  We consider unitarity and causality in a higher-derivative theory of infinite
order, where propagators fall off more quickly in the ultraviolet due to the
presence of a transcendental entire function of the momentum. Like Lee-Wick
theories, these field theories might provide new avenues for addressing the
hierarchy problem; unlike Lee-Wick theories, tree-level propagators do not have
additional poles corresponding to unobserved particles with unusual properties.
We consider microscopic acausality in these nonlocal theories. The acausal
ordering of production and decay vertices for ordinary resonant particles may
provide a phenomenologically distinct signature for these models.
