1. into three pions Opportunities in p pbar annihilation S. Ong IPN Orsay
GDR Nucleon, Clermont-Ferrand, June 2009

2. Motivations for three-pion annihilation channels study
To identify the relevant degrees of freedom in medium energy strong interaction physics. This channel represents a particular challenge in this respect
II. Three pion channels, in particular pi+ pi- pi0 is a serious background of the hadronic or electromagnetic channels of our Panda group interest namely :

3. Distribution of the missing mass F. Sai et al. , Nucl. Phys
Distribution of the missing mass F. Sai et al., Nucl. Phys. B (1983)

4. Uncorrelated 3 pions diagrams + two mesons ρπ,…

6. Total cross section vs momentum in the Lab frame M. Betz et al. , Phys
Total cross section vs momentum in the Lab frame M. Betz et al., Phys. Lett. B398, 12 (1997)

7. Compilations : V. Flaminio et al., CERN-HERA 79-03 (1979)

8. Outlook on Transition Distribution amplitudes (TDA)
Recently, interest has emerged to study nucleon structure with the TDA formalism in pi+pi-pi0 channel with large invariant mass of the (pi+pi-) system and pi0 produced in the forward direction.
(B. Pire, private communication)

9. Why to measure the two pion channels at large angle ?
No available data at high enough energy and large angle to QCD tests
The open question of the Landshoff independent scattering mechanism and the interference of the Brodsky-Farrar and Landshoff mechanisms would be elucidated through the two exclusive pion channels of p pbar annihilation study with the Panda detector

10. Hard Brodsky Farrar mechanism b) Landshoff independent scattering mechanism ( C.E. Carlson et al., Phys. Rev. D46, 2891 (1992))

11. Expected PANDA counting rate for one week of beam time at full luminosity within a 0.1 wide cosθ bin at θcm=60 °
S(GeV2)
Number of events
13.5
~ 10^6 16
~ 2 10^5 20
~ ^4

12. J. Van de Wiele and S. Ong

13. P. V. Landshoff, Phys. Rev. D10 (1974) 1024
Independant multiple scattering «  Landshoff » contributions to proton-proton elastic scattering at wide angle are important to understand the oscillation of the
differential cross section with the energy.
Landshoff amplitude dominates at large energy but is long distance sensitive and suppressed by Sudakov form factor. Gluonic radiative corrections to the Landshoff amplitude give rise to an energy dependent phase.
J. Botts and G. Sterman, Nucl. Phys. B325 (1989) 62

14. J.P. Ralston and B. Pire, Phys. Rev. Lett. 49 (1982) 1605
Possible oscillation scenario :
Interference between the hard scattering (Brodsky, Farrar) and the Landshoff mechanism amplitudes
The energy dependent phase in the Sudakov factor gives rise to the energy dependent oscillation

16. Color transparency phenomenon
However, Hard and Landshoff amplitudes are not sensitive to the same part of the hadron wave function.
The Landshoff hadron is not a « mini hadron »
The nucleus filters out the Landshoff amplitude
It would be interesting to check the oscillation behavior of the cross section in the vaccum and the nucleus

17. Why to measure e+ e- π° channel at Panda/Fair
Fundamental degrees of freedom to quantify strong interaction phenomena :
Quarks and Gluons degrees of freedom ?
Effective theory with collective hadronic degrees of freedom ?
At « Low energy » F. Maas, E. Tomasi-Gustafsson et al. :
Subthreshold electromagnetic form factors ? and Axial form factor in the time-like region by using a neutron(deuteron) target ?
At «  High energy » B. Pire et al. :
QCD Factorization theorem with the TDA Formalism ?

18. Conclusion
Two or three pions channels : same difficulties for
theoretical investigations.
Details simulations with the PandaRoot need to be done for two and three pions exclusive channels in p pbar annihilation for feasibility studies of measurements.