Tensor gluons and proton structure

TL;DR

This paper explores the theoretical possibility of tensor-gluons inside protons, deriving their splitting functions, evolution equations, and impact on the beta function, suggesting a conformal invariant theory at high energies.

Contribution

It introduces a novel framework for tensor-gluons, derives their splitting probabilities, evolution equations, and calculates the one-loop beta function, extending the understanding of proton structure.

Findings

Tensor-gluons can be generated by gluon emission.

The splitting functions satisfy symmetry relations via a splitting index.

The beta function contribution from all spins vanishes, indicating conformal invariance.

Abstract

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.