General cubic interacting vertex for massless integer higher spin fields

We consider a massless higher spin field theory within the BRST approach and construct general off-shell cubic vertex corresponding to irreducible fields of helicities $s_1, s_2, s_3$. Unlike previous works on vertices, which do not take into account trace constraints, we use complete operator, including constraints that describe an representation with definite integer helicity. As result, generalize found in [arXiv:1205.3131 [hep-th]] calculate new contributions vertex, contain additional terms smaller number space-time derivatives as well without derivatives.