The self-energy corrections to the light-cone two-body equation in ø 3-theories

Abstract

The light-cone ladder approximation in the Wick-Cutkosky model is extended to the lowest order light-cone Tamm-Dancoff approximation which includes the self-energy corrections and counter-terms. The light-cone two-body equation is modified by the term corresponding to the self-energy corrections and counter-terms. The analytic relation between the coupling constant, α, and the binding energy, β, which was previously derived for all nlstates with l= n−1 under the light-cone ladder approximation is also modified by these corrections and compared with the numerical results obtained by a variational principle. The numerical estimate of this modification shows that self-energy effects are as repulsive as relativistic kinematic corrections and retardation effects and makes β become frozen as α increases. The probability of finding the three-body component inside the bound-state is also compared with that of finding the two-body component and the ratio of two probabilities is calculated for several different α values investigating the self-energy effects to this ratio.