Regge approach to large angle scattering
in p pbar annihilation
GDR- Nucleon, 11 Feb. 2010
J. Van de Wiele and S. Ong
IPN Orsay
Motivations
The FAIR facility project at GSI and the Panda detector will allow
one to reexamine the two-body hadronic reactions in p pbar
annihilation with unprecedented high accuracy and large
kinematical range of momentum transfer(arXiv:hep-ex/0903.3905).
Possible tests :
• Dimensional counting rules and Quark interchange dominance
model
• Landshoff independent scattering mechanism
• Interference between the Brodsky-Farrar and Landshoff
mechanisms . Oscillation of the cross section with energy
observed in p p elastic scattering (Pire, Ralston 1982).
• Same oscillation scenario in two-body antiproton induced
reactions ?
Color transparency phenomenon ?
• « Saturation » of the Regge pole trajectory at large momentum
transfer |t| ?
Is Regge approach consistent at large momentum transfer
|t| ? (Blankenbecler, Brodsky, Gunion, Savit ,1973)
and (Collins, Kearney, 1984)
•
Extrapolation of the Regge model to the larger momentum
transfer region is based on the « saturing » Regge
trajectories and the introduction of the hadronic form factor
in order to respect the dimensional counting rules ( Brodsky,
Farrar, 1973 and Matveev, Muradian, Tavkhelidze ,1973) .
•
In principle, different observables of exclusive two-body
hadronic reactions could be calculated from QCD :
- Huge number of diagrams
- Pinch singularities from the independant multiple scattering
mechanism
a)
Hard Brodsky Farrar mechanism
b) Landshoff independent scattering mechanism
( C.E. Carlson et al., Phys. Rev. D46, 2891 (1992))
pp 
 
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 10^4
pp




Gunion, Brodsky, Blankenbecler 1973 (QIM Model)
Data from CERN , 1975,76
and BNL 1994
• Regge phenomenology is an alternative and economical
way to fit the available data of two-body hadronic
reactions
• Parametrization of the amplitude in term of Regge
trajectories is succesfully investigated in photo- and
electroproduction of mesons and kaons
(Guidal, Laget, Vanderhaeghen 1997,98)
(J. Van de Wiele 2000)
(Sibirtsev, Haidenbauer, Krewald, Lee, Meiβner, Thomas, 2007)
Calculation « à la Regge »
1 GeV
2 GeV
p  p0
4 GeV
3 GeV
Good agreement
theory-experiment
at high energy only
-p  0n « à la Regge » AD. Martin, TD. Spearman
(1970)
-t < 1.5 (GeV/c)2
d/dt ≈
e-b|t|
up to –t=0.6
5.85 GeV/c
9.8 GeV/c
13.3 GeV/c
18.2 GeV/c
-p  0n « à la Regge » G. Hohler et al. (1966)
 Regge trajectory
t<0
pp  -+
n exchange in t channel
0 exchange in t channel
++ exchange in u channel
 in s channel
pp  00
p exchange in t channel
p exchange in u channel
+ exchange in t channel
+ exchange in u channel
Nucleon and  Regge trajectories
(9382)=1/2
(16802)=5/2
J()=3/2
J=2
etc….
Kinematics of pp  
At cos(CM)=0, one
reaches large –t values
(~10 (GeV/c)2)
 terra incognita for
new data
-t=14 (GeV/c)2
at T=14 GeV !
Kaons ?
Unsaturated Regge trajectories
Degenerated trajectory
Non-degenerated trajectory
Guide for choosing: best
agreement to data
Saturated Regge trajectories
and hard scattering
Different form factors adopted in our model
Data from
FermiLab (1997)
CERN (1975,76); BNL (1994)

pp  K K

Data from
CERN 1975,76
Data from CERN 1975,76
How many parameters for our model ?
For two pions channels :
Xsat-N
ΛNNπ
Xsat-Δ
ΛNΔπ
-2.6
0.85
-3
0.55
-1.4
(GeV)
(GeV 2)
(GeV 2)
(GeV)
(GeV 2)
X0-N = X0-Δ
λρ
Λρππ
0.9
0.95
(GeV)
Three new parameters for two kaons channels :
Xsat-Λ
ΛNΛK
Xsat-Σ
ΛNΣK
-3
1.05
-3
1.05
-1.4
(GeV)
(GeV 2)
(GeV 2)
(GeV)
(GeV 2)
X0-Λ = X0-Σ
λФ
ΛФKK
1
1.3
(GeV)
Quark interchange model versus Regge approach
Conclusions
With a few numbers of parameter and Regge approach
formalism, we are able to fit reasonably the two
pseudoscalar mesons production in p pbar annihilation.
Need more data !!! (FAIR/PANDA !!!)
especially in the large angle scattering region to determine
the values of different parameters.
Wait for a reliable perturbative QCD calculation
for comparison, toward a consistent conclusion.