Sensitivity of Polarization Observables in ${\gamma}\boldsymbol{d\to}{\pi}^{\mathbf{0}}\boldsymbol{d}$ Reaction Near Threshold to the Choice of Elementary ${\gamma}\boldsymbol{N\to}{\pi}\boldsymbol{N}$ Amplitude and Deuteron Wave Function

Abstract

We study the sensitivity of polarization observables in $\gamma d\to\pi^{0}d$ reaction near threshold to the choice of elementary $\gamma N\to\pi N$ amplitude and $NN$ potential model adapted for the deuteron wave function (DWF). Numerical results for various beam, target, and beam–target polarization observables are presented and systematic uncertainties caused by the use of different elementary operators and DWFs are evaluated. The calculations are based on a $\gamma d\to\pi^{0}d$ approach in which realistic models for the elementary pion production amplitude and the DWF are used. We find considerable dependencies of the estimated results for all possible polarization observables on the elementary amplitude. The spin asymmetries $\Sigma$, $T_{21}^{c}$, $T_{10}^{l}$, and $T_{20}^{l}$ show large sensitivities to the DWF. In contrast, the asymmetries $T_{11}$, $T_{2M}$ ($M=0,1,2$), $T_{10}^{c}$, and $E$ as well as the helicity difference $d(\sigma^{P}-\sigma^{A})/d\Omega$ have slight dependence on the DWF only at photon energies very close to $\pi$-threshold. The unpolarized differential cross section is also predicted and compared with the available experimental data, and a satisfactory agreement is obtained only at forward pion angles. We expect that the results presented here may be useful to interpret the recent measurements from Jefferson Lab, TAPS@ELSA, A2 and GDH@MAMI Collaborations.