Abstract
We consider both "bottom-up" and "top-down" approaches to the origin of gauge kinetic mixing. We focus on the possibilities for obtaining kinetic mixings $\epsilon$ which are consistent with experimental constraints and are much smaller than the naive estimates ($\epsilon \sim 10^{-2} - 10^{-1}$) at the one-loop level. In the bottom-up approach, we consider the possible suppression from multi-loop processes. Indeed we argue that kinetic mixing through gravity alone, requires at least six loops and could be as large as $\sim 10^{-13}$. In the top-down approach we consider embedding the Standard Model and a $U(1)_X$ in a single grand-unified gauge group as well as the mixing between Abelian and non-Abelian gauge sectors.
Highlights
While we can be quite certain of the existence of dark matter (DM), we can with equal certainty claim that we have no idea as to the nature or identity of the dark matter, as it pertains to its connection to fundamental particle physics
Because simple dark matter candidates such as a fourth generation heavy neutrino with mass of order a few GeV, or the lightest supersymmetric particle such as a neutralino with mass of order a few hundred GeV, have been excluded, and severely constrained, a plethora of dark matter candidates have arisen with varying degrees of simplicity
There are many theories with a presumed stable dark matter candidate which has no Standard Model (SM) gauge interactions, and instead carries a charge under some hidden sector gauge group which is often assumed to be Uð1ÞX. This opens up the possibility that the gauge field associated with the hidden Uð1ÞX, can have a kinetic mixing term with the SM photon
Summary
While we can be quite certain of the existence of dark matter (DM), we can with equal certainty claim that we have no idea as to the nature or identity of the dark matter, as it pertains to its connection to fundamental particle physics This is not because of the lack of options, but rather due to a great multitude of possibilities for DM. Given the lack of a clear top-down preference for DM, an alternative approach has been pursued in recent years, that consists of investigating simple UV-complete theories of particle DM This approach has led to the concept of “dark sectors,” which include the DM particles and. Constrained only by the fundamental principles of gauge invariance, anomaly cancellation etc., such an approach leaves many possibilities open, and usually does not predict the strength of the interaction from first principles. Assuming that the kinetic mixing vanishes at a high scale and there are fields charged under both Uð1Þ’s, the Feynman diagram in Fig. 1 yields the well-known result [26,27]
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