New limits on "odderon" amplitudes from analyticity constraints

In studies of high energy pp and (p) over barp scattering, the odd (under crossing) forward scattering amplitude accounts for the difference between the pp and (p) over barp cross sections. Typically, it is taken as f(-)=-p/4 pi Ds(alpha-1)e(i pi(1-alpha)/2) (alpha similar to 0.5), which has Delta sigma, Delta rho -> 0 as s ->infinity, where rho is the ratio of the real to the imaginary portion of the forward scattering amplitude. However, the odd-signatured amplitude can have in principle a strikingly different behavior, ranging from having Delta sigma -> nonzero constant to having Delta sigma -> lns/s(0) as s ->infinity, the maximal behavior allowed by analyticity and the Froissart bound. We reanalyze high energy pp and (p) over barp scattering data, using new analyticity constraints, in order to put new and precise limits on the magnitude of "odderon" amplitudes.