Unparticle physics constraints from the hydrogen atom

Unparticle stuff has been proposed as an extension of the Standard Model of particle physics by including scale invariant fields. In the framework of effective field theory, it describes the low-energy limit of a so-called Banks-Zaks sector which exhibits scale invariance below an energy scale Λ_U. Unparticle fields are characterized by a non-integer canonical scaling dimension d_U, which leads to unusual properties like resembling a fractional number of (un)particles. The existence of unparticle stuff may be detected experimentally through the interaction with conventional matter. After a review on the unparticle theory and the static potential due to virtual unparticle exchange, we focus on its impact on hydrogen atom energy levels. We obtain the energy shift of the ground state by using Rayleigh-Schroedinger perturbation theory and compare it with experimental data. In this way, bounds on the energy scale Λ_U as a function of d_U are derived. Finally, we offer a comparison with existing constraints in literature like the lepton magnetic anomaly. For some parameter regimes, the hydrogen bound provides competitive results.