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Forward Elastic Scattering Analysis for PAX Experiment in Antiproton-Proton Interactions

This paper compares theoretical predictions to experimental data on antiproton-proton elastic scattering in the forward direction, focusing on the energy range of 3-10 GeV anticipated for the PAX experiment. Notable discrepancies are examined, leveraging dispersion theory to connect total cross-section with forward angle and invariant momentum transfer. By applying scattering dispersion relations, we predict the ρ parameter associated with scattering amplitudes. Observations indicate no significant spin contribution to the differential cross-section, suggesting future investigations into original E760 data and spin contributions in dispersion relations.

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Forward Elastic Scattering Analysis for PAX Experiment in Antiproton-Proton Interactions

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  1. The Analysis of Elastic pp Scattering in the Forward Direction for PAX Experiment Energy Range.S.B. Nurushev, M.F. Runtso, Moscow Engineering Physics Institute (State University), Russia Abstract Comparison is made between theoretical predictions and experimental data for antiproton-proton elastic scattering in the forward direction for future PAX experiment energy range (3-10) GeV. Some discrepancy is discussed.

  2. Dispersion theory gives us the relation between total cross-section and forward angle, or zero invariant momentum transfer ( ) elastic scattering amplitudes . This leads to the well known optical theorem. • . For scattering dispersion relations predict the value of parameter ρ, defined as the ratio of real to imaginary part of forward scattering amplitude .

  3. E760 experiment[Armstrong T.A. et al., Physics Letters B385 (1996) 479]Dispersion relation calculation [Kroll P. and Schweiger W., Nucl. Phys. A503 (1989) 865].

  4. E760 experiment[Armstrong T.A. et al., Physics Letters B385 (1996) 479]

  5. where and Here is the fine structure constant, the proton dipole form factor with (GeV/c)2. The Coulomb phase was used in the form from [Cahn R., Z. Phys. C15 (1982) 253]. , ρ and b. free parametersof fit

  6. Spin contribution into the differential cross-section [Bourrely C., Soffer J. and Wray D., Nucl. Phys. B77 (1974) 386] In the Coulomb-nuclear interference region, t varies approximately between 10-3 and 10-2 (Gev/c)2 so and assuming the exponential fall off with t for the amplitudes we can write for fixed energy Spin parameter

  7. No spin contribution With spin contribution

  8. antip-p 5.94 GeV/c [E760]

  9. Table 1.

  10. Conclusion • Our investigation doesn’t show the spin contribution into the differential cross-section of antip-p inelastic scattering • Next steps: • - comparison with original data of E760 experiment • - analysis of spin contribution in dispersion relations

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