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

TL;DR

This paper develops a recursive method to compute tree-level scattering amplitudes involving high-spin non-Abelian tensor gauge bosons in generalized Yang-Mills theory, extending known formulas and confirming consistency with gauge invariance.

Contribution

It introduces a BCFW recursion relation for high-spin tensor gauge bosons and generalizes the Parke-Taylor formula within this framework.

Findings

Amplitudes vanish at infinity under complex deformation.

Derived a holomorphic formula for two tensor bosons and multiple gluons.

Tree amplitudes with all positive helicities vanish, but those with one negative helicity are nonzero.

Abstract

The BCFW recursion relation allows to calculate tree-level scattering amplitudes in generalized Yang-Mills theory and, in particular, four-particle amplitudes for the production rate of non-Abelian tensor gauge bosons of arbitrary high spin in the fusion of two gluons. The consistency of the calculations in different kinematical channels is fulfilled when all dimensionless cubic coupling constants between vector bosons (gluons) and high spin non-Abelian tensor gauge bosons are equal to the Yang-Mills coupling constant. There are no high derivative cubic vertices in the generalized Yang-Mills theory. The amplitudes vanish as complex deformation parameter tends to infinity, so that there is no contribution from the contour at infinity. We derive a generalization of the Parke-Taylor formula in the case of production of two tensor gauge bosons of spin-s and N gluons (jets). The expression is holomorhic in the spinor variables of the scattered particles, exactly as the MHV gluon amplitude is, and reduces to the gluonic MHV amplitude when s=1. In generalized Yang-Mills theory the tree level n-particle scattering amplitudes with all positive helicities vanish, but tree amplitudes with one negative helicity particle are already nonzero.