  In a recent article we were considering a possibility that inside a proton
and, more generally, inside hadrons there could be additional partons -
tensor-gluons, which carry a part of the proton momentum. Tensor-gluons have
zero electric charge, like gluons, but have a larger spin. Therefore we call
them tensor-gluons. The nonzero density of tensor-gluons can be generated by
the emission of tensor-gluons by gluons. Tensor-gluons can further split into
the pairs of tensor-gluons through a different channels. To describe all these
processes one should know the general splitting probabilities for
tensor-gluons. These probabilities should fulfill very general symmetry
relations, which we were able to resolve by introducing a splitting index. This
approach allows to find out the general form of the splitting functions, to
derive corresponding DGLAP evolution equations and to calculate the one-loop
Callan-Simanzik beta function for tensor-gluons of a given spin. Our results
provide a nontrivial consistency check of the theory and of the Callan-Simanzik
beta function calculations, because the theory has a unique coupling constant
and its high energy behavior should be universal for all particles of the
spectrum. We argue that the contribution of all spins into the beta function
vanishes leading to a conformal invariant theory at very high energies.
