Predictions for polarized-beam and/or vector-polarized-target observables in elastic Compton scattering on the deuteron

Motivated by ongoing developments at High-Intensity Gamma Source (HIγS) at Triangle Universities Nuclear Laboratory (TUNL) that include increased photon flux and the ability to circularly polarize photons, we calculate several beam-polarization and/or target-spin-dependent observables for elastic Compton scattering on the deuteron. This is done at energies of the order of the pion mass within the framework of heavy-baryon chiral perturbation theory. Our calculation is complete to $\mathcal{O}(Q^3)$ and at this order there are no free parameters. Consequently, the results reported here are predictions of the theory. We discuss paths that may lead to the extraction of neutron polarizabilities. We find that the photon/beam polarization asymmetry is not a good observable for the purpose of extracting ${\alpha }_n$ and ${\beta }_n$. However, one of the double polarization asymmetries, ${\Sigma }_x$, shows appreciable sensitivity to ${\gamma }_{1n}$ and could be instrumental in pinning down the neutron spin polarizabilities.