The sensitivity of the spin dependence of high energy pp scattering, particularly the asymmetry A NN , to the odderon is demonstrated. Several possible ways of determining the spin dependence of the odderon coupling from small-t data are presented.PACS number͑s͒: 13.88.ϩe, 13.60.Hb The odderon is a latecomer to the family of Regge poles and, to date, there is not any firm experimental evidence for it. It is the putative negative charge conjugation partner to the Pomeron, the dominant Regge singularity at high energy. The exact nature of the Pomeron is even now not well understood. Two aspects are virtually certain, almost by definition: ͑1͒ it is a singularity, no doubt more complicated than a simple pole, in the t-channel angular momentum plane that lies at Jϭ1 when the momentum transfer tϭ0, and ͑2͒ it has charge conjugation Cϭϩ1, signature (Ϫ1) J ϭϩ1 and isospin Iϭ0. The odderon, also by definition, will lie at or a little below Jϭ1 at tϭ0. It too has Iϭ0 but Cϭ(Ϫ1) J ϭϪ1. The possiblity of such a Reggeon was first recognized in ͓1͔ and its properties and implications have been extensively explored in ͓2-5͔. The work of Lipatov and his collaborators ͓6͔ on the Pomeron in QCD strongly suggests that the odderon exists on equal footing with the Pomeron ͓7͔. The QCD Pomeron is generated by the exchange of two Reggeized gluons in a Cϭ1, colorless state while the odderon is generated by three Reggeized gluons in a CϭϪ1, colorless state. The QCD calculations yield a Pomeron intercept slightly above 1 and an odderon slightly below 1. We know from unitarity that ultimately the Pomeron intercept will lie at ͑or below͒ 1 in order to satisfy the Froissart bound; we do not know quantitatively what such effects will do to the odderon. ͑We do know that it cannot ultimately lie above the Pomeron in order for both the pp and p p total cross sections to be positive.͒ In the following we shall simply assume that both singularities are very close to 1. At BNL Relativistic Heavy Ion Collider ͑RHIC͒ energies the effective intercepts may even be slightly above 1.The most clear-cut implication of the existence of the odderon is that it would lead to asymptotically different amplitudes for the scattering of a particle and its anti-particle off the same target. This means that the total cross sections and the differential cross sections for, say, pp and p p scattering at high energy will remain different as ͱs, the total center-of mass energy, increases; in the absence of an odderon they would become the same, roughly as 1/ͱs. Unfortunately, a decisive test of this feature is not possible because of the absence of data at the same energy for the two cases. There are suggestions that the odderon might be important because the difference between the pp and p p differential cross sections in the dip region appears to persist as the energy grows ͓8,9͔. At the same time fits to tot and (tϭ0), the ratio of real to imaginary parts of the forward, helicity-diagonal amplitudes, over a wide energy range for both pp and p p leave little room ...
