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This work presents a nonperturbative investigation of relativistic bound states with spin $(1/2)^+$, described within an effective fermion–boson model featuring vector interaction (NORONHA et al.,2023). The system, formulated as a quark–diquark approximation to the proton, is analyzed through the homogeneous Bethe–Salpeter equation, which is solved in Minkowski space for different covariant gauge choices. The bound-state dynamics is treated within a one-particle-exchange ladder kernel, employing free propagators and pointlike vertices. The solution of the equation is made possible by the use of the Nakanishi Integral Representation combined with light-front projection, leading to a set of coupled integral equations for the Nakanishi weight functions associated with the Bethe–Salpeter amplitude. The ultraviolet behavior of the model is examined in detail, revealing the emergence of scale invariance, particularly in the chiral limit. Within this framework, we analyze how the choice of gauge affects the critical value of the coupling constant, observing an increase when moving from the Feynman gauge to the Landau gauge. In addition, the asymptotic properties of the light-front amplitudes are investigated, as well as the dependence of the eigenfunction structure on transverse momentum and longitudinal momentum fraction, providing a characterization of the bound state in the high-momentum regime.
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