1. The comparative study of spin-dependent total cross-sections in antiproton-proton and proton-proton interactions. Runtso M.F., Bogdanov A.A., Nurushev S.B., Okorokov V.A., Strikhanov M.N. (Moscow Engineering Physics Institute) • PAX experiment project and FAIR facility; • Reaction matrix and L , T for pp and (pp) interactions; • L , T measurements for (pp) at PAX: methods and detectors.

2. Fig. 1. FAIR facility. FAIR – Facility for Antiproton and Ion Research, APR – Antiproton Polarizer, CSR – Cooler Synchrotron Ring, HESR – High Energy Storage Ring, PAX - Polarised Antiproton Experiment . 1.5 – 15 GeV/c - Fixed Target Mode, (1.5 – 15) GeV/c x 3.5 GeV/c – Collider Mode.

3. Fig.2. PAX detector.

4. Reaction matrix. - reaction matrix definition (1) Independent amplitudes (from generalized Pauli principle and parity Conservation in the strong interaction) + and - - helicities in c.m. [1] M. Jacob and G.C. Wick, Ann. Phys. (N.Y.), 7 (1959) 404. From helicity conservation 4(0)=0=5(0). From generalized optical theorem [2,3]. (2) Real parts can be found throw dispersion relations.

5. [5] E.A. Andreeva et al., Int. J. Mod. Phys., A13 (1998) 1515-1522. (3) [2] S.M. Bilenky and R.M. Ryndin, Phys. Lett. 6 (1963) 217; [3] R.T.N. Phillips, Nuclear Physics, 43 (1963) 413; (4) Total spin dependent contribution 1 and spin projection dependent contribution 2 can be got from 3 observables: 0 with unpolarized beam and target; T = 21 with transversally polarized beam and target; L =  2(1+2) with longitudinally polarized beam and target (transverse and longitudinal total cross-section differencies). (5)

6. Fig. 3. Previous measurements of L(pp) PAX energies [4] D. P. Grosnick et al., Physical Review D, 55, 3 (1997) 1159 – 1187. E704 (200 Gev/c): L(pp) (b)= 42  48 (stat)  53 (sist), L(pp) (b) = - 256  124 (stat)  109 (sist) .

7. Fig. 4. s-dependence of total cross-section p-p and antip-p interaction in PAX energy range. Particle data (2004): tot(pp) = 35.48 + 0.31 ln2(s/30.25) + 41.35 (1/s)0,417 – 31.04 (1/s)0,547 tot(pp) = 35.45 + 0.308 ln2(s/28.94) + 42.53 (1/s)0,458 – 33.34 (1/s)0,545 (6)

8. Fig. 5. T(plab). Fig. 6. -L(plab) Solid line - =0.079, dashed line - =0, dotted line – Regge pole model. . [4], [6] W. de Boer et al., Phys. Rev. Lett. 34 (1975) 558. [7] I.P. Auer et al., Phys. Lett., 67B (1977) 113; Phys. Rev. Lett. 41 (1978) 354. [8] I.P. Auer et al., Phys. Lett., 70B (1977) 475; Phys. Rev. D. 34 (1986) 2581; Phys. Rev. Lett., 62 (1989) 2649.

9. [9] S.A Dunne, Phys. Rev. Lett. 19 (1967) 1299. Asimptotic relation , derived from the Regge model with cuts. (7) putting n=3 (number of exchanged reggeons). 3(0) - 1 = 3 , where  is an excess of pomeron intercept over 1 at t=0, one can gets the final expression for the fit of experimental data: [10] L.I. Lapidus, Proc. of the XI LINP Winter Scool, 1976, p. 55. (8) For high energies (tot rises) tot= 22,0  s 0,079+ 56,1  s-0,46 (9) [11] Review of particle Physics, Phys. Rev., 54D (1996) 191. For low energies only one exchanged Reggeon is supposed, so =0.

10. E704 Fig. 7. |L|(s) for pp interaction. From fit to experiments [5] 31=-2 and from (5) L=-2T

11. With the PAX detector the transverse cross section difference T, as it was declared in PAX proposal, can be accessed by two methods [12] (1) from the rate of polarization buildup for a transversely polarized target when only a single hyperfine state is used; (2) from the difference in beam lifetime for a target polarization parallel or antiparallel to the beam. An accuracy at the 10-4 level has been achieved by the TRIC experiment at COSY using this method. [12] Technical proposal for Antiproton-Proton Scattering Experiments with polarization (PAX collaboration), Julich, 2005.

12. Total cross-section from elastic differential cross-section Fig. 8. The |t| dependence of the elastic pp differential cross-section. Region I – a pure Coulomb scattering, II – Coulomb – Nuclear Interference region, III – nuclear (diffraction) scattering region.

13. [13] A.A. Bogdanov et al., Jadernaja Fizika (rus.), 66 (2003), N 12, 1-11. • - the fine structure constant and F(t) - the proton electromagnetic form factor. where

14. Peculiar points for del/dt(|t|) Detector dimentions Fixed target mode

15. Collider mode p11=p22 elastic scattering conditionfor antisimmetric collider. Detector dimentions

16. [14] P. Kroll, W. Shweiger, Nuclear Physics, A503 (1989) 865-884. Fig. 9. The pp  parameter vs plab.

17. The Indirect method of the measurement of total cross section. The best precision by this method, 0.5 – 1 %, was achieved at ISR.

18. Detector dimentions Fixed target mode t=0.01 p= 1.5 GeV/c R10m=66.8 cm p= 15 GeV/c R10m=6.7 cm t=0.1 p= 1.5 GeV/c R10m=213 cm p= 15 GeV/c R10m=21 cm Collider mode t=0.01 p= 12.3 GeV/c R10m=8.1 cm p= 114 GeV/c R10m=1.6 cm t=0.1 p= 12.3 GeV/c R10m=25.5 cm p= 114 GeV/c R10m=5.0 cm

19. Fig.10. Possible constructions of silicon strip detector (a) and scintillation detectors for PAX total cross-section measurements.

20. Summary. The interest in the spin dependent total cross-sections measurements at PAX energy range is justified by the following reasons: - at any energy one needs to reconstruct the imaginary parts of elastic scattering amplitudes 1, 2 and 3; - at high energy we hope to reveal the spin contributions to the total cross-sections by separating the singlet and triplet states; - several schemes of the spin-dependent total cross-sections measurement are discussed.