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The BCFW recursion relation allows to calculate tree-level scatteringamplitudes in generalized Yang-Mills theory and, in particular, four-particleamplitudes for the production rate of non-Abelian tensor gauge bosons ofarbitrary high spin in the fusion of two gluons. The consistency of thecalculations in different kinematical channels is fulfilled when alldimensionless cubic coupling constants between vector bosons (gluons) and highspin non-Abelian tensor gauge bosons are equal to the Yang-Mills couplingconstant. There are no high derivative cubic vertices in the generalizedYang-Mills theory. The amplitudes vanish as complex deformation parameter tendsto infinity, so that there is no contribution from the contour at infinity. Wederive a generalization of the Parke-Taylor formula in the case of productionof two tensor gauge bosons of spin-s and N gluons (jets). The expression isholomorhic in the spinor variables of the scattered particles, exactly as theMHV gluon amplitude is, and reduces to the gluonic MHV amplitude when s=1. Ingeneralized Yang-Mills theory the tree level n-particle scattering amplitudeswith all positive helicities vanish, but tree amplitudes with one negativehelicity particle are already nonzero.

Production of non-Abelian tensor gauge bosons. Tree amplitudes in generalized Yang-Mills theory and BCFW recursion relation