  We propose a new class of single-field scalar quantum field theories with
non-polynomial interactions leading to a two-point Green's function that can be
naturally continued beyond the naive cutoff scale. This provides a new prospect
for self-completing theories in the UV-domain. In our approach, the formal
power series for the scalar potential has a vanishing radius of convergence and
is defined through Borel resummation. We discuss concrete examples, among
others with a spectral function that vanishes at large momenta, potentially
leading to an asymptotically free theory. Finally, we give an outlook on future
research, with a view towards possible applications to inflation and gravity.
