$J^{--}$ Glueballs and a Low Odderon Intercept

We report an odderon Regge trajectory emerging from a field theoretical Coulomb gauge QCD model for the odd signature $J^{PC}$ ($P=C=-1$) glueball states. The trajectory intercept is clearly smaller than the Pomeron and even the $\omega$ trajectory’s intercept which provides an explanation for the nonobservation of the odderon in high energy scattering data. To further support this result we compare to glueball lattice data and also perform calculations with an alternative model based upon an exact Hamiltonian diagonalization for three constituent gluons.

Figure 1

Interaction diagrams for the $ggg$ state in the $H_{\mathrm{eff}}^g$ approach. Top to bottom corresponds to the gluonic self-energy, scattering, and annihilation interactions, respectively.

Figure 2

Odderon trajectory from three-gluon spectroscopy and lattice compared to the $\omega$ meson Regge trajectory.