Fermionic bound states in Minkowski-space: Light-cone singularities and structure

Understand

The Bethe-Salpeter equation for two-body bound system with spin $1/2$ constituent is addressed directly in the Minkowski space.

• In order to accomplish this aim we use the Nakanishi integral representation of the Bethe-Salpeter amplitude and exploit the formal tool represented by the exact projection onto the null-plane.
• This formal step allows one i) to deal with end-point singularities one meets and ii) to find stable results, up to strongly relativistic regimes, that settles in strongly bound systems.
• We apply this technique to obtain the numerical dependence of the binding energies upon the coupling constants and the light-front amplitudes for a fermion-fermion $0^+$ state with interaction kernels, in ladder approximation, corresponding to scalar-, pseudoscalar- and vector boson exchanges, respectively.