Modern Physics Letters A

c World Scientific Publishing Company

MKPH-T-02-10

PRESENT STATUS OF ELECTROMAGNETIC REACTIONS

ON THE DEUTERON ABOVE PION THRESHOLD^{*}^{*}*Supported by
Deutsche Forschungsgemeinschaft (SFB 443).

H. ARENHÖVEL, E.M. DARWISH^{†}^{†}†Supported
by Deutscher Akademischer Austauschdienst. Present
address: Physics Department, Faculty of Science, South Valley
University, Sohag, Egypt. , A. FIX, M. SCHWAMB

Institut für Kernphysik, Johannes Gutenberg-Universität

55099 Mainz, Germany

Received (received date)

Revised (revised date)

The present status of the theoretical description of electromagnetic reactions on the deuteron above pion threshold is reviewed. Three major topics are considered: (i) retardation effects in -meson exchange contributions to -interaction and meson exchange currents in deuteron photodisintegration above -threshold in the -resonance region, (ii) off-shell effects in the one-body current treated in a simple pion cloud model in deuteron photodisintegration in and above the -resonance region, and (iii) final state interaction effects in photoproduction of and mesons on the deuteron.

## 1 Introduction

In view of the fact that at present QCD in the non-perturbative regime can at best be described by effective degrees of freedom only, one uses a framework with meson, nucleon and isobar degrees of freedom. Hadron properties are either described phenomenologically or by effective quark models. The central question then is: How accurate is this effective description, and where is the borderline beyond which explicit quark-gluon degrees of freedom have to be considered? It is very likely that no clear cut answer exists.

However, the study of electromagnetic reactions on few-nucleon systems may give at least a partial answer because lightest nuclei (deuteron, helium-3) allow reliable theoretical descriptions, and approximations, which are unavoidable in more complex many-body systems, are not necessary. Therefore, such systems constitute reliable test laboratories for the investigation of effective degrees of freedom. Furthermore, the electromagnetic interaction is well known and sufficiently weak, in order to allow conclusive interpretations in terms of charge and current matrix elements. Finally, reactions above pion threshold are of particular interest with respect to explicit meson degrees of freedom and internal baryon structure.

The main points of interest are (i) the role of meson and isobar degrees of freedom in medium energy reactions, (ii) many-body phenomena, induced by the effective description in terms of meson, nucleon and isobar d.o.f., e.g., the role of pion retardation in interaction and two-body meson exchange operators, and (iii) properties of the neutron like, e.g., the elementary and photoproduction on the neutron, in other words, the use of light nuclei as effective neutron targets. Particularly suited are quasifree reactions on the deuteron in order to minimize final state interaction effects. However, for a reliable interpretation it is mandatory to correct for medium influences as, e.g., described by two-body effects.

## 2 Pion Retardation in above Pion Threshold

Most sophisticated theories of photodisintegration in the region, which are based on a coupled channel approach and use a excitation operator from a fit of photoproduction on the nucleon, encounter various problems (see Fig. 2):

(i) Underestimation of the total cross section by 20-30%. (ii) Angular distributions develop a dip around 90 degree, especially above 300 MeV. (iii) The shape of the photon asymmetry is at variance with experimental data. A detailed analysis of the role of the Born terms and their correspondence to MEC has lead to the conjecture, that retardation in potential and exchange current might be important. Indeed, in a recent calculation the importance of retardation in both, the -interaction as well as MEC has been shown. For the total cross section this is demonstrated in Fig. 2 where a quantitative agreement with experimental data is achieved. Also for the differential cross section and the photon asymmetry shown in Fig. 2 one notes a much improved description. In particular, the dip in the angular distribution has disappeared completely. Thus any realistic description of e.m. reactions on light nuclei in this energy regime has to use retarded interactions and MEC.

## 3 Off-shell Effects in One-Body Current

It is a well-known fact that the e.m. current of a particle with internal structure becomes in general more complicated in an off-shell situation. Consider, for example the e.m. current of a proton. Its on-shell Dirac current is determined by two structure functions, the Dirac and Pauli form factors and , respectively, which depend on , the four momentum transfer squared, only. However, for e.m. reactions on nuclei the interacting nucleons are off-shell, i.e. .

