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

TL;DR

This work studies a vector-portal dark sector where a kinetically mixed dark photon $U$ couples to the SM and to a stable DM particle $\\chi$, across visible and invisible decay channels. By extending the PHSD transport approach to include $U$ production and decay into dileptons, it derives heavy-ion-based limits on the kinetic mixing $\\varepsilon^2$ and couples these to cosmological relic-density targets and velocity-dependent SIDM constraints computed with CLASSICS and ReD-DeLiVeR. The analysis maps viable regions in the $(m_\\chi,m_U)$ plane for Dirac, Majorana, and complex-scalar DM, highlighting that a sub-GeV mediator with $m_U<2m_\\chi$ and $m_U>2m_e$ is particularly favorable when all constraints are combined, while invisible decays tighten the allowed relic-density parameter space. The work provides a unified framework linking high-energy heavy-ion observables with early-Universe freeze-out and astrophysical structure, identifying benchmark scenarios that can guide future experimental searches and cross-disciplinary tests of dark-sector models.

Abstract

We investigate a dark sector coupled to the Standard Model (SM) through a kinetically mixed dark photon $U$ associated with a new $U(1)'$ gauge symmetry. Kinetic mixing $\varepsilon$ induces an effective coupling to the electromagnetic current, while $U$ interacts with stable dark matter (DM) $χ$ via a dark gauge coupling $g_χ$. Our analysis is based on the parton-hadron-string dynamics (PHSD) transport approach, extended to include dark photon production and decay into dileptons ($U\!\to e^+e^-$). In PHSD, dark photons are produced in high-energy collisions through Dalitz decays of light mesons ($π^0,η,η',ω$), Delta-resonances ($Δ\!\to N U$), direct vector meson decays ($ρ,ω,φ\!\to U$), kaon decays, and $q\bar q\!\to U$ annihilation. Building on previous PHSD benchmarks against dilepton data, we extract upper limits on $\varepsilon^2(m_U,m_χ,α_χ)$ in both the visible regime ($m_U<2m_χ$), where $U\!\to e^+e^-$ dominates, and the invisible regime ($m_U>2m_χ$), where $U\!\toχ\barχ$ is kinematically open. Cosmological and astrophysical constraints are incorporated in two complementary ways. First, we compute the velocity-dependent self-interaction cross section $σ/m_χ$ 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 $Ω_{\rm DM}h^2\simeq 0.12$, consistent with \textit{Planck} measurements of the cosmic microwave background. Combining PHSD limits on $\varepsilon^2$ with relic density and self-interaction requirements, we exclude regions of the $(m_χ,m_U)$ 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.

Figures (8)

