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The persistence of the hierarchy problem points to a violation of effectivefield theory expectations. A compelling possibility is that this results from aphysical breakdown of EFT, which may arise from correlations betweenultraviolet (UV) and infrared (IR) physics. To this end, we studynoncommutative field theory (NCFT) as a toy model of UV/IR mixing whichgenerates an emergent infrared scale from ultraviolet dynamics. We explore therange of such theories where ultraviolet divergences are transmogrified intoinfrared scales, focusing particularly on the properties of Yukawa theory,where we identify a new infrared pole accessible in the $s$-channel of theLorentzian theory. We further investigate the interplay between UV-finitenessand UV/IR mixing by studying properties of the softly-broken noncommutativeWess-Zumino model as soft terms are varied relative to the cutoff. While theLorentz violation inherent to noncommutative theories may limit their directapplication to the hierarchy problem, these toy models provide general lessonsto guide the realization of UV/IR mixing in more realistic theories.

IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem