1. Unified systematic of elastic Pbar-P, Pbar-A A.Galoyan and V. Uzhinsky
scattering data
A.Galoyan and V. Uzhinsky
13/12/2011
● Application of Glauber theory for antiproton-nucleus interactions
● Our parametrization of Pbar-P total and elastic cross sections
● Glauber amplitudes and black disk model with diffuse boundary approximation
● Effective parameters of the black disk model with diffuse boundary
● Geant4 class “G4AntiNuclElastic” - for simulation of Anti-proton – Nucleus Elastic scattering
● Simulation method of Coulomb and Hadron scatterings
● New parameterization of Anti-P P Elastic Scattering, Imaginary and Real parts
of Elastic Scattering Amplitude
● Description of recent Totem data on elastic pp-interactions at 7 TeV ! 1

2. Glauber theory for antiproton-nucleus interactions
adTa_Fig8
Amplitude of hadron-nucleus elastic scattering
Differential elastic scattering cross section
Amplitude of elastic hN scattering in impact parameter representation
ß is the slope parameter of hN differential elastic cross section
Square module of the wave function is written as:
Diagen: Generator Of Inelastic Nucleus-nucleus Interaction Diagrams. S. Shmakov, V.Uzhinsky, A.Zadorozhny, Comp. Phys. Comm., 54 (1989) 125 2

3. Our parameterization of PbarP cross sections
σel/σtot=1/(2 Csh)≈1/3, according to the quasi-eikonal approach of the reggeon field theory
(K.A. Ter-Martirosyan, A.B. Kaidalov) 3

4. V. Uzhinsky, J. Apostolakis, A. Galoyan et al. , Phys
V. Uzhinsky, J. Apostolakis, A. Galoyan et al., Phys. Lett B705 (2011) 235
Calculation results in G4ComponentAntiNuclNuclearXS, Pbar – Nuclei 4

5. Calculation results for Profile functions in Glauber model
Generator of inelastic nucleus-nucleus interaction diagrams
Computer Physics Communications, 54 (1989)125
S. Yu. Shmakov, V. V. Uzhinskii, A. M. Zadorozhny
Profile functions P(b) for pbar+Pb at Plab=0.1, 1, 1000 GeV/c
According to black disk model approximation 2-dimensional
Fourie transform of P(b):
(1)
W.E. Frahn, R.H. Venter// Ann. Phys. 24 (1963) 234;
D.C. Choudhury// Phys. Rev. C22 (1980) 1848; 5
Yu.A. Berezhnoy, V.Yu. Korda// Inter. J. Mod. Phys. 7 (1998) 723

6. Glauber amplitudes and black disk model approximation
Pbar+Pb elastic scattering Glauber amplitudes at P=0.1 and 1000GeV/c
(blue lines) and J1(Rq)/(Rq) (black lines)
First zero of F(q) can be used for determination of R, R=3.832/q_zero
F(0)=πR2 at such choice of R 6

7. Interpolation of effective parameters of black disk model7

8. Interpolation of Effective parameters of black disk model8

9. Class: G4VHadronElastic G4AntiNuclElastic Data of class: Base class
GEANT4
Class:
G4VHadronElastic
Base class
Class for elastic Pbar-P, Pbar-A simulations
G4AntiNuclElastic
G4double SampleInvariantT (
const G4ParticleDefinition* p,
G4double plab, G4int Z, G4int A);
Derived methods
Sampling of polar angle Theta
Methods:
G4double SampleThetaCMS( particle, plab, Z, A);
G4double SampleThetaLab( p, plab, Z, A);
and other methods
cs, fTeta1, fTetaCMS, fThetaLab, fRa, fRef et al.
Data of class: 9

10. SampleInvariantT (p, plab, Z, A);
G4AntiNuclElastic::
SampleInvariantT (p, plab, Z, A);
Coulomb – Wentzel scattering ( V.M. Grishine/ CPC 181 (2010) 921 )
Hadronic part
─ Magorant function 10

