Solar constraints on hidden photons re-visited

TL;DR

Problem: quantify solar production of hidden photons via kinetic mixing and derive robust bounds on χ. Approach: combine thermal-field-theory calculations of HP self-energy with a kinetic-density-matrix treatment of photon-HP oscillations in a hot plasma, covering both longitudinal and transverse channels and resonant emission. Findings: the longitudinal channel is resonantly enhanced by a factor $omega_P^2/m^2$, yielding a solar bound $chi<4e-12$ eV/m for $m\lesssim 3$ eV; for larger masses the transverse channel and other stellar bounds apply; XENON10 and future experiments (ALPS-II) can probe solar HPs. Impact: strengthens stellar energy-loss limits in the sub-eV range and guides future laboratory and astrophysical searches for solar HPs.

Abstract

We re-examine solar emission of hidden photons gamma' (mass m) caused by kinetic mixing. We calculate the emission rate with thermal field theory methods and with a kinetic equation that includes "flavor oscillations" and photon absorption and emission by the thermal medium. In the resonant case both methods yield identical emission rates which, in the longitudinal channel, are enhanced by a factor w_P^2/m^2 (plasma frequency w_P) in agreement with An, Pospelov and Pradler (2013). The Sun must not emit more energy in a "dark channel" than allowed by solar neutrino measurements, i.e., not more than 10% of its photon luminosity. Together with the revised emission rate, this conservative requirement implies a bound χ<4\times 10^-12 eV/m for the kinetic mixing parameter. This is the most restrictive stellar limit below m ~ 3 eV, whereas for larger masses the transverse channel dominates together with limits from other stars. A recent analysis of XENON10 data marginally improves the solar limit, leaving open the opportunity to detect solar hidden photons with future large-scale dark matter experiments. Detecting low-mass hidden photons with the ALPS-II photon-regeneration experiment also remains possible.

Figures (4)

• Figure 1: Self-energy for hidden photons (curly lines) in a thermal medium by mixing with thermal photons of the medium (double line).
• Figure 2: Solar $^8$B neutrino flux. Yellow band: Measurements. Red band: Expectation in the presence of longitudinal HP emission for a solar model with new opacities (low $Z$). Green band: Same for old opacities (high $Z$). The vertical line corresponds to $L_{S_L}<0.1\,L_\odot$ (our adopted limit).
• Figure 3: Bounds on hidden photons. The solar energy-loss constraints in the L and T channels as well as the bounds based on horizontal branch (HB) stars and red giants (RG) were derived here. We also show the CAST Redondo:2008aa and recent XENON10 An:2013yua limits on solar HPs (see also Mizumoto:2013jyHorvat:2012yv) as well as limits from modifications of Coulomb's law Bartlett:1970js, distortions of the CMB spectrum Jaeckel:2008fi, the ALPS photon-regeneration experiment Ehret:2010mh, atomic spectroscopy Jaeckel:2010xx and from decays of relic dark matter HPs Pospelov:2008jkRedondo:2008ec. Also shown are prospects for the ALPS-II experiment Bahre:2013ywa.
• Figure 4: Flux at Earth of L-HPs in the limit $m\to 0$. For non-zero masses multiply with $\sqrt{1-m^2/\omega^2}$. The dashed line is the resonant flux based on the analytic arguments described in the text.