Effects of odderon spin on helicity amplitudes in \(pp\) elastic scattering

In recent years, the discovery of the odderon, a colorless \(C\)-odd gluonic compound, has been confirmed in the TOTEM and D0 collaborations. However, the spin quantum number of the odderon remains unidentified. In this work, we aim to attribute a spin of \(J=3\) to the odderon in \(pp\) elastic scattering by calculating the helicity amplitudes and the corresponding complex parameter \(r_5\), the ratio of helicity's single-flip to non-flip amplitudes, for the spin-3 tensor odderon with the standard spin-2 tensor pomeron exchanges. Then, we apply these results to the constraints obtained from the STAR experiment at RHIC. By comparing to the contributions of the spin-1 vector odderon and spin-2 tensor pomeron, we demonstrate that the spin-3 tensor odderon, i.e. \(J=3\), provides a better explanation for the observable in \(pp\) elastic scattering.