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The Lagrangian of non-Abelian tensor gauge fields describes the interactionof the Yang-Mills and massless tensor bosons of increasing helicities. We havefound a metric-independent gauge invariant density which is a four-dimensionalanalog of the Chern-Simons density. The Lagrangian augmented by thisChern-Simons-like invariant describes massive Yang-Mills boson, providing agauge-invariant mass gap for a four-dimensional gauge field theory. We presentinvariant densities which can provide masses to the high rank tensor bosons.

Topological mass generation in four-dimensional gauge theory