Gauge Coupling Unification with Hidden Photon, and Minicharged Dark Matter

Abstract

We show that gauge coupling unification is realized with a greater accuracy in the presence of a massless hidden photon which has a large kinetic mixing with hypercharge. We solve the renormalization group equations at two-loop level and find that the GUT unification scale is around $10^{16.5}$ GeV which sufficiently suppresses the proton decay rate, and that the unification is essentially determined by the kinetic mixing only, and it is rather insensitive to the hidden gauge coupling or the presence of vector-like matter fields charged under U(1)$_H$ and/or SU(5). Matter fields charged under the unbroken hidden U(1)$_H$ are stable and they contribute to dark matter. Interestingly, they become minicharged dark matter which carries a small but non-zero electric charge, if the hidden gauge coupling is tiny. The minicharged dark matter is a natural outcome of the gauge coupling unification with a hidden photon.