Ultralight Dark Photons

• Ultralight dark photons are hypothetical spin-1 bosons with sub-eV masses and feeble kinetic mixing from an extra U(1)' gauge symmetry.
• They display unique in-medium suppression and resonance effects in plasma, governing the efficiency of photon-to-dark-photon conversion.
• Production via cosmic strings, dilaton-resonance, and defect-free models, along with astrophysical and laboratory constraints, offers concrete avenues for experimental tests.

Ultralight dark photons are hypothetical spin-1 bosons associated with an extra $U(1)'$ gauge group in theories beyond the Standard Model, characterized by a tiny (sub-eV) mass and feeble kinetic mixing with the visible photon. They are motivated as dark matter candidates and as potential mediators of new physics, with distinctive phenomenology in environments ranging from compact objects to laboratories and cosmology. Their dynamics, observable signatures, constraints, and production mechanisms have been extensively analyzed in recent theoretical and experimental research.

1. Theoretical Framework: Lagrangian and Mixing

The minimal extension introduces a dark photon $A'_\mu$ kinetically mixed with the Standard Model photon $A_\mu$. In the interaction basis, the relevant Lagrangian is

$$\mathcal{L} = -\tfrac14F_{\mu\nu}F^{\mu\nu} - \tfrac14F'_{\mu\nu}F'^{\mu\nu} - \tfrac12\,m_{A'}^2\,A'_\mu A'^\mu - \varepsilon\,m_{A'}^2\,A_\mu A'^\mu + j^\mu A_\mu$$

where

• $F_{\mu\nu}$ and $F'_{\mu\nu}$ are the field strengths,
• $m_{A'}$ is the dark-photon Proca mass,
• $\varepsilon$ is the kinetic-mixing parameter, $\varepsilon \ll 1$,
• $j^\mu = e n_e(r) v^\mu$ is the plasma current (only for the visible photon).

In a plasma of density $n_e$, ordinary photons acquire an effective mass $\omega_p(r)^2=4\pi\alpha_{\rm EM} n_e(r)/m_e$, while the dark photon remains decoupled from plasma effects (Cannizzaro et al., 24 Jun 2024).

2. Dispersion Relations and In-Medium Suppression

Local propagation in a plasma leads to a coupled mode structure governed by

$$i\,\frac{d}{dr_*} \begin{pmatrix} A_\gamma \ A_{A'} \end{pmatrix} = \frac{1}{2k(r)} \begin{pmatrix} m_\gamma^2(r) & -\varepsilon m_{A'}^2 \ -\varepsilon m_{A'}^2 & m_{A'}^2 \end{pmatrix} \begin{pmatrix} A_\gamma \ A_{A'} \end{pmatrix}$$

with diagonalization giving an in-medium mixing angle

$$\tan 2\theta(r) = \frac{2\varepsilon m_{A'}^2}{m_{A'}^2 - \omega_p^2(r)}$$

and resonance at $\omega_p(r_{\rm res}) = m_{A'}$.

The conversion probability from photon to dark photon is, near resonance,

$$P_{\gamma \rightarrow A'} \simeq \frac{\varepsilon^2 m_{A'}^4}{ [m_{A'}^2 - \omega_p^2(r)]^2 + (\omega \Gamma)^2 } \sin^2 \left( \frac{1}{2} \Delta k L \right )$$

and far from resonance (for $\omega_p \gg m_{A'}$),

$$P_{\gamma \rightarrow A'} \propto \left( \frac{\varepsilon m_{A'}}{\omega_p} \right )^2 \ll 1$$

This is termed in-medium suppression: dense plasma environments strongly quench photon$\leftrightarrow$dark photon conversion except in finely tuned resonant regions (Cannizzaro et al., 24 Jun 2024).

3. Ultralight Dark Photon Dark Matter Production Mechanisms

3.1 Cosmic String Networks

Near-global Abelian-Higgs cosmic string networks can efficiently radiate the longitudinal dark photon mode (would-be Goldstone) when $H > m_A$. The emission dominates up to the epoch $H \sim m_A$, yielding a near-monochromatic nonrelativistic population and correctly saturated cold dark matter abundance for $m_A \sim 10^{-22}\,$eV, provided the symmetry breaking scale $v \sim 10^{15-16}$ GeV (Long et al., 2019). Parametric estimates show

$$\Omega_A h^2 \simeq 0.12 \left( \frac{m_A}{10^{-13}\text{ eV}} \right )^{1/2} \left( \frac{\sqrt{\mu(t_*)}}{10^{14}\text{ GeV}} \right )^2 \left( \frac{\xi(t_*)}{16} \right )$$

where $\mu$ is the string tension and $\xi$ encodes the Hubble volume string density.

3.2 Dilaton-Resonance

An oscillating dilaton field $\phi$ coupled to the dark photon kinetic term can produce dark photons via a narrow Mathieu-type resonance, maximally efficient for $m_A = m_\phi / 2$, even for very small oscillation amplitudes. The predicted relic density is

$$\Omega_A h^2 \simeq 0.12 \left ( \frac{m_A}{10^{-17}\,\text{eV}} \right )^{1/2} \left ( \frac{\phi_{0,i}}{10^{16}\,\text{GeV}} \right )^2$$

and parameter space is open for $m_A$ down to $10^{-20}\,$eV, subject to CMB isocurvature and structure formation constraints (Adshead et al., 2023).

