Higher-order calculations of electron–deuteron scattering in nuclear effective theory

Motivated by recent advances in the application of effective field theory techniques to light nuclei we revisit the problem of electron–deuteron scattering in these approaches. Applying Weinbergʹs power counting for two-nucleon processes to this reaction leads, in the first instance, to an effective field theory expansion that does not converge for virtual photon momenta of order 300 MeV. However, here we show that this breakdown is not the result of an inability to describe deuteron physics: instead it results from the effective field theoryʹs failure to describe the nucleonʹs isoscalar electromagnetic form factor once these momentum transfers are reached. Analyzing ratios of deuteron to (isoscalar) nucleon form factors within the effective field theory overcomes this difficulty. We show that when such an analysis is performed the effective theory expansion for deuteron physics converges well up to virtual photon momenta of order 700 MeV, and agrees with experimental data for the deuteron charge and quadrupole form factors over a similar range.