In this case, one has ten additional structure functions depending not only on alone but also on the off-shell masses and . The problem is that for the off-shell structure functions one needs a dynamical model for the internal structure, because these form factors are intimately connected to the underlying hadronic interaction. Thus, such a model has to be consistent with the -interaction. Moreover, off-shell effects as such are not independently observable.

Recently, we have completed a study of off-shell effects in deuteron photodisintegration using a consistent dynamical approach in which the nucleon is dressed by pion loops, i.e. the internal nucleon structure is described by a pion cloud. Correspondingly, one finds for the e.m. one-nucleon current the representation depicted in Fig. 3. For the resulting off-shell one-nucleon current one finds in the nonrelativistic limit

with , and and denote final and initial nucleon energies, respectively. The structure functions fulfil the on-shell condition, i.e. for and

The correct on-shell current is ensured by an appropriate counter term. Within this meson-nucleon model, which is also used for the -interaction including retardation effects, one finds a sizeable influence from off-shell effects on the differential cross section of deuteron photodisintegration in and above the region of the -resonance as is seen in Fig. 3. They show up predominantly at forward and backward angles, leading to a decrease of the cross section. In the future, more realistic nucleon models should be studied with respect to such off-shell effects.

## 4 Final State Interaction in Incoherent Pion Photoproduction

Meson photoproduction on the nucleon provides valuable information on its internal structure and serves as a test of hadron models. The production on light nuclei is of particular interest because it allows one to study the elementary neutron amplitude, medium effects and nuclear structure. Recently, we have completed a calculation of pion photoproduction on the deuteron including besides the impulse approximation complete rescattering in all two-body subsystems as depicted in Fig. 4.

Deuteron wave function and interaction are taken from the Paris potential, and the and interactions in separable form. The complete -matrices are obtained from solutions of the corresponding LS-equations. For rescattering all partial waves with , and for rescattering through waves are included. Total cross sections are shown in Fig. 4. For charged pion production the rescattering effect is small, but for neutral pion production quite sizeable, which mainly stems from the fact that in IA quite a fraction of the coherent production is included due to the non-orthogonality of the final plane wave to the deuteron bound state. In all cases -rescattering is very small compared to -rescattering due to the much weaker -interaction. The inclusion of such rescattering contributions leads to a satisfactory description of the experimental total cross sections for as well as for production as shown in Fig. 4. A corresponding good agreement is achieved for the differential cross sections of production depicted in Fig. 4. One readily notices that the major rescattering effects appear at forward meson angles. This is also true for charged pion production.

## 5 Two-Body Effects in Coherent Eta Photoproduction

Photoproduction of mesons is an interesting tool for studying the -nucleon resonances. The plays a special role because of its strong coupling to the channel. While the incoherent reactions yields estimates of the modulus of the neutron amplitude, the coherent process provides the phase information. Furthermore, the deuteron with serves as isospin filter and thus yields the ratio of isoscalar to proton amplitude . Until recently, a seeming discrepancy was noted between extraction from the coherent reaction, , and from the incoherent one, . The latter value was extracted from the incoherent production on the deuteron, yielding at resonance .

In recent work on coherent photoproduction on the deuteron we have taken for the elementary production amplitude a coupled channel model of, which considers the channels , , , and . Specific features of the model are the inclusion of self energy contributions from and loops and the dressing of the e.m. vertex by hadronic rescattering.

A good description of photoproduction on the proton is achieved with the important result that the dressing leads to complex values for proton and neutron amplitudes, i.e., , , yielding the ratios , and . Thus there is no contradiction for this ratio anymore between the extraction of this ratio from the coherent and the incoherent reaction.

