Hidden sector photon coupling of resonant cavities

Many beyond the standard model theories introduce light paraphotons, a hypothetical spin-1 field that kinetically mixes with photons. Microwave cavity experiments have traditionally searched for paraphotons via transmission of power from an actively driven cavity to a passive receiver cavity, with the two cavities separated by a barrier that is impenetrable to photons. We extend this measurement technique to account for two-way coupling between the cavities and show that the presence of a paraphoton field can alter the resonant frequencies of the coupled cavity pair. We propose an experiment that exploits this effect and uses measurements of a cavity’s resonant frequency to constrain the paraphoton-photon mixing parameter $\chi$. We show that such an experiment can improve the sensitivity to $\chi$ over existing experiments for paraphoton masses less than the resonant frequency of the cavity, and that it can eliminate some of the most common systematics for resonant cavity experiments.

Figure 1

Numerical simulation of the absolute value of geometry factors as a function of the paraphoton mass ratio, $\mathrm{mr}=m_{\gamma \prime }/{\omega }_0$, for two identical cube cavities overlapping in space ($G_S$, full line) and separated by a distance of L ($G$, dashed line) where L is the length of the cubic cavities, in this case set to 1. The normalized resonant mode used is given by $A(\mathbf{x})=2\sin (\pi x)\sin (\pi y)$ and the resonant frequency is ${\omega }_0=\sqrt{2}\pi$ [19].

Figure 2

Log-log plot of resonant frequencies relative to a common central frequency ${\omega }_0$, as a function of detuning for a pair of cavities that are coupled [black solid line, Eq. (13)] and uncoupled [gray dashed line, ${\omega }_{1,2}/{\omega }_0=(1\pm x/2)$]. The detuning x is given as a factor of the square of the paraphoton kinetic mixing parameter, $\chi$. The magnitude of the fractional frequency shift is proportional to the values of parameters $Q_1$, $Q_2$, $G$, $G_S$ and $\chi$ used in Eq. (13).

Figure 3

Schematic of a rotating paraphoton coupled cavity experiment. The two empty cavities are separated by an impenetrable barrier (red plane) and actively driven at frequency $\omega$, although the resonant frequencies of the cavities may be slightly detuned (${\omega }_{+}$ and ${\omega }_{-}$). One cavity is rotated orthogonally to the other. The frequency of the stationary cavity is compared to a stable frequency reference (${\omega }_{\mathrm{REF}}$) to produce the beat frequency ($\delta \omega$).

Figure 4

Log-log plot of the normalized fractional resonant frequency shift due to paraphoton cavity coupling as a function of cavity frequency detuning and losses [from Eqs. (13, 14)]. Both the cavity frequency detuning $x$ and the cavity losses $Q^{-1}$ are given as a factor of ${\chi }^2$. The frequency shift is plotted as a function of $x$ (with $Q^{-1}=0$) and as a function of $Q^{-1}$ (with $x=0$); both curves overlap. The vertical gray dashed line indicates where the dependence of the frequency shift changes. In the first region the frequency shift is proportional to ${\chi }^2$, and in the second region it is proportional to ${\chi }^4$.