Combined constraints on dark photons from high-energy collisions, cosmology, and astrophysics

We investigate a dark sector coupled to the Standard Model (SM) through a kinetically mixed dark photon $U$ associated with a new $U(1{)}^{\mathrm{\prime }}$ gauge symmetry. Kinetic mixing $\epsilon$ induces an effective coupling to the electromagnetic current, while $U$ interacts with stable dark matter (DM) $\chi$ via a dark gauge coupling $g_{\chi }$. Our analysis is based on the parton-hadron-string dynamics (PHSD) transport approach, extended to include dark photon production and decay into dileptons ($U\text{\hspace{0.17em}⁣}\to e^{+}{e}^{-}$). In PHSD, dark photons are produced in high-energy collisions through Dalitz decays of light mesons (${\pi }^0,\eta ,{\eta }^{\mathrm{\prime }},\omega$), Delta-resonances ($\mathrm{\Delta }\text{\hspace{0.17em}⁣}\to NU$), direct vector meson decays ($\rho ,\omega ,\phi \text{\hspace{0.17em}⁣}\to U$), kaon decays, and $q\bar{q}\text{\hspace{0.17em}⁣}\to U$ annihilation. Building on previous PHSD benchmarks against dilepton data, we extract upper limits on ${\epsilon }^2(m_U,m_{\chi },{\alpha }_{\chi })$ in both the visible regime ($m_U<2m_{\chi }$), where $U\text{\hspace{0.17em}⁣}\to e^{+}{e}^{-}$ dominates, and the invisible regime ($m_U>2m_{\chi }$), where $U\text{\hspace{0.17em}⁣}\to \chi \bar{\chi }$ is kinematically open. Cosmological and astrophysical constraints are incorporated in two complementary ways. First, we compute the velocity-dependent self-interaction cross section $\sigma \mathrm{/}{m}_{\chi }$ for Yukawa-mediated SIDM and confront it with bounds from dwarf galaxies, galaxy groups, and clusters. Second, we determine thermal relic target curves by computing the relic abundance and requiring ${\mathrm{\Omega }}_{\mathrm{D}\mathrm{M}}{h}^2\simeq 0.12$, consistent with $\mathit{\text{Planck}}$ measurements of the cosmic microwave background. Combining PHSD limits on ${\epsilon }^2$ with relic density and self-interaction requirements, we exclude regions of the $(m_{\chi },m_U)$ plane for each DM realization (Dirac, Majorana, or complex scalar) and identify benchmark scenarios in which heavy-ion, cosmological, and astrophysical constraints are simultaneously satisfied.