Exotic spin-dependent interactions through unparticle exchange

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.