Abstract
We address the issue of radiative corrections to Kaluza-Klein (KK) masses in five-dimensional QED supplemented by aether Lorentz-violating terms. Specifically, we compute the corrections to the KK photon masses from one fermion loop. In general, the KK masses receive radiative corrections due to breaking the five-dimensional Lorentz invariance by compactification. As we show, the presence of the additional Lorentz violating factor - an aether background, leads to the non-trivial modification of these corrections. This model may be of interest in addressing important phenomenological issues such as the relation between radiative corrected KK mass splitting of a particular mode and uncertainties in the measurements and/or possible spatial variation of the fine-structure constant. For the recent data on the fine-structure constant, we find a KK mass splitting of magnitude $\sim 0.01$ MeV for the first excited Kaluza-Klein gauge boson at TeV scale. On the other hand, the large KK modes limit displays a very interesting phenomenon, showing the very special role of the aether in protecting the higher modes from the quantum corrections.
Highlights
In [3], this issue was addressed by considering the one-loop radiative corrections to KK masses in five- and six-dimensional theories. Such a computation has been shown to produce a finite result since the nontrivial winding number contributions to Feynman loop diagrams are well defined and cutoff independent even if higher dimensional theories are not renormalizable. Because this exactly corresponds to the part of loop diagrams that leads to the violation of the five-dimensional Lorentz invariance induced by the presence of a compact dimension, it contributes to the correction of the KK masses. (See [4] for a comprehensive study on Lorentz violation in extra dimensions and [5,6] for the further study of phenomenology of a simple KK model with the improved one-loop mass spectrum.) On the other hand, for the zero winding number, i.e., for the short-distance physics, the contribution to loop diagrams is Lorentz invariant
In the present study we have considered the aether compactification in a five-dimensional quantum electrodynamics
The aether compactification modifies the mass spacing between different Kaluza-Klein states as a consequence of the interaction with the aether field aligned along the compact fifth dimension
Summary
Such a computation has been shown to produce a finite result since the nontrivial winding number (corresponding to the compactification) contributions to Feynman loop diagrams are well defined and cutoff independent even if higher dimensional theories are not renormalizable Because this exactly corresponds to the part of loop diagrams that leads to the violation of the five-dimensional Lorentz invariance induced by the presence of a compact dimension (as probed by IR or large-distance physics), it contributes to the correction of the KK masses. The main goal of the present study is to investigate the one-loop radiative corrections to the KK masses in the Lorentz-violating five-dimensional QED (QED5) extended by a vector (aether) field with expectation value aligned along the extra dimension To this end, we apply the subtraction prescription introduced in [3] and briefly summarized above.
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