  The potential discovery of unparticles could have far-reaching implications
for particle physics and cosmology. For over a decade, high-energy physicists
have extensively studied the effects of unparticles. In this study, we derive
six types of nonrelativistic potentials between fermions induced by unparticle
exchange in coordinate space. We consider all possible combinations of scalar,
pseudo-scalar, vector, and axial-vector couplings to explore the full range of
possibilities. Previous studies have only examined scalar-scalar (SS),
pseudoscalar-pseudoscalar (PP), vector-vector (VV), and axial-axial-vector (AA)
type interactions, which are all parity even. We propose SP and VA interactions
to extend our understanding of unparticle physics, noting that parity
conservation is not always guaranteed in modern physics. We explore the
possibilities of detecting unparticles through the long-range interactions they
may mediate with ordinary matter. Dedicated experiments using precision
measurement methods can be employed to search for such interactions. We discuss
the properties of these potentials and estimate constraints on several coupling
constants based on existing experimental data. Our findings indicate that the
coupling between vector unparticles and fermions is constrained by up to 9
orders of magnitude more tightly than the previous limits.
