Deuteron binding energies and form factors from light-front Hamiltonian field theory
This paper investigates how the breaking of manifest rotational invariance in light-front dynamics affects the binding energy and the form factors of the deuteron. To do this, we derive new light-front nucleon-nucleon one- and two-meson-exchange potentials, and use the potentials to solve for the deuteron wave function and binding energy. We find that including two-meson-exchange (TME) potentials partially repairs the broken rotational invariance of the one-meson-exchange (OME) potential. This is shown by a decrease in the binding energy difference of different m states of the deuteron. We calculate the matrix elements of the electromagnetic current using the deuteron wave functions obtained from the OME and $\mathrm{OME}+\mathrm{TME}$ potentials. Rotational invariance requires that the matrix elements satisfy an angular condition, but in light-front dynamics that condition is only partially satisfied. The current matrix elements from the OME calculation satisfy the angular condition better than the ones from the $\mathrm{OME}+\mathrm{TME}$ calculation. The matrix elements of the axial current satisfy the angular condition to the same extent regardless of which wave functions are used for the calculation. Finally, we find that at momentum transfers greater than about $2{\mathrm{GeV}}^{2},$ the breaking of rotational invariance causes less uncertainty in the computed deuteron form factors than do the uncertainties in the nucleon form factors.