Odderon as Regge oddball spin-3 in $pp$ and $p\bar{p}$ elastic scattering

In this work, we propose that the odderon is a Regge odd-glueball tensor spin-3. To demonstrate our proposal, we study the $pp$ and $p\bar{p}$ elastic scattering by including contributions of the spin-3 odderon and spin-2 pomeron exchange in the processes. The phenomenological effective Lagrangian approach is used to calculate the $pp$ and $p\bar{p}$ elastic scattering amplitudes at the tree level. In addition, a Donnachie-Landschoff ansatz of the odderon and pomeron propagators has been used in this work. We fit the theoretical results with the various experimental data of the $pp$ and $p\bar{p}$ scattering at the TeV scale to determine the model parameters in the present work. By using the model parameters, the Chew-Frautschi plot of the tensor odderon Regge trajectory is evaluated. As a result, the odderon spin-3 mass is predicted to be 3.2 GeV. In addition, the total cross-section of our model is compatible with the results from TOTEM and its extrapolation from D0 collaboration. Moreover, the total cross-section also satisfies the Friossart bound at the Regge limit.