Constraints on Kinetic Mixing of Dark Photons from Dilepton Spectra

TL;DR

The paper investigates the kinetic mixing of dark photons with the SM via the vector portal, aiming to constrain $\varepsilon^2(M_U)$ by analyzing dilepton spectra from heavy-ion collisions across SIS–LHC energies. It extends the PHSD transport model to include dark-photon production through Dalitz decays, direct vector-meson decays, kaon decays, and $q\bar{q}$ annihilation, with $U\to e^+e^-$ decays feeding the dilepton channel. By comparing SM+U predictions to data with an allowed surplus $C_U$ in each dilepton-mass bin, the work derives upper limits on $\varepsilon^2(M_U)$ that vary with $M_U$ and collision energy, reproducing known exclusions at low masses but requiring increasingly stringent surpluses to satisfy latest LHC constraints for higher masses. The results underscore the utility of high-precision dilepton measurements in heavy-ion collisions as a competitive probe of dark photons and delineate the parameter space where future experiments can tighten bounds. Overall, the study provides a comprehensive, theory-driven framework to translate dilepton yields into robust kinetic-mixing limits across a broad mass range.

Abstract

Dark photons, the hypothetical gauge bosons associated with an additional $U(1)^{\prime}$ symmetry, can couple to Standard Model particles through a small kinetic mixing parameter $\varepsilon$ with the ordinary photon. This mechanism provides a portal between the dark sector and visible matter. In this study, we present a procedure to derive theoretical upper bounds on the kinetic mixing parameter $\varepsilon^2(M_U)$ by analyzing dilepton spectra from heavy-ion collisions across a broad energy range, from SIS to LHC energies. Our analysis is based on the microscopic Parton-Hadron-String Dynamics (PHSD) transport approach, which successfully reproduces the measured dilepton spectra in $p+p$, $p+A$, and $A+A$ collisions across the same energy range. Besides the dilepton channels resulting from interactions and decays of Standard Model particles (such as mesons and baryons), the PHSD has been extended to include the decay of hypothetical dark photons into dileptons, $U \to e^+ e^-$. The production of these dark photons occurs via Dalitz decays of $π^0$, $η$, $ω$, $η^{\prime}$, and $Δ$ resonances; direct decays of $ρ$, $ω$, and $φ$; the kaon mode $K^+ \to π^+ U$; and thermal $q\bar q$ annihilation in the quark-gluon plasma. Our results show that high-precision measurements of dilepton spectra in heavy-ion collisions provide a sensitive and competitive probe of dark photons in the MeV to multi-GeV mass range. Furthermore, we quantify the experimental accuracy required to constrain the remaining viable parameter space of kinetic mixing in dark photon scenarios.

Figures (7)

