Deuteron Compton Scattering in Effective Field Theory: Spin-Dependent Cross Sections and Asymmetries

Polarized Compton scattering on the deuteron is studied in nuclear effective field theory. A set of tensor structures is introduced to define 12 independent Compton amplitudes. The scalar and vector amplitudes are calculated up to $\mathcal{O}((Q\mathrm{/}\mathrm{\Lambda }{)}^2)$ in low-energy power counting. Significant contribution to the vector amplitudes is found to come from the spin-orbit type of relativistic corrections. A double-helicity dependent cross section ${\mathrm{\Delta }}_1\sigma =({\sigma }_{+1-1}-{\sigma }_{+1+1})\mathrm{/}2$ is calculated to the same order, and the effect of the nucleon isoscalar spin-dependent polarizabilities is found to be smaller than the effect of isoscalar spin-independent ones. Contributions of spin-independent polarizabilities are investigated in various asymmetries, one of which has as large as 12 (26) percent effect at the center-of-mass photon energy 30 (50) MeV.