  Ultraviolet completions for axion-like particles (ALPs) lighter than the
neutral pion generically induce ALP-neutral pion mixing, and are therefore
sensitive to direct constraints on the mixing angle. For ALPs below the pion
mass, we demonstrate that strong and novel bounds on the ALP-pion mixing angle
can be extracted from existing rare pion decay data, measured by the PIENU and
PIBETA experiments.
