Nucleon polarisabilities from Compton scattering on the deuteron

An analytic calculation of the differential cross section for elastic Compton scattering on the deuteron at photon energies ω in the range of 20–50 MeV is presented to next-to-next-to-leading order, i.e., to an accuracy of ∼3%. The calculation is model-independent and performed in the low energy nuclear Effective Field Theory without dynamical pions. The iso-scalar, scalar electric and magnetic nucleon polarisabilities α0 and β0 enter as free parameters with a theoretical uncertainty of about 20%. We argue that a window exists at ω∼20–50 MeV in which nucleon polarisabilities can be extracted in a model-independent way without having to know detailed pion dynamics. In a feasibility study, we use data at ωLab=49 MeV to find α0=8.4±3.0(exp)±1.7(theor), β0=8.9±3.9(exp)±1.8(theor), each in units of 10−4 fm3. With the experimental constraint for the iso-scalar Baldin sum rule, α0=7.2±2.1(exp)±1.6(theor), β0=6.9∓2.1(exp)∓1.6(theor). A more accurate result can be achieved (i) predominantly by better experimental data, and (ii) by a higher order theoretical calculation including contributions from so far undetermined four-nucleon–two-photon operators.