few body-18santos, brazil august 25, 20061 meson exchange currents in pion double charge exchange...

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


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


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


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.


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


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


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


Forward scattering DCX

potential exchangepion - one is )(

)(2

112

NNrV

rVmmf

T

)2()(

))((1

22

22221

22

2

mmq

qq

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


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


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


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

qq

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


p

p

n

n

q

p

p

n

n

q

q+

qq

p

p

n

n

+f0 qq

p

p

n

n

+

22

2 )(

F

ts

F

mM

Weinberg

amplitude


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


Dotted line- two step mechanism

Solid line – , and f0 mesons contribution + contact diagram

Dashed line – Born approximation

(Pole + contact diagram)

Ne),O( 1818


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.


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

few body-18santos, brazil august 25, 20061 meson exchange currents in pion double charge exchange...

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