final state interaction effects in production near threshold
DESCRIPTION
Final state interaction effects in production near threshold. V.F. Dmitriev and A.I. Milstein Budker Institute of Nuclear Physics. Ratio of electric and magnetic formfactors In the threshold region. p (Ν). q. R.Bijker, F.Jachello, Phys.Rev. C69 (2004). Γ. _. - p (N). - PowerPoint PPT PresentationTRANSCRIPT
Final state interaction effects in production near threshold
V.F. Dmitriev and A.I. Milstein
Budker Institute of Nuclear Physics
NN
Ratio of electric and magnetic formfactors In the threshold region.
2
1 2 2
1 2
,4
.
Ep
M
qG F F
m
G F F
21 2 p
FF q
m
qp (Ν)
-p (N)
Γ
_210 MeVpT
R.Bijker, F.Jachello, Phys.Rev. C69 (2004)
General features of the processq
p
-p1/ 2 0.1 fmpm
P P formation scale _
At distances 0.1 < r < 1.4 fm there is a strong interaction between slowly moving P and Pbar. This scale corresponds to the energies starting from few ten’s MeV. Strong final state interaction in this energy scale is very likely responsible for the energy dependence of the formfactors near threshold.
QUANTUM NUMBERS of P Pbar state
PHOTON J=1, P=-1, C=-1
P Pbar
1P ( 1) , C ( 1) , L L S J = L +S
3 31 1S DL - even S = 1
Isospin not fixed I=0,1
Elementary amplitude of N Nbar production
2 1
† †1 2 2 1
1 1( ) ( ) ( )( ) 3 ( )
3 3N NN N
EF FE ME F F E M F F
M E M
e e e e
2T p p p p
M – proton mass, E – nucleon energy,
1 2 and F F -Dirac formfactors responsible for short distance behaviour
1 2 and F F are smooth functions, nearly constants in threshold region
e - polarization of virtualphoton
Accounting for N Nbar interaction
† 3 †( )( ) ' ( ) ( )T d p pT p p' T p'
†( ) ( )
p r - N Nbar scattering state with asymptotic behaviour
†( ) * *( ) | .ipr
ir
ee
r
prp r
* † is the spin polarization vector for S=1 state of N Nbar pair
†( ) †( )ˆ( ) ( ) ( )H E M p pr r
2
ˆ ( ) ( )H U iWM
p
r r
Paris N Nbar potential, Phys.Rev. C 50 (1994) 2710
Real part - meson exchange for r > 0.84 - 1 fm and fit
2 3 20 1 2 3 0 1 2 or a a r a r a r b b r b r for r < 0.84 - 1 fm.
In both I=0,1 channels
p n
p n
Coupled channels
Imaginary part 0 (2 )( ) ~
K MrW r
r
Production amplitude becomes
*0 2 2
ˆ4 2 ,1 | 211 ( )mT G G m Y p
S-wave D-wave
Electromagnetic formfactors
211 01 21 M1 01
200 00 20 M0 00
1 0 1 0
2 , G2
2 , G2
,
E
E
Ep E E Mp M M
GG G G G
GG G G G
G G G G G G
1 0 1 0, En E E Mn M MG G G G G G
Results for | / |Ep MpG G
2
1
1Re
2
V
V
F
F
2
1
1Im
2
V
V
F
F
1
1
Re 1.12S
V
F
F
1
1
Im 1.20S
V
F
F
2
1
Re 0.96S
V
F
F
2
1
Im 1.15S
V
F
F
Summary
• We developed an approach to account for final state interaction (FSI) in P Pbar production near threshold.
• The effects of FSI are considerable; they lead to strong energy dependence near threshold.
• The approach is not a parameter free one. More data are necessary to check its validity.