Four-Body Bound-States Systems in Relativistic Scalar Quantum Field Theory: Variational Basis-State Approach

The variational method within the Hamiltonian formalism of quantum field theory has been used in order to investigate the effect of virtual pairs for four-body scalar systems consisting of two particles and two antiparticles of the same mass. The scalar particles and antiparticles interact via a massive or massless mediating scalar field. The ground state energy solutions of Fock-space variational trial states ((|N{bar {N}}N{bar {N}}{ rangle }+|N{bar {N}}N{bar {N}}N{bar {N}rangle })) of the relativistic wave equations have been studied. We have compared these results with the previous work of four-body system (variational trial states of the form (|N{ bar {N}}N{bar {N}}{rangle })) and we have shown that the inclusion of virtual pairs has a noticeable effect at low coupling and at high coupling the energy of the system is changed by an important amount. In other words, the calculations show that the inclusion of virtual pairs augments the binding energy of the four-body system by a substantial amount at strong coupling. This study can pave the way for some new ideas in order to investigate the effect of virtual pairs, for example, for a bound-states quark-antiquark or tetraquark systems in future.