Covariant spectator theory of $np$ scattering: Deuteron quadrupole moment

The deuteron quadrupole moment is calculated using two covariant spectator theory model wave functions obtained from the 2007 high-precision fits to $np$ scattering data. Included in the calculation are a new class of isoscalar $np$ interaction currents automatically generated by the nuclear force model used in these fits. The prediction for model WJC-1, with larger relativistic $P$-state components, is $2.5\%$ smaller than the experimental result, in common with the inability of models prior to 2014 to predict this important quantity. However, model WJC-2, with very small $P$-state components, gives agreement to better than 1%, similar to the results obtained recently from chiral effective field theory predictions to next-to-next-to-next-to-leading order.

Figure 1

Diagrammatic representation of the two-body current operator in the covariant spectator theory using vertex functions with particle 2 off-shell. The interaction current contributions are contained in diagrams $\left({\mathrm{A}}_{\pm }\right)$ and parts of the (B) diagrams, as discussed in the text. Off-shell nucleon lines are thicker than on-shell lines, which are also labeled with an $\times$. Diagrams (A) and $\left({\mathrm{A}}_{\pm }\right)$ describe the interaction of the photon with particle 2, allowing particle 1 to be on-shell in both the initial and final states. Diagrams $\left({\mathrm{B}}_{\pm }\right)$ describe the interaction of the photon with particle 1, so that both particles must off-shell in either the initial state (diagram ${\mathrm{B}}_{+})$ or in the final state (diagram ${\mathrm{B}}_{-})$.

Figure 2

Running sum of the corrections (in %) to the quadrupole moment, in the order that they are listed in Tables 2 and 3. Panel (a) is model WJC-1 and panel (b) is model WJC-2. The dashed line is the experimental value (zero correction). The error bars are $\pm 0.002=\pm 0.2\%$, an estimate of the size of the terms missing from the approximation of Eq. (A79).