amplitudes are used to form the complete 1-loop all-plus integrandwith any number of gluons, expressed in the Q-cut representation.

General expressions for extra-dimensional tree amplitudes and all-plus 1-loop integrands in Q-cut representaion