3.3 Defect-Free Nonminimal Models

Production via runaway scalar-induced tachyonic resonance can evade cosmic string constraints, allowing cold dark photons in regions accessible to future haloscope experiments. Here, delayed production ensures that the energy density $\rho_{A'}$ never restores $U(1)_D$ symmetry, and kinetic mixing $\epsilon$ can be as large as $10^{-10}$ for $m_{A'} \sim 10^{-15}$–$10^{-3}$ eV (Cyncynates et al., 2023).

4. Astrophysical and Laboratory Constraints

4.1 In-Medium Suppression in Astrophysical Environments

In plasma-rich systems such as accretion flows or interstellar environments ($n_e \sim 10^{-3}$–$10$ cm$^{-3}$, $\omega_p \sim 10^{-12}$–$10^{-10}$ eV), both superradiant growth and direct conversion are suppressed unless $m_{A'} \simeq \omega_p(r)$ locally (“resonance shells”). This quenching, $$\Gamma_{\rm sr}^{(\mathrm{plasma})} \simeq \Gamma_{\rm sr}^{(0)} (\varepsilon m_{A'}/\omega_p)^2$$, closes most of the superradiance window for $m_{A'} \lesssim 10^{-11}$ eV except for finely tuned regions (Cannizzaro et al., 24 Jun 2024).

4.2 Constraints from Radio Telescopes and Solar Observations

Resonant conversion in the solar corona and solar wind ($n_e \sim 10^6$–$10^{10}$ cm$^{-3}$, $\omega_p \sim 4 \times 10^{-8}$–$4 \times 10^{-6}$ eV, corresponding to 10–1000 MHz frequencies) and in terrestrial arrays (e.g. LOFAR, SKA) probes $\epsilon \lesssim 10^{-13}$–$10^{-16}$ in the $m_{A'}$ window $4 \times 10^{-8}$–$4 \times 10^{-6}$ eV (An et al., 2020, An et al., 2023).

Long integration times and high collecting area yield superior constraints: SKA phase 1 can achieve $\epsilon \sim 10^{-16}$ (100 h observation) over this region, outperforming laboratory haloscopes and CMB-distortion limits.

4.3 Sub-MHz Radio Constraints

In the sub-MHz regime ($m_{A'} \lesssim 2 \times 10^{-17}$ eV), dark inverse Compton scattering of cosmic-ray electrons with DPDM yields detectable excess background radiation. Observations from Explorer 43, RAE-2, and PSP set constraints $\epsilon \lesssim 2 \times 10^{-6}$ at $m_{A'} \sim 10^{-18}$–$10^{-17}$ eV, surpassing haloscope, fifth-force, and stellar cooling limits in the ultralight mass regime (Acevedo et al., 2 Jan 2025).

5. Phenomenology Around Compact Objects

Ultralight dark photons can undergo superradiant growth around rotating black holes, forming clouds if $m_{A'} M \ll 1$. The vacuum growth rate for the $\ell = m = 1$ mode scales as

$$\Gamma_{\rm sr}^{(0)} \simeq \frac{1}{48} a_* (m_{A'} M)^7 \frac{1}{M}$$

however, environmental in-medium suppression effectively quenches photon emission for $\omega_p \gg m_{A'}$.

Coherent electromagnetic signals (radio/X-ray lines) at $\nu \simeq m_{A'}/2\pi$ may arise only in low-density or cavity-like plasma regions. Non-observation of such lines provides constraints on $\epsilon$ complementary to laboratory bounds (Cannizzaro et al., 24 Jun 2024).

6. Cosmological Impact and Parameter Space

Ultralight dark photons, particularly in the $m \sim 10^{-27}$–$10^{-25}$ eV range, may behave as “early dark matter” during the pre-recombination universe ($z > 3000$), briefly taking a radiation-like equation of state ($w=1/3$), then redshifting as cold dark matter ($w=0$). This modifies the expansion rate and reduces the baryon acoustic oscillation (BAO) sound horizon, enabling a higher inference of the Hubble constant, $H_0 \simeq 73$ km s$^{-1}$ Mpc$^{-1}$, thus addressing the Hubble tension (Flambaum et al., 2019).

Parameter space for viable kinetic mixing is strongly bounded by defect-formation constraints (cosmic string network avoidance), especially in minimal models. In postinflationary scenarios, upper envelopes of the allowed region satisfy

$$\varepsilon_{\max}(m_{A'}) \sim 10^{-15}\left(\frac{m_{A'}}{10^{-12}\,\text{eV}}\right)^{-1/2}$$

and can rise to $10^{-13}$ with delayed production (Cyncynates et al., 18 Oct 2024).

7. Observational and Experimental Prospects

Current and proposed laboratory searches (haloscopes, LC circuits, dish antennas) and radio observatories (LOFAR, SKA, NOIRE, SunRISE) are sensitive to $10^{-16} \lesssim \varepsilon \lesssim 10^{-10}$ for $10^{-22}$–$10^{-7}$ eV dark photon masses. Astrophysical channels—CMB spectral distortions, black hole superradiance, stochastic gravitational wave backgrounds from strings—probe complementary regions of parameter space.

The distinctive phenomenology of ultralight dark photons, especially the in-medium suppression and resonance, sets unique experimental targets and closes many regions of theoretical parameter space, with future observational efforts poised to test large parts of the viable landscape.