Few Body-18Santos, Brazil August 25, Meson Exchange Currents in Pion Double Charge Exchange Reaction Roman Ya. Kezerashvili NY City College of Technology The City University of New York

Few Body-18Santos, Brazil August 25, 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

Few Body-18Santos, Brazil August 25, 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-18Santos, Brazil August 25, DCX Reaction Mechanisms  nn  p p  pp  nn   p ppp  nn   pp  nn  Two Step Mechanism Meson Exchange Current Mechanism Pole DiagramContact 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 Wilkin Robilotta and Wilkin Pion-induced pion production is followed by two- nucleon absorption of one of the two final pions Jeanneret et. al.

Few Body-18Santos, Brazil August 25, 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-18Santos, Brazil August 25, MEC Mechanism p p  n n  Pole diagram n n  p p  Contact diagram For example, the transition amplitude for the      →     process can be expressed through the invariant amplitudes A(s,t,u) as

Few Body-18Santos, Brazil August 25, 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-18Santos, Brazil August 25, Forward scattering DCX 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-18Santos, Brazil August 25, Dual Model Veneziano 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 where λ is a constant, Γ(x) is gamma function and  (s) is linear Redge trajectory For forward scattering pion DCX Oset et.al. In Veneziano model the DCX amplitude is real and does not satisfy the unitarity condition

Few Body-18Santos, Brazil August 25, Unitarization of the MEC Amplitude 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 We can reconstruct the real part of the amplitude using the dispersion relation with three subtractions

Few Body-18Santos, Brazil August 25, MEC in Composite Meson Model The vertex box corresponding to  scattering can be considered at the quark level and includes the quark diagrams which successfully describe  scattering p p  n n  q  qq p p   n n + p p  n n  f0f0 qq p p   n n + p  p n n   q q + = The quark-box diagram corresponds to the Pole diagram and represents the Born approximation in the effective 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%) f 0 (975 MeV)   (>90%)

Few Body-18Santos, Brazil August 25, p p  n n  q p  p n n   q q +  qq p p   n n + f0f0 qq p p   n n + Weinberg amplitude

Few Body-18Santos, Brazil August 25, Solid line – ,  and f 0 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

Few Body-18Santos, Brazil August 25, Dotted line- two step mechanism Solid line – ,  and f 0 mesons contribution + contact diagram Dashed line – Born approximation (Pole + contact diagram)

Few Body-18Santos, Brazil August 25, Conclusions  Forward scattering pion DCX in the Born approximation does not depend on the energy when the pion distortion is neglected    and f 0 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-18Santos, Brazil August 25, Vicente Vagas, 1996 Composite Meson Model