Electromagnetic structure of A=2 and 3 nuclei in chiral effective field theory

Abstract

Background: The $A=2$ and 3 form factors are among the observables of choice for testing models of nuclear interactions and associated electromagnetic charge and current operators. Here we investigate the validity of the chiral-effective-field-theory ($\ensuremath{\chi}$EFT) approach to describe the strong-interaction dynamics in these few-nucleon systems and their response to electromagnetic probes.Purpose: The objectives of the present work are twofold. The first is to address and resolve some of the differences present in independent, $\ensuremath{\chi}$EFT derivations up to one loop, recently appearing in the literature, of the nuclear charge and current operators. The second objective is to provide a complete set of $\ensuremath{\chi}$EFT and hybrid predictions for the structure functions and tensor polarization of the deuteron, for the charge and magnetic form factors of ${}^{3}$He and ${}^{3}$H, and for the charge and magnetic radii of these few-nucleon systems.Methods: The calculations use wave functions derived from either chiral or conventional two- and three-nucleon potentials and Monte Carlo methods to evaluate the relevant matrix elements.Results: In reference to the two objectives mentioned earlier, we find that (i) there are no differences between the $\ensuremath{\chi}$EFT magnetic dipole operator at one loop derived in our formalism and that obtained by K\olling et al. [Phys. Rev. C 80, 045502 (2009)] with the unitary transformation method and (ii) there is excellent agreement between theory and experiment for the static properties and elastic form factors of these $A=2$ and 3 nuclei up to momentum transfers $q\ensuremath{\lesssim}2.0$--2.5 fm${}^{\ensuremath{-}1}$. A complete analysis of the results is provided.Conclusions: Nuclear $\ensuremath{\chi}$EFT provides a very satisfactory description of the isoscalar and isovector charge and magnetic structure of the $A=2$ and 3 nuclei at low momentum transfers $q\ensuremath{\lesssim}3{m}_{\ensuremath{\pi}}$. In particular, contributions from two-body charge and current operators are crucial for bringing theory into close agreement with experiment. At higher $q$ values the present $\ensuremath{\chi}$EFT predictions are similar to those obtained in the hybrid approach, as well as in older studies based on the conventional meson-exchange picture, and fail to reproduce the measured $A=2$ and 3 form factors in the diffraction region.