Few Body-18 Santos, Brazil August 25, 2006 1
Meson Exchange Currents in Pion Double Charge Exchange Reaction
Roman Ya. Kezerashvili
NY City College of TechnologyThe City University of New York
Few Body-18 Santos, Brazil August 25, 2006 2
Double charge exchange of pions on nuclei occupies a particular position among all known nuclear reactions. It is unique because through the reaction one can obtain nuclei for which the Z component of the isospin differs by two units from that of the original nuclei. This is possible by double isospin flip of the pion.
•de Shalit, Drell, and Lipkin in 1961 predicted existence of DCX
•Experimentally this process was discovered in the Laboratory of Nuclear Problems at the JINR in 1963
•During the 45 years after the discovery the pion double charge exchange reaction has generated a significant amount of theoretical and experimental work
)2,2(),( NZBNZA
Few Body-18 Santos, Brazil August 25, 2006 3
What makes it attractive to study pion DCX reaction on nuclei?
In DCX at least two nucleons must participate in order to conserve the electric charge
DCX reaction is more sensitive to the two-nucleon effects, manifested here in the first order, than reactions in which there is no need to consider two nucleons and in which the effects of the two nucleons dynamics are manifested indirectly
pion DCX can give direct information on the two nucleons aspect of nuclear dynamics as short-range two nucleons correlations and meson exchange currents
In pion DCX we produced neutron-rich and proton-rich nuclei and can obtain and study nuclei far from the stability region
To obtain information about double-isobar states of nuclei
We hope of studying the expected deference between the neutron and proton densities in nuclei
Pion DCX reaction is sensitive to the details of the pion-nucleus interactions
Few Body-18 Santos, Brazil August 25, 2006 4
DCX Reaction Mechanisms
nn
p p pp
nn
p
ppp
nn
pp
nn
Two Step Mechanism Meson Exchange Current Mechanism
Pole Diagram Contact Diagram Absorption Mechanism
The incoming pion undergoes two sequential single charge exchange scatterings on nucleons
within a nucleus
The incoming pion scatters wih a virtual pion of opposite
charge in the "cloud"surrounding the target
nucleon of the nucleus, and is itself absorbed on
another nucleon. Germond and WilkinRobilotta and Wilkin
Pion-induced pion production
is followed by two-nucleon absorption
of one of the two final pions
Jeanneret et. al.
Few Body-18 Santos, Brazil August 25, 2006 5
Dotted curve - without Dibarion
Solid curve - with Dibarion
The energy dependence of the forward scattering pion DCX cross section on nuclei in the energy range from 0 to 300 MeV
• Dibarion Mechanism: Bilger e.a. assuming the production of the hypothetical d′ dibaryon, a resonance in the NN subsystem with mass 2063 MeV and baryon number B=2
• Before accepting such an interpretation, it is important to consider the more conventional ones
• The peak in low-energy pion double charge exchange can be reproduced by the two-step mechanism when distorted waves obtained from a realistic optical model are used. Gibbs e.a.
Meson Current
Mechanism
Few Body-18 Santos, Brazil August 25, 2006 6
MEC Mechanism
)(
),;,(22
1
21
mq
qkqkMT iiNNc
))((
),;,(
4
))(()(
222
221
212
22112
mqmq
qkqkM
m
qqgiT iip
p
p
n
n
Pole diagram
n
n
p
p
Contact diagram
),,(),,( ustAutsAM
For example, the transition amplitude for the → process can be expressed through the invariant amplitudes A(s,t,u) as
Few Body-18 Santos, Brazil August 25, 2006 7
Effective Lagrangian Formalism
p
p
n
n
n
n
p
p
The sum of the pole and contact diagram
For forward scattering DCX amplitude in the Born approximation becomes
Few Body-18 Santos, Brazil August 25, 2006 8
Forward scattering DCX
potential exchangepion - one is )(
)(2
112
NNrV
rVmmf
T
)2()(
))((1
22
22221
22
2
mmq
fm
gT B
In PWA the forward scattering DCX cross section does not depend on the pion energy
In the Born approximation the DCX amplitude is real
and does not satisfy the unitarity condition
Few Body-18 Santos, Brazil August 25, 2006 9
Dual ModelVeneziano suggested the amplitude with local duality assuming that Redge trajectories are linear and the resonances have infinitimise width. In other words, poles lay on the real s and t. The corresponding amplitude is a function of trajectories. The model satisfy Adler's consistency condition and designed for off-shell extrapolation
0 ,))()(1(
))(1())(1(),(
tt
tstsA
where λ is a constant, Γ(x) is gamma function and (s) is linear Redge trajectory
)(
)(
2
1
2
1)(
22
2
mm
mss
)423.11(369.1)(
))((22
2
22
2
22221
mm
q
mm
q
mq
qqT
For forward scattering pion DCX Oset et.al.