• Figure 1: Branching fraction $\mathrm{Br}(U\to e^{+}e^{-})$ as a function of the mediator mass $m_{U}$ and the dark matter mass $m_{\chi}$ for $\alpha_{\chi}=0.1$, shown for three benchmark dark matter candidates: a Dirac fermion (left), a Majorana fermion (center), and a complex scalar (right). A sharp drop occurs along the kinematic threshold $m_{U}=2m_{\chi}$, where the invisible decay $U\to\chi\bar{\chi}$ (or $U\to \varphi\varphi^\dagger$) opens and rapidly dominates the total width. Below threshold ($m_{U}<2m_{\chi}$), decays proceed exclusively into standard model final states and the dileptonic branching fraction remains close to unity, modulated by hadronic contributions near the $\rho$, $\omega$, and $\phi$ resonances. Differences among the three panels reflect the distinct spin structures and threshold behaviour of the invisible partial width $\Gamma_{\rm inv}$ for fermionic and scalar dark matter. The visible widths are taken from Ref. Ilten:2015hya, while $\Gamma_{\rm inv}$ is computed from Eqs. (\ref{['eq:width_dirac']})-(\ref{['eq:width_scalar']}).
• Figure 2: Branching fractions of the dark photon $U$ as a function of its mass $m_{U}$ in the visible and invisible regimes. Left: visible regime, $m_{U}<2m_{\chi}$, where decays into the dark sector are kinematically forbidden and the total width is shared among standard model final states. We show $U\!\to e^{+}e^{-}$ (solid blue), $U\!\to\mu^{+}\mu^{-}$ (dashed blue), $U\!\to\tau^{+}\tau^{-}$ (dotted green), the inclusive hadronic mode (solid green), and the exclusive $\pi^{+}\pi^{-}$ channel (dotted red). Right: invisible regime for fermionic dark matter, illustrated for $R\equiv m_{U}/m_{\chi}=3$ and $\alpha_{\chi}=0.05$. In this benchmark the invisible decay $U\!\to\chi\bar{\chi}$ (solid black) dominates over most of the mass range, while the standard model channels retain the same threshold and resonance structure as in the visible case but are globally suppressed. Prominent QCD resonances ($\rho$, $\omega$, $\phi$, …) produce localized features in the hadronic curves and induce corresponding dips and peaks in the leptonic branching fractions. The visible (hadronic and leptonic) widths entering $\Gamma_{\rm vis}(m_U)$ are taken from Ref. Ilten:2015hya, while $\Gamma_{\rm inv}$ is computed from Eqs. (\ref{['eq:width_dirac']})-(\ref{['eq:width_scalar']}).
• Figure 3: Upper limits on the kinetic–mixing parameter for visible and invisible dark photon decays, $\varepsilon^{2}_{\rm vis}(m_U)$ (left) and $\varepsilon^{2}_{\rm inv}(m_U)$ (right), obtained from PHSD fits to dilepton spectra in $p+p$ at $E_{\rm lab}=$ 3.5 AGeV (brown), $Au+Au$ at $E_{\rm lab}=$ 1.23 AGeV (orange), $p+Nb$ at $E_{\rm lab}=$ 3.5 AGeV (blue), and $Ar+KCl$ at $E_{\rm lab}=$ 1.76 AGeV (red). We assume a Dirac fermion as the dark matter candidate for the invisible kinetic mixing. For comparison, the left panel includes existing exclusion limits from HADES, HPS, NA62, NA64, APEX, A1, KLOE, BaBar, LHCb, FASER, NuCal and CMS Fabbrichesi:2020wbtIlten:2018crw, while the right panel shows the leading invisible search bounds from NA64, E787/E949, BaBar and BESIII BaBar:2017tizBESIII:2022owwCrivelli:2023pxa. Horizontal green lines indicate benchmark values $\varepsilon^{2}=10^{-7}$ (dot dashed) in the left panel, and $\varepsilon^{2}=10^{-6}$ (dotted) in the right panel. PHSD curves correspond to surplus parameters $C_U$ as indicated in the legends: $C_U=0.1\%$ for all systems, with additional curves for $C_U=10\%$ in $p+p$ at $E_{\rm lab}=$ 3.5 AGeV (both panels) and $C_U=0.05\%$ in $p+Nb$ at $E_{\rm lab}=$ 3.5 AGeV (left panel). A Dirac fermion has been used as a DM candidate.
• Figure 4: Invisible decay constraints on the kinetic mixing parameter, $\varepsilon_{\rm inv}^{2}(m_U,m_\chi,\alpha_\chi)$, obtained from PHSD for $p+Nb$ collisions at $E_{\rm lab}=$ 3.5 AGeV with surplus parameter $C_{U}=0.1\%$, assuming a Dirac fermion as dark matter candidate. The vertical axis shows the upper limit on $\varepsilon_{\rm inv}^{2}$ as a function of the mediator mass $m_{U}$, while the coloured bands illustrate the impact of varying the dark coupling $\alpha_{\chi}$ and the mass ratio $m_{U}/m_{\chi}$. The blue band corresponds to $m_{U}=3m_{\chi}$ with $\alpha_{\chi}$ varied between $0.05$ and $0.5$. The red band shows $\alpha_{\chi}=0.1$ for two representative mass ratios, $m_{U}/m_{\chi}=2.1$ and $10$, and the green band displays the analogous variation for $\alpha_{\chi}=0.05$. Existing invisible search bounds from NA62, NA64, E787/E949, BaBar, and BESIII BaBar:2017tizBESIII:2022owwCrivelli:2023pxa are shown as hatched filled regions. Horizontal grey lines indicate reference values $\varepsilon^{2}=10^{-6}$ (dotted) and $10^{-7}$ (dot-dashed).
• Figure 5: Velocity-averaged momentum-transfer cross section per unit mass, $\langle \sigma v \rangle/m_\chi$, as a function of the mean relative velocity $\langle v\rangle$, for Yukawa-mediated SIDM with a dark-photon mediator. We added the group/cluster constraints taken from Ref. Sagunski:2020spe for direct comparison. Grey diagonal dotted lines correspond to constant values of $\sigma/m_\chi$ multiplied by $\langle v \rangle$. Left: Dirac-fermion dark matter for three benchmark choices of $(m_\chi,m_U,\alpha_\chi)$ shown in the legend; solid (dashed) lines denote repulsive (attractive) interactions. Right: comparison between scalar and fermionic dark matter for the benchmark shown in the legend, again distinguishing repulsive (solid) and attractive (dashed) potentials. Blue and red points with error bars indicate the inferred interaction strengths for galaxy groups and clusters, respectively, as compiled in Ref. Sagunski:2020spe; in our combined analysis these points are used as a high-velocity viability band, effectively excluding significantly larger cross sections at group/cluster velocities. Grey diagonal lines correspond to constant values of $\sigma/m_\chi = 0.1,\,1,\,10$ and $100~\mathrm{cm^2\,g^{-1}}$. The orange band marks the approximate range $0.1 \lesssim \sigma/m_\chi \lesssim 10~\mathrm{cm^2\,g^{-1}}$ at $\langle v\rangle\sim 10$-$200~\mathrm{km\,s^{-1}}$ that is typically required to alleviate the core-cusp problem in dwarf and low-surface-brightness galaxies. All theory curves are computed with CLASSICSColquhoun:2020adl.