Bound states and fermiophobic unparticle oblique corrections to the photon

Abstract

We study the effects of fermiophobic scalar/pseudo-scalar oblique corrections on bound state energy levels in muonic atoms. To make the treatment sufficiently general, while including ordinary scalar and axion-like pseudo-scalar fields as special cases, we consider Unparticle scalar/pseudoscalar operators with couplings predominantly to photons. We derive the relevant vacuum polarization functions and comment on the functional forms of the Unparticle Uehling potentials for various scaling dimensions in the point nucleus and finite nucleus approximations. It is estimated that for an infra-red fixed point near the scale of electroweak symmetry breaking, in the low TeV range, and natural values for the model parameters, the energy shifts in the low-lying muonic lead transitions are typically of the order of a few times 0.1 eV to a few times 0.01 eV. The energy level structure of the Unparticle Uehling shifts are inferred using general methods for the scalar and pseudo-scalar cases and it is shown that the two cases contribute to the energy shifts with the same sign. It is shown that this conclusion is not changed even when scale invariance is broken and is in fact relatively insensitive to the scale at which it is broken. It is pointed out nevertheless that the estimated magnitude of the Unparticle Uehling shift (based on some natural values for the model parameters) is a factor of 1000 − 10000 below the discrepancy in QED/nuclear theory and precision muonic lead spectroscopy from about two decades ago. We briefly comment on scenarios where the Unparticle induced energy shift, if it exists, may be experimentally measurable. One possibility in this direction is if the UV-sector, from which the Unparticle sector arises, has a large number of fermions. Comments are also made on the possibility of further studying muonic atoms, as a probe for beyond-standard-model physics, in the context of forthcoming experiments, such as those probing lepton flavor violation through coherent muon-electron conversions. For completeness we explore some of the astrophysical and cosmological consequences of a fermiophobic scalar/pseudoscalar Unparticle sector. In the fermiophobic context we also estimate a minimum value for the conformal invariance breaking scale.