In Veneziano model the DCX amplitude is real and does not satisfy the unitarity condition
)()( rVm
rV
BA
Few Body-18 Santos, Brazil August 25, 2006 10
Unitarization of the MEC Amplitude
)1()]()[/11()(Im 2 ssAssA BL
0012
0220
0 )()(c ))((
)(Im)(Re csscstdx
xxsx
xAP
sssA
LL
2
1
f
p
p
n
n
In effective Lagrangian formalism only the contribution of the "tree" diagrams are included and no pionic or baryonic closed loop diagrams. The tree diagrams correspond to the Born approximation for scattering, and their contribution is defined by the first term of the expansion of the -amplitude in terms of
LLL AAA ImRe
)(4
)()(2
22
2
sF
msAsA B
We can reconstruct the real part of the amplitude using the dispersion relation with three subtractions
Few Body-18 Santos, Brazil August 25, 2006 11
MEC in Composite Meson ModelThe vertex box corresponding to scattering can be considered at the quark level and includes the quark diagrams which successfully describe
scattering
uddup
p
n
n
q
p
p
n
n
+
p
p
n
n
f0 qq
p
p
n
n
+
p
p
n
n
q
q+
=
The quark-box diagram corresponds to thePole diagram and
represents the Born approximation in theeffective Lagrangian
method.
The choice of the other diagram is based on the probability of the two pion decay of mesons:
(770 MeV) (100%) (600 MeV) (>90%)f0 (975 MeV) (>90%)
qτg
πτiff
mmiqL qq
2
sincos 50
Few Body-18 Santos, Brazil August 25, 2006 12
p
p
n
n
q
p
p
n
n
q
q+
p
p
n
n
+f0 qq
p
p
n
n
+
22
2 )(
F
ts
F
mM
Weinberg
amplitude
Few Body-18 Santos, Brazil August 25, 2006 13
Solid line – , and f0 mesons contribution + contact diagram
Dotted line – Born approximation
(Pole + contact diagram)
Red line- Born approximation + pion loop diagram
MEC in Composite meson model and unitarization of the amplitude lead to the energy dependence of the forward scattering pion DCX
Ne),O( 1818
Few Body-18 Santos, Brazil August 25, 2006 14
Dotted line- two step mechanism
Solid line – , and f0 mesons contribution + contact diagram
Dashed line – Born approximation
(Pole + contact diagram)
Ne),O( 1818
Few Body-18 Santos, Brazil August 25, 2006 15
Conclusions Forward scattering pion DCX in the Born approximation does not depend on the
energy when the pion distortion is neglected
and f0 mesons contribution, appreciably changes the cross section,
leads to the energy dependence of the cross section and it shows the importance of these mesons at the energies above 600 MeV
Unitarization of the amplitude leads to the large correction and the energy dependence of the forward scattering pion DCX
MEC mechanism can reveal in the pion DCX and becomes the dominant because it has a substantial contribution at the considered energy region
The distortion of the pion waves will generally reduce the cross section in the composite-meson model as well as the contribution of the one loop diagram but it will not change the conclusion of the importance of the inclusion the pion resonances and the pion loop diagram into the MEC mechanism.
Interference of MEC with the two step mechanism can dramatically change the forward scattering DCX cross section.
Few Body-18 Santos, Brazil August 25, 2006 16
0.01
0.1
1
10
600 800 1000 1200 1400
T, MeV
d/dW
, mb
/sr
Ne),O( 1818
Vicente Vagas, 1996
Composite Meson Model