Searching Hidden-sector Photons inside a Superconducting Box

Abstract

We propose an experiment to search for extra "hidden-sector" U(1) gauge bosons with gauge kinetic mixing with the ordinary photon, predicted by many extensions of the Standard Model. The setup consists of a highly sensitive magnetometer inside a superconducting shielding. This is then placed inside a strong (but sub-critical) magnetic field. In ordinary electrodynamics the magnetic field cannot permeate the superconductor and no field should register on the magnetometer. However, photon -- hidden-sector photon -- photon oscillations would allow to penetrate the superconductor and the magnetic field would "leak" into the shielded volume and register on the magnetometer. Although this setup resembles a classic ``light shining though a wall experiment'' there are two crucial differences. First, the fields are (nearly) static and the photons involved are virtual. Second, the magnetometer directly measures the field-strength and not a probability. This improves the dependence of the signal on the kinetic mixing chi (\ll 1) to chi^2 instead of chi^4. For hidden photon masses in the range 0.002-200 meV the projected sensitivity for the mixing parameter lies in the 5 10^-9 to 10^-6 range. This surpasses current astrophysical and laboratory limits by several orders of magnitude -- ample room to discover new physics.

Figures (3)

• Figure 1: Current bounds on hidden-sector photons from Coulomb law tests Williams:1971msBartlett:1988yy (yellow), searches of solar hidden photons with the CAST experiment (purple) Popov:1991Popov:1999Andriamonje:2007ewRedondo:2008aa and light-shining-through-walls (LSW) experiments Cameron:1993mrRobilliard:2007bqChou:2007zzAhlers:2007rdAhlers:2007qf (grey) as well as CMB measurements of the effective number of neutrinos $\Delta N^{\rm eff}_{\nu}$ and the blackbody nature of the spectrum (black) Mangano:2006urIchikawa:2006vmKomatsu:2008hkJaeckel:2008fi. Improvements of the solar bounds can be achieved using the SuperKamiokande detector or upgrading the CAST experiment Gninenko:2008pz. The region $m_{\gamma^{\prime}}\lesssim 1\, {\rm meV}$ could be tested by an experiment using microwave cavities Jaeckel:2007ch. The lightly shaded areas bounded by lines give the projected sensitivity for the experiment proposed in this note. The blue area corresponds to a relatively conservative estimate for the magnetometer sensitivity ${\mathbf{B}}_{\rm{detect}}\sim 10^{-14}\,{\rm T}$, and a thickness of the shielding $d\sim 0.1\,{\rm mm}$ -- much greater than the theoretical minimum required to have sufficient shielding --, an external field of ${\mathbf{B}}_{0}=0.05\, {\rm T}$ is assumed. The red area is an optimistic scenario, ${\mathbf{B}}_{\rm{detect}}\sim 5\,10^{-18}\,{\rm T}$, $d\sim 50\,\lambda_{\rm Lon}\sim 1\mu{\rm m}$ and ${\mathbf{B}}_{0}=0.2\,{\rm T}$. (For both scenarios we used $L_{1}=10\,{\rm cm}$ for the distance from the magnetic field source to the shield and $L_{2}=5\,{\rm cm}$ for the distance from the shield to the magnetometer.)
• Figure 2: Sketched setup for the experiment proposed in this note. Ordinary magnetic fields are shielded by the superconductor. However, if a hidden U(1) field mixes with the ordinary electromagnetic field some of the magnetic field can convert into a hidden magnetic field, pass through the superconductor and reconvert into an ordinary magnetic field inside the shielding. This field can then be measured by a highly sensitive magnetometer.
• Figure 3: Dependence of the magnetic field ${\mathbf{B}}$ (blue) and hidden magnetic field ${\mathbf{B_{hid}}}$ (red) as a function of the distance from the source ($x_1$) in our 1-dimensional set up. Both quantities are normalized to the value ${\mathbf{B}}_0$. The dotted line represents the evolution of ${\mathbf{B}}$ in absence of the hidden field ($\chi\rightarrow 0$). Near the external (left) surface of the superconducting shield ${\mathbf{B_{hid}}}$ changes sign, from negative to positive. For better visibility we have chosen not too extreme values $\chi=10^{-4}$, $m_{\gamma^{\prime}} L_1=m_{\gamma^{\prime}} L_2=5$, $m_{\gamma^{\prime}} d=1$ and $23\, m_{\gamma^{\prime}} = M_{\rm Lon}$. For $m_{\gamma^{\prime}} d \ll 1\ll L_{1,2}m_{\gamma^{\prime}}$ the evolution approaches $\chi^2$, but for the chosen parameters the result is a bit smaller because the hidden field is a bit damped inside the shielding due to $m_{\gamma^{\prime}} d=1$.