Parametrically enhanced hidden photon search

Many theories beyond the Standard Model contain hidden photons. A light hidden photon will generically couple to the Standard Model through a kinetic mixing term, giving a powerful avenue for detection using “light-shining-through-a-wall”-type transmission experiments with resonant cavities. We demonstrate a parametric enhancement of the signal in such experiments, resulting from transmission of the longitudinal mode of the hidden photon. While previous literature has focused on the production and detection of transverse modes, the longitudinal mode allows a significant improvement in experimental sensitivity. Although optical experiments such as ALPS are unable to take useful advantage of this enhancement, the reach of existing microwave cavity experiments such as CROWS is significantly enhanced beyond their published results. Future microwave cavity experiments, designed with appropriate geometry to take full advantage of the longitudinal mode, will provide a powerful probe of hidden-photon parameter space extending many orders of magnitude beyond current limits, including significant regions where the hidden photon can be dark matter.

Figure 1

Schematic setup of a microwave cavity search for hidden photons, designed to take advantage of the improved transmission of longitudinal hidden-photon waves, and give the largest possible signal field ${\overrightarrow{E}}_{\mathrm{rec}}\sim {ϵ}^2{m}_{{\gamma }^{\prime }}^2/{\omega }^2{\overrightarrow{E}}_{em}$. Optimizing the sensitivity requires only a slight modification of the setup proposed in [25, 26]: the $\overrightarrow{E}$-field of the driven emitter-cavity mode should point coherently in the direction of the receiver cavity.

Figure 2

The reach of cavity searches for hidden photons, taking advantage of the improved transmission of the longitudinal modes. The solid blue region is the published limit from the CROWS experiment [29], calculated using the results of [25]. The solid blue line shows the bound we obtain by reanalyzing the CROWS results, taking into account longitudinal hidden-photon modes. The dashed blue line shows the reach of a realistic future cavity experiment. See Sec. 6 for more details. The gray shaded regions show various preexisting astrophysical and laboratory constraints, compiled from Refs. [9, 34], while the gray dashed line shows the projected reach of the ALPS-II experiment [39].

Figure 3

(a) shows the radiation pattern from an oscillating electric dipole, which is similar to that from the emitter cavity shown on the right. Transverse modes are mainly emitted perpendicular to the dipole/emitter $E$-field, while the longitudinal hidden-photon mode is emitted mainly parallel to it. (b) examples of cavity setups that are (upper $\text{left}+\text{upper}$ right) and are not (upper $\text{left}+\text{lower}$ left) well designed to efficiently receive the longitudinal mode from the emitter (see Secs. 6a, 5b). The distinctive dependence of the signal on the orientation of the cavities is a useful way to distinguish a true signal from an unexpected field leakage.