Long-ranged spin-spin interaction of electron from unparticle exchange

Unparticles as recently suggested by H. Georgi are identities that are not constrained by dispersion relations but are governed by their scaling dimension, d. We show that their coupling to particles results in macroscopic interactions between matter. The interaction potentials are generally an inverse non-integral power of distance depending on d. This is totally different from known macroscopic forces. We use specifically the precisely measured long-ranged spin-spin interaction of electrons to constrain the unparticles couplings to the electron. For 1 < d < 1.5 the axial vector unparticle coupling is excluded; and for 1 < d < 1.3 the pseudoscalar and vector couplings are also ruled out. These bounds and the ones for other ranges of d exceed or are complementary to those obtained previously from exotic positronium decays. PACS: 12.90.+b, 14.80.-j, 12.38.Qk, 04.90.+e