  A series of relativistic one-boson-exchange potentials for two-nucleon
system, denoted as OBEP$\Lambda$, is constructed with a momentum cutoff
$\Lambda$ ranging from $\infty$ to 2 fm$^{-1}$. These potentials are developed
by simultaneous fitting to nucleon-nucleon ($NN$) scattering phase shifts,
low-energy scattering length, effective range, and the binding energy of the
deuteron. The momentum-space matrix elements of the low-momentum OBEP$\Lambda$
($\Lambda\leqslant 3$ fm$^{-1}$) demonstrate consistency with the universal
behaviors observed in other realistic $NN$ potentials evolved by
renormalization group methods. These OBEP$\Lambda$s are applied to calculate
the equation of state of symmetric nuclear matter (SNM) within either the
nonrelativistic (NR) Brueckner-Hartree-Fock (BHF) or relativistic
Brueckner-Hartree-Fock (RBHF) frameworks. The results show that the saturation
properties of SNM are reproduced qualitatively from the RBHF calculation, but
not from the NR-BHF calculation. This study highlights the relativistic
mechanism in explaining the saturation properties of nuclear matter. The
remaining discrepancy in reproducing empirical saturation properties in the
RBHF calculation using the OBEP$\Lambda$s signals the necessity of including
three-nucleon correlations or genuine three-nucleon forces.