• Figure 1: Branching ratio $Br(U\!\to\!e^+e^-)$ as a function of the dark‐photon mass $M_U$ (GeV/$c^2$). Colored lines correspond to different theoretical predictions: the dispersive analysis of Batell Batell:2009yf (green dot–dash), the tuned $R$–ratio model of Liu Liu:2014cma (black dotted), the thermal‐production estimate of Fradette Fradette:2015xka (blue dashed), and the vector‐meson dominance fit of Ilten Ilten:2018crw (orange solid). The gray dashed line shows the analytic low‐mass approximation from Eq. (\ref{['Bree']}), which is only valid for $M_U\lesssim0.6\,$GeV/$c^2$.
• Figure 2: Branching ratios as a function of the dark photon mass for meson decays to dark photons ($U$-bosons) and subsequent dilepton decays. The left panel shows the branching ratios for mesons decaying into dark photons: $\pi^0 \to \gamma U$, $\eta \to \gamma U$, $\omega \to \pi^0 U$, $\eta' \to \gamma U$, and $K^+ \to \pi^+ U$. The right panel shows the branching ratios for meson decays into dark photons and subsequent dilepton decays: $\pi^0 \to \gamma U \to \gamma e^+ e^-$, $\eta \to \gamma U \to \gamma e^+ e^-$, $\omega \to \pi^0 U \to \pi^0 e^+ e^-$, $\eta' \to \gamma U \to \gamma e^+ e^-$, and $K^+ \to \pi^+ U \to \pi^+ e^+ e^-$. In both panels, the lines represent different meson decay channels. The kinetic mixing parameter $\varepsilon^2$ is set to 1.
• Figure 3: Dark photon yield spectra $\mathrm{d}N_{U}/\mathrm{d}M$ as a function of the invariant mass $M_{ee}$ (GeV/$c^2$) for minimum-bias Au+Au collisions at $\sqrt{s_{_{NN}}}=200\,$GeV, assuming a constant kinetic mixing parameter $\varepsilon^2=10^{-6}$. Colored lines indicate the contributions from individual production channels: $\pi^0\to\gamma U$ (light red), $\eta\to\gamma U$ (gray), $\omega\to\pi^0 U$ (green), $\eta'\to\gamma U$ (dark green), $\phi\to\eta U$ (magenta), $K^+\to\pi^+ U$ (brown), $\Delta\to N U$ (orange), $q\bar{q}\to U$ (dashed red), and the blue dashed line is the total sum.
• Figure 4: The PHSD simulations of the differential cross section $d\sigma/dM_{ee}$ for $e^+e^-$ production in $p+p$ (top left panel) and $p+Nb$ collisions (top right panel) at a beam energy of 3.5 AGeV. Additionally, the calculations provide the mass differential dilepton spectra $dN/dM$, normalized to the $\pi^0$ multiplicity, for $Ar+KCl$ collisions at 1.76 AGeV (bottom left panel) and for $Au+Au$ collisions at 1.23 AGeV (bottom right panel). These results are compared with experimental data from the HADES Collaboration. The light gray lines denote the SM channels included in the PHSD calculations. The HADES measurements are represented by solid dots: the $p+p$ data are taken from Ref. HADES:2011ab, $p+Nb$ results from Refs. HADES:2011jqbAgakishiev:2012vj, $Ar+KCl$ data from Ref. Agakishiev:2011vf, and $Au+Au$ data from Ref. HADES:2019auv. The various SM contributions to dilepton production in PHSD are illustrated by individual colored lines, with the specific channels indicated in the legend. Dileptons arising from $U \rightarrow e^+e^-$ processes, allowing for a 10% surplus over the total SM yield, are included. Dark photon contributions are categorized by their sources: Dalitz decays of $\pi^0$ (red), $\eta$ (black), $\Delta$ resonances (orange), $\omega$ (olive) and direct vector meson decays $\rho, \omega, \phi$ (magenta, dark yellow, purple) respectively. The combined yield from these decays is shown as a dashed blue line, while the total dilepton yield including both SM and dark photon contributions are represented by cyan dots. We used the HADES acceptance criteria, incorporating its mass and momentum resolution.
• Figure 5: The invariant mass spectra of dileptons produced in Au+Au collisions at $\sqrt{s_{NN}} = 27$ GeV (left panel) and $200$ GeV (right panel) are calculated using PHSD and compared to STAR experimental data Han:2024nzrSTAR:2024bpc and STAR:2015tnn respectively. The total dilepton yields predicted by the PHSD model are represented by solid blue lines, while the individual contributions from different production channels are detailed in the legends. The light gray lines denote the SM channels included in the PHSD calculations. Dark photon contributions are categorized by their sources: Dalitz decays of $\pi^0$ (red), $\eta$ (black), $\eta^{\prime}$ (gray), $\Delta$ resonances (orange), $\omega$ (olive), direct vector meson decays of $\rho, \omega, \phi$ (magenta, dark yellow, purple) respectively, $K^+$ decay (brown) and $q\bar{q}$ annihilation (dashed red). In addition, the solid lines reflect the inclusion of $U \rightarrow e^+e^-$ decays, allowing for a 10% surplus over the total SM yield. The combined yield from these decays is shown as a dashed blue line, while the total dilepton yield including both SM and dark photon contributions are represented by cyan dots. The STAR experimental data points are depicted as solid black dots. To facilitate a direct comparison, the theoretical calculations are adjusted to align with the STAR acceptance criteria, incorporating its mass and momentum resolution.