In the left panel of Fig. 5 the various mechanisms, taken into account in, are displayed. The box labeled Born contains disconnected diagrams where the photon is absorbed by one nucleon and the is emitted by the other. Hadronic rescattering is indicated by boxes T, T, T, and T and meson exchange current contributions by boxes N[2]. As resonances “R” we have included , and . The hadronic interaction is considered in static as well as retarded form as displayed in the right panel of Fig. 5. For coherent photoproduction on the deuteron, the effect of various mechanisms on the differential cross section are displayed in the left panel of Fig. 5. One notes an opposite effect between static and retarded rescattering. The total cross section is shown in the right panel of Fig. 5, where a sizeable influence from all two-body effects is seen. Furthermore, the first order rescattering approximation overestimates considerably the total cross section. For the differential cross section a reasonable though not perfect agreement with experiment is achieved as is shown in the left panel of Fig. 5. In the right panel of this figure the photon asymmetry is displayed. One notes a sizeable influence from hadronic rescattering but little effect from MEC.

## 6 Final State Interaction in Incoherent Eta Photoproduction

Near threshold the impulse approximation yields a very small cross
section for due to the large momentum mismatch
and indeed fails drastically compared to experiment yielding
a cross section much too low.

Fig. 14. meson spectrum for . Dotted: IA, dashed: first order rescattering, solid: complete thre-body calculation.

Fig. 14. meson spectrum for . Dotted: IA, dashed: first order rescattering, solid: complete thre-body calculation.

Therefore, we first have performed an approximate treatment of FSI in complete analogy to pion photoproduction on the deuteron, i.e. taking into account only complete rescattering in the two-body and subsystems in the final state. In the following, this is called first order rescattering. In this case the -matrix is determined from the Bonn OBEPQ potential and for the -matrix an isobar model is taken describing the intermediate excitation. The first order rescattering, restricted to -waves of and subsystems in view of the near-threshold region, leads to a considerable improvement (see left panel of Fig. 6). The spectrum of the outgoing meson (middel and right panels of Fig. 6) shows the distinct signature of the final state rescattering exhibiting the prominent peak near the scattering threshold.

The differential cross sections near threshold are shown in Fig. 6. The left panel of Fig. 6 indicates that first order rescattering still fails to explain quantitatively the enhancement of the data right above threshold. This is corroborated by very recent more precise near-threshold data of Hejny et al..

For this reason, we then have performed a three-body treatment of the final state interaction, because the very strong effect in first order rescattering suggests that a genuine three-body treatment is required. A considerable simplification is achieved by restriction to only -waves which is justified because of threshold region. For the interaction a simple Yamaguchi form is used. The resulting spectrum is displayed in Fig. 6 where again one notes clearly the peak as in Fig. 6. However, for the lower photon energy one readily sees a substantial underestimation of the first order rescattering compared to the three-body calculation, althoug the forms are similar. Total and differential cross sections are shown in Fig. 6. The inclusive total cross section data exhibit a distinct enhancement near threshold which is reproduced by the 3-body approach (left panel of Fig. 6) but not in first order, the latter being considerably lower right at threshold. This is also the case for the differential cross sections (middel and right panels of Fig. 6). It remains to be seen, whether a more realistic treatment of the -interaction is also able to describe the data.

## 7 Conclusions and outlook

In summary, we may conclude that the electromagnetic probe is a very important tool in order to reveal the internal structure of hadrons. Only the new generation of high duty cycle machines allows one to exploit its full power and the thrust of future experimental research lies on the study of exclusive reactions. Polarization observables will give us much more detailed information and thus will provide much more stringent tests for theoretical models.

Reactions on the deuteron are of particular importance for testing present theoretical frameworks for describing strong interaction physics in terms of effective degrees of freedom, thus serving as a test laboratory. Of special interest are e.m. reactions above the pion threshold. An important example is photodisintegration with respect to the study of retardation and off-shell effects.

Furthermore, meson production on the deuteron offers the possibility to study the elementary production amplitude on the neutron provided one has the two-body effects from final state interaction and e.m. current under control. In particular, the -interaction can be studied in incoherent eta production near threshold. However, a first order rescattering calculation as used, e.g. in, is not reliable for that purpose, because right above threshold a three-body approach is mandatory.

Finally, for increased energy and momentum transfers, the effects which arise from relativity should be carefully considered.

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