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We consider a family of $\kappa$-Poincar\'e invariant scalar field theorieson 4-d $\kappa$-Minkowski space with quartic orientable interaction, that isfor which $\phi$ and its conjugate $\phi^\dag$ alternate in the quarticinteraction, and whose kinetic operator is the square of a$U_\kappa(iso(4))$-equivariant Dirac operator. The formal commutative limityields the standard complex $\phi^4$ theory. We find that the 2-point functionreceives UV linearly diverging 1-loop corrections while it stays free of IRsingularities that would signal occurrence of UV/IR mixing. We find that allthe 1-loop planar and non-planar contributions to the 4-point function are UVfinite, stemming from the existence of the particular estimate for thepropagator partly combined with its decay properties at large momenta, implyingformally vanishing of the beta-functions at 1-loop so that the couplingconstants stay scale-invariant at 1-loop.

$\kappa$-Poincar\'e invariant orientable field theories at 1-loop