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.

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 .

E760 experiment [Armstrong T. A. et al 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].

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

with (GeV/c)2. The Coulomb phase was used in the form from 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 parameters of fit

Spin contribution into the differential cross-section [Bourrely C 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

No spin contribution With spin contribution

antip-p 5.94 GeV/c [E760]

Table 1. plab, (Gev/c)2 fit σT, mb b, (Gev/c)2 ρ β χ2/d.o.f. 5.60 E760 61.3 12.5(3) -0.030(7) - 1.04 Our without spin 61.30±0.09 12.4±0.2 -0.033±0.002 0.80 Our with spin 61.3±69 12.4±0.5 -0.03±0.07 0.01±100 0.82 5.72 60.9 12.2(4) -0.018(8) 1.20 60.8±0.1 12.1±0.3 -0.022±0.002 0.999 60.6±77 12.1±0.5 -0.02±0.07 0.08±15 1.02 5.94 60.2 12.6(3) -0.035(8) 1.26 60.2±0.1 12.7±0.3 -0.040±0.002 0.97 60.2±4.1 12.57±0.03 -0.039±0.005 0.01±6.2 0.003 6.23 59.4 12.2(6) -0.029(10) 0.50 59.32±0.08 12.3±0.2 -0.032±0.002 0.65 59.3±63 12.3±0.5 0.01±83 0.67

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