ar X iv : h ep - p h / 97 07 34 6 v 2 1 3 N ov 1 99 7 Evidence for eikonal zeros in the momentum transfer space

We present the results of fitting elastic pp differential cross section data at 23.5 ≤ √ s ≤ 62.5 GeV with a novel analytic parametrization for the scattering amplitude. Making use of a fitting method, the errors from the free parameters are propagated to the imaginary part of the eikonal in the momentum transfer space. A novel systematic study of the effects coming from data at large momentum transfer is also performed. We find statistical evidence for the existence of eikonal zeros in the interval of momentum transfer 5-9 GeV 2. 1 Several authors have investigated elastic pp scattering at high energies in the context of the impact parameter formalism and/or eikonal approximation. Model-independent analyses , performed through fits to differential cross section data, play an important role as a source of empirical information for theoretical developments. Inspired by some of these model-independent approaches [1–6] and based on experimental information presently available [7,8] we retake two crucial aspects of the empirical analyses: (a) a systematic study of the effect of experimental informations at large momentum transfer; (b) development of a statistical procedure in order to estimate the eikonal uncertainties in the momentum transfer space. In this work we briefly report some results that can contribute with a better understanding of the above aspects, and bring important insights for the development of theoretical approaches. We shall analyze experimental data on elastic pp differential cross section and the ρ parameter (ratio of the forward real to imaginary part of the scattering amplitude) between √ s = 23.5 GeV and √ s = 62.5 GeV. Our basic set corresponds to the data compiled and normalized by Amaldi and Schubert at the energies based on the evidence that these differential cross section data do not depend on the energy for momentum transfer above q 2 ∼ 3.0 GeV 2 [9,10] we shall also take account of the data available at √ s = 27.5 GeV, in the interval 5.5 ≤ q 2 ≤ 14.2 GeV 2 [7]. Our strategy in performing a systematic study of this experimental information is to consider two different ensembles of data, characterized and denoted by the following. Five sets of ensemble A including at each energy the data at √ s = 27.5 GeV [7]. 2 We want to investigate the effects in the eikonal (transfer momentum space) coming from the fits to both ensembles.