Abstract
In the present work we study the effect of unparticle modified static potentials on the energy levels of the hydrogen atom. By using Rayleigh-Schr\"odinger perturbation theory, we obtain the energy shift of the ground state and we compare it with experimental data. Bounds on the unparticle energy scale $\Lambda_\mathcal{U}$ as a function of the scaling dimension $d_\mathcal{U}$ and the coupling constant $\lambda$ are derived. We show that there exists a parameter region where bounds on $\Lambda_\mathcal{U}$ are stringent, signalling that unparticles could be tested in atomic physics experiments.
Highlights
Unparticle physics is an extension of the Standard Model, consisting in the possibility of having a non-trivial scale invariant, yet undiscovered sector of particle physics.At first sight, unparticles appear as a generalization of neutrinos because they share the following properties: scale invariance and only very weak interaction with other fields
The unparticle field is controlled by a canonical scaling dimension dU which is in general a non-integer number
After a short review of the basic formalism of unparticle physics (Section 2), we present the calculation of the energy shift by a perturbative solution of the Schrödinger equation in the presence of an unparticle modified electrostatic potential (Section 3)
Summary
Unparticle physics is an extension of the Standard Model, consisting in the possibility of having a non-trivial scale invariant, yet undiscovered sector of particle physics. When the manifold topological dimension is 2, the un-spectral dimension turns out to be 2dU , i.e., it depends only on the scaling dimension dU This fact explains the complete “fractalizazion” of the event horizon of un-gravity black holes [19,20], as well as of metallic plates for the Casimir effect in the presence of an un-photon field [23]. In this paper we want to address one of the basic parameters of unparticle physics, i.e., the value of U , the typical energy scale of the theory. To achieve this goal, we consider the modifications of static potentials that emerge from virtual unparticle exchange.
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