11. Differential Cross sections of Elastic Pbar Nucleus interactions11

12. Differential Cross sections of Elastic Pbar Nucleus interactions12

13. Differential Cross sections of Elastic Pbar Nucleus interactions13

14. A, Galoyan, J. Ritman, A. Sokolov, V. Uzhinsky// arXiv:0809
A, Galoyan, J. Ritman, A. Sokolov, V. Uzhinsky// arXiv: [hep-ex]
Parameterization of the anti-P P Elastic Scattering Differential Cross Section Between 2-GeV/c <= P(lab) <= 16-GeV/c. 14

15. Parameterization of the anti-P P Elastic Scattering Differential Cross Section Between 2-GeV/c <= P(lab) <= 20-GeV/c. 15

16. Real part of elastic pbar-p amplitude. Derivative dispersion relations
New parameterization of anti-P P elastic scattering differential cross section
adTa_Fig8
Black disk model approximation with diffuse boundary
with Imaginary and Real parts of elastic scattering amplitude
Real part of elastic pbar-p amplitude. Derivative dispersion relations
J.B. Bronzan, G.L. Kane, U.P. Sukhatme, Phys. Lett. 49B (1974) 227;
M.M. Block, R.N. Cahn, Rev. Mod. Phys. 57 (1985) 563 16

17. Fitting results Fitting expression:
adTa_Fig8
94 sets of exp data were used from Plab=181 MeV/c up to sqrt(S)=1800 GeV
Fitting results (low energy)
Fitting results 17

18. Fitting results (intermediate and high projectile momenta)
94 sets of exp data were used from Plab=181 MeV/c up to sqrt(S)=1800 GeV 18

19. Interpolation of parameters R_eff and c_eff
New parameters of R, C and ρ are implemented Geant4 class: G4AntiNuclElastic 19

20. Interpolation of Ratio of Real to Imaginary parts of the elastic Pbar-P scattering amplitude
“Structure of antiproton-proton elastic scattering amplitude” A. Galoyan, V. Uzhinsky, JETP Letters, v. 94, No 7 (2011) 20

21. Extrapolation results for elastic Pbar-P differential cross sections21

22. The Totem results, pp-interactions at 7 TeV!
EPL, 95 (2011) 41001, EPL 96 (2011) 21002
Reff=1.07 fm, Ceff=0.375 fm 22

23. Description of the High Momentum Part of the exp. data
V. Uzhinsky, A. Galoyan, Nov e-Print: arXiv:
"Description of the Totem experimental data on elastic pp-scattering at sqrt(s)=7 TeV in the framework of unified systematic of elastic scattering data.“
Description of the High Momentum Part of the exp. data
At |t|> 2 (GeV/c)2 all the cross sections have the same shape at sqrt(S)> 10 GeV.
To reproduce the shape we add to imaginary part of elastic amplitude “hard” part 23

24. Description of the Totem data and our predictions for other LHC En.
V. Uzhinsky, A. Galoyan, Nov e-Print: arXiv:
"Description of the Totem experimental data on elastic pp-scattering at sqrt(s)=7 TeV in the framework of unified systematic of elastic scattering data.“
Description of the Totem data and our predictions for other LHC En. 24

25. Conclusion and plans
1. G4 Class G4AntiNuclElastic for simulation of anti-nucleon and anti-
nucleus nucleus elastic scattering has been created. The class is
based on Black Disk Model with Diffuse Boundary and Coulomb-
Wentzel model.
Effective parameters “R” and “c” of Black Disk model are found.
3. Differential cross sections of elastic scattering of antiprotons with
nuclei were calculated using the class G4AntiNuclElastic.
Good description of known exp. data were obtained.
New parametrization of antiproton-proton elastic scattering based on
the Black Disk Model with Diffuse Boundary taking into account the
real part of elastic amplitude is proposed.
5. Exp. data on antiproton-proton elastic scattering are described well.
Good results are obtained for recent Totem data!
Take into account the real part of PbarP amplitude in simulation
of anti-P nucleus elastic scattering.
2. More accurate treating of the Coulomb scattering in the PbarP and Pbar nucleus elastic scatterings .
Implementation of new parametrization of antiproton-proton elastic
scattering in DPM generator in Panda-Root 25