(Strauch, Berman)

Photoproduction of two pions is very sensitive to couplings of resonances to photons and mesons [Nac02]. While unpolarized cross sections provide valuable information on the reaction mechanisms and impose important constraints on theoretical models, much stronger constraints are to be found in polarization observables.

The general form of the cross section can be written as s = S + P_<D, where P_< is the degree of circular polarization of the photon and S and D are the unpolarized and polarized cross sections. The reaction with a two-body final state is always coplanar and has an identical cross section for unpolarized or circularly polarized photons, i.e., D = 0 [Bof96]. For reactions with more than two particles in the final state, however, new information can be obtained with circular beam polarization, even if the target is unpolarized and the recoil polarization is not measured. The cross-section asymmetry obtained by flipping the helicity h of the incident electron is defined by:

We have analyzed the cross-section asymmetry for the ¹H double-charged-pion channel. The data from the g1c run were obtained with circularly polarized photons, produced by longitudinally polarized electrons hitting an amorphous radiator. The circular polarization of the photon beam can be determined from the electron-beam polarization and the ratio of photon and incident electron energies [Ols59]. No nuclear polarizations (target or recoil) were specified.

Owing to the large angular acceptance of the CLAS, complete angular distributions of the cross-section asymmetries are observable. Figure 5 shows the azimuthal angle F^* between the scattering plane, containing the photon and the target momentum, and the decay plane, containing the two particles x₁ and x₂, which was used in the analysis.

Our preliminary analysis of the double-charged-pion channels for polarization effects has revealed large asymmetries in the helicity-dependent cross sections. Figure 6 shows preliminary results for the p(g_<,p⁺p^-)p reaction for two different energy bins. The asymmetry is not a simple function of F^*, but can be expressed as a series of sine functions:

Figure 6. Preliminary angular distribution for two different center-of-mass energy bins of the cross-section asymmetry A in the p(g_<,p⁺p^-)p reaction; configuration p^-[p,p⁺]. The solid curve is the result of a calculation by Mokeev [Mok03]; the dotted curve is a fit of a series of sine-functions to the data.

There are no cosine terms in this series, since for F^* = 0^o or 180^o, all of the particles are in one plane, and for this case, there is no helicity dependence of the cross section because of parity conservation. The energy dependence of Fourier coefficients a₁ and a₂ are shown in Fig. 7 for different angular and invariant-mass cuts. The Fourier coefficients depend strongly on the photon energy, the reaction channel, and the details of the kinematics.

We are collaborating with various theory groups in order to interpret these data. Preliminary calculations for these cross-section asymmetries have been done by Mokeev [Mok03]. These phenomenological predictions use available information on N^* and D states. The results are shown as the solid curve in Fig. 6, where an excellent description of the data is achieved at W = 1.64 GeV. However, at higher energies there is room for improvement in the model parameters. Subsequent model studies have indicated a strong sensitivity of the helicity asymmetries both to production amplitudes (e.g., the r diffractive production amplitude) and to resonance couplings. Calculations also have been carried out by Oed and Roberts within an effective-Lagrangian approach [Rob97].

Figure 7. Fourier components of the cross-section asymmetry for photoproduction of p⁺p^- from the proton with circularly polarized photons: left, for -1.0 £ cos(q^*) £ -0.3 (blue); 0.3 £ cos(q^*) £ 1.0 (green); right, for invariant mass IM of the p⁺p^- system < 0.7 GeV (blue); IM > 0.7 GeV (green).

We will finalize the technical part of the data analysis of the g1c data shortly. The next steps include detailed comparisons of the experimental data on the proton with theory and the extension of the analysis to the two-charged-pion photoproduction channel on the light nuclei, ²H (g2 data), ³He (g3 data), and ⁴He (g3 data) (see Section IB6). These data have been presented at the Workshop on New Aspects of Quark Nuclear Physics with Polarized Photons in Honolulu [Ber03], at the APS Meeting in Philadelphia [Str03b], at the International Conference on Nuclear and Particle Physics with CEBAF/JLab at Dubrovnik [Str03c], and at the International Conference on Few-Body Problems in Physics at Durham earlier this year [Str03d]. An analysis report to the CLAS collaboration is being written in preparation for submission of a publication.

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