Proton structure and tensor-gluons

We consider the possibility that inside the proton and, more generally, inside the hadrons there are additional partons—tensor-gluons—that can carry part of the proton momentum. The tensor-gluons have zero electric charge, like gluons, but have a larger spin. Inside the proton, the nonzero density of the tensor-gluons can be generated by the emission of tensor-gluons by gluons. The last mechanism is typical for non-Abelian tensor gauge theories, in which there exists a gluon-tensor-tensor vertex of order g. Therefore, the number of gluons changes not only because a quark may radiate a gluon or because a gluon may split into a quark–antiquark pair or into two gluons, but also because a gluon can split into two tensor-gluons. The process of gluon splitting suggests that part of the proton momentum that was carried by neutral partons is shared between vector and tensor-gluons. We derive evolution equations for the parton distribution functions that take into account these new processes. The momentum sum rule allows us to find the tensor-gluons' contribution to the Callan–Simanzik beta function and to calculate the corresponding anomalous dimensions. This contribution changes the behavior of the structure functions, and the logarithmic correction to the Bjorken scaling becomes milder. This also influences the unification scale at which the coupling constants of the standard model merge, shifting its value to lower energies of the order of 40 TeV. (paper)