Hard Pomeron Contribution to Forward Elastic Scattering

Some time ago1, it has been suggested that a pomeron model la Donnachie-Landshoff2, where the leading singularity in the complex j plane is given by a simple pole, could not provide the best fits to the data for total cross sections, and for the ratio ρ of the real to the imaginary part of the forward elastic scattering amplitude. This conclusion was based on an analysis of all available data at t = 0 for p̄p, pp, πp, Kp, γp and γγ scattering, where three kinds of parametrisations were used: • a triple-pole singularity, which makes total cross sections rise as log(s) at high energy; • a double-pole singularity, which gives σtot ∼ log(s); • a simple-pole singularity, which gives a power rise s. In each case, non-leading exchanges were accounted for by two simple-pole contributions contributing to non-degenerate crossing-odd and crossing-even trajectories. The conclusions were that the best fit was always given by the triple-pole pomeron, closely followed by the double pole, and that the simple-pole parametrisation was excluded if one went down in energy to √ s = 5 GeV, or if one included the ρ parameter in the fit. In 3, we re-examined this question. First of all, we found that a few sub-leading effects improved the fits significantly: • the use of the theoretical variable, (s − u)/2 ∝ cos θt rather than s, and of the flux factor 2mtarget p lab beam instead of s; • the use of subtraction constants in the dispersion relations giving ρ from ImA. These effects indicate that √ s = 5 GeV is not really in the asymptotic region: the fit is affected by sub-leading terms, but these are under control. However, all the fits are improved, so that the triple-pole and the double-pole still give a better description of the data, as shown in Table 1. However, these two parametrisations work better for rather peculiar reasons: the dipole becomes negative below √ s = 9.5 GeV, whereas the tripole has a minimum at √ s = 5.8 GeV, and so rises if s decreases. Both of these features significantly modify the fit at lower energy, by adding a more complicated s dependance to a power in the C = +1 sector. Hence it is natural to check whether a more complicated C = +1 exchange could lead to a better fit in the simple-pole case. Given the hadronic amplitude A, we define the total cross section as