We study bound states in a model with scalar nucleons interacting via an exchanged scalar meson using the Hamiltonian formalism on the light front. In this approach manifest rotational invariance is broken when the Fock space is truncated. By considering an effective Hamiltonian that takes into account two meson exchanges, we find that this breaking of rotational invariance is decreased from that which occurs when only one meson exchange is included. The best improvement occurs when the states are weakly bound.

We consider the ground state in a model with scalar nucleons and a meson using the formalism of light-front dynamics. Light-front potentials for twonucleon bound states are calculated using two approaches. First, light-front time-ordered perturbation theory is used to calculate one-and two-mesonexchange potentials. These potentials give results that agree well with the ladder and ladder plus crossed box Bethe-Salpeter spectra. Secondly, approximations that incorporate non-perturbative physics are used to calculate alternative one-meson-exchange potentials. These non-perturbative potentials give better agreement with the spectra of the full non-perturbative groundstate calculation than the perturbative potentials. For lightly-bound states, all of the approaches appear to agree with each other. PACS number(s): 21.45.+v, 03.65.Ge, 03.65.Pm, 11.10.Ef Typeset using REVT E X Recent experiments at Thomas Jefferson National Accelerator Facility have measured the A(Q 2 ) structure function of the deuteron for momentum transfers up to 6 (GeV/c) 2 [1], and measurements for B(Q 2 ) are planned. At such large momentum transfers, a relativistic description of the deuteron is required. One approach that gives such a description is light-front dynamics, which we will examine here. To separate the effects of the using lightfront dynamics from the effects of the model, we choose to use the massive Wick-Cutkosky model. This is a "toy model" investigation, instead of the full nuclear theory calculation. Using this model, the light-front Hamiltonian approach is used to solve for the bound-state wavefunction. The results of our calculation can then be compared to other calculations done with the same model but different approaches. The simplest observable that can be compared is the relationship between the bound-state mass and the coupling constant.The utility of the light-front dynamics was first discussed by Dirac [2]. We start by expressing the four-vector x µ in terms of the light-front variables. This is simply a change of variables, but an especially convenient one. Using this coordinate system and defining the commutation relations at equal light-front time (x + = t LF ), we obtain a light-front Hamiltonian [3][4][5]. The Hamiltonian is used in the light-front Schrödinger equation to solve for the ground state.There are many desirable features of the light-front dynamics and the use of light-front coordinates. First of all, high-energy experiments are naturally described using light-front coordinates. The wave front of a beam of high-energy particles traveling in the (negative) three-direction is defined by a surface where x + is (approximately) constant. Such a beam can probe the wavefunction of a target described in terms of light-front variables [3,6]: the Bjorken x variable used to describe high-energy experiments is simply the ratio of the plus momentum of the struck constituent particle to the total plus momentum (p + ) of the bound state. Secondly, the vacuum for a theory with massive particles can be very simple on ...

In this model the other mesons are not affected by the transformation because they are not chiral partners of the pion. This is in contrast to the Lagrangian given in Refs. ͓6,28͔, where the mass and scalar interaction terms of the nucleon were written as M Uϩg s instead of U(M ϩg s ). B. Noninteracting nucleon-nucleon theory

We investigate the symptoms of broken rotational invariance, caused by the use of light front dynamics, for deuterons obtained using one- and two-pion-exchange potentials. A large mass splitting between states with m=0 and m=1 is found for the deuteron obtained from the one-pion-exchange (OPE) potential. The size of the splitting is smaller when the chiral two-pion-exchange (TPE) potential is used. When the TPE potential constructed without chiral symmetry is used, the deuteron becomes unbound. These results arise from significant relativistic effects which are much larger than those of the Wick-Cutkosky model because of the presence of the tensor force.Comment: 5 pages, 1 figure, REVTeX4 (style files included