Light-front spin-dependent spectral function and nucleon momentum distributions for a three-body system

Poincaré covariant definitions for the spin-dependent spectral function and for the momentum distributions within the light-front Hamiltonian dynamics are proposed for a three-fermion bound system, starting from the light-front wave function of the system. The adopted approach is based on the Bakamjian–Thomas construction of the Poincaré generators, which allows one to easily import the familiar and wide knowledge on the nuclear interaction into a light-front framework. The proposed formalism can find useful applications in refined nuclear calculations, such as those needed for evaluating the European Muon Collaboration effect or the semi-inclusive deep inelastic cross sections with polarized nuclear targets, since remarkably the light-front unpolarized momentum distribution by definition fulfills both normalization and momentum sum rules. Also shown is a straightforward generalization of the definition of the light-front spectral function to an $A$-nucleon system.