  The renormalization in a Lorentz-breaking scalar-spinor higher-derivative
model involving $\phi^4$ self-interaction and the Yukawa-like coupling is
studied. We explicitly de- monstrate that the convergence is improved in
comparison with the usual scalar-spinor model, so, the theory is
super-renormalizable, with no divergences beyond four loops. We compute the
one-loop corrections to the propagators for the scalar and fermionic fields and
show that in the presence of higher-order Lorentz invariance violation, the
poles that dominate the physical theory, are driven away from the standard
on-shell pole mass due to radiatively induced lower dimensional operators. The
new operators change the standard gamma-matrix structure of the two-point
functions, introduce large Lorentz-breaking corrections and lead to
modifications in the renormalization conditions of the theory. We found the
physical pole mass in each sector of our model.
