Impacts of ALP on the Constraints of Dark Photon

Dark sector may exist and interact with Standard Model (SM) through the $U(1)$ kinetic mixing. Through this portal-type interaction, dark photon from dark sector couples to SM fermions, and may explain the discrepancy between experimental data and SM calculations on muon anomalous magnetic moment, muon $g-2$. However, current searches for dark photon impose stringent constraints on the mixing parameter $\varepsilon$ for various dark photon masses, excluding the favorite parameter space for muon $g-2$. In this paper, we study the case where a global $U(1)$ in dark sector is spontaneously broken, resulting a light pseudo-Goldstone, axion-like particle (ALP) $a$, which couples to dark photon and SM photon, $g_{aγγ’}$. Through this interaction, dark photon may decay into photon and ALP when this channel is kinematically allowed. As a result, the experimental constraints on dark photon change significantly, and dark photon is able to explain the muon $g-2$ anomaly when its mass is heavier than $10$ GeV.

💡 Research Summary

The paper investigates how the presence of an axion‑like particle (ALP) in the dark sector modifies existing experimental constraints on dark photons (γ′) that couple to the Standard Model (SM) via kinetic mixing. In the conventional dark‑photon framework, a kinetic‑mixing parameter ε governs the interaction between the dark photon and the SM electromagnetic current, leading to visible decays γ′→e⁺e⁻, μ⁺μ⁻, or hadrons. Numerous experiments—BaBar, NA48/2, NA64, LHCb, and various beam‑dump facilities—have placed stringent limits on ε across a wide mass range (1 MeV–100 GeV). These limits essentially exclude the region (ε≈10⁻³–10⁻⁴, m_{γ′}≲1 GeV) that would explain the long‑standing muon g‑2 anomaly.

The authors propose that the dark sector also possesses a global U(1) symmetry that is spontaneously broken, giving rise to a light pseudo‑Goldstone boson, the ALP (a). The ALP couples to both the SM photon and the dark photon through a dimension‑5 operator g_{aγγ′} a F_{μν} \tilde F′^{μν}. When kinematically allowed (m_{γ′}>m_a), the decay channel γ′→aγ opens, with a partial width Γ(γ′→aγ)=g_{aγγ′}² m_{γ′}³/(96π)(1−m_a²/m_{γ′}²)³. For m_{γ′}≫m_a this width scales as m_{γ′}³, quickly dominating over the ε‑suppressed SM fermion channels for masses above a few hundred MeV.

The paper first reviews the standard dark‑photon phenomenology, presenting analytic expressions for the leptonic (Eq. 2.2) and hadronic (Eq. 2.3) decay widths, and then introduces the new ALP‑induced width (Eq. 2.4). Figure 1 illustrates branching ratios for benchmark values ε=10⁻² and 10⁻³ with g_{aγγ′}=10⁻² GeV⁻¹. For ε=10⁻², the aγ mode dominates once m_{γ′} exceeds ~1 GeV; for ε=10⁻³, the transition occurs near 100 MeV. The authors also discuss limits on the product ε g_{aγγ′} from light‑shining‑through‑a‑wall experiments, noting that for very light dark photons (∼10⁻⁴ eV) the bound relaxes to ε g_{aγγ′}≲10⁻³ GeV⁻¹.

In Section 3 the authors compile existing constraints on the ε–m_{γ′} plane, emphasizing that all current limits are derived from searches for visible e⁺e⁻ pairs. Section 4 re‑derives these limits in the presence of the new decay channel. The observable event count N=L·σ_prod·BR·η is modified because (i) the production cross section still scales as ε², (ii) the branching ratio to e⁺e⁻ is reduced by the factor 1/(1+Γ(γ′→aγ)/Γ_tot^old), and (iii) the detector efficiency η, which depends on the dark‑photon lifetime, changes dramatically for beam‑dump experiments. By equating the expected number of events with and without the ALP, the authors obtain a relation ε_new²·BR_new·η_new≈ε_old²·BR_old·η_old, which they solve numerically for various values of g_{aγγ′}.

Figure 3 presents the resulting exclusion regions for g_{aγγ′}=10⁻⁵, 10⁻², 10⁻¹, and 1 GeV⁻¹. For modest couplings (10⁻⁵ GeV⁻¹) only a narrow band around m_{γ′}≈0.1 GeV in beam‑dump experiments is affected. As g_{aγγ′} increases to 10⁻² GeV⁻¹, the aγ decay dominates for m_{γ′}>10 MeV, causing the sensitivity of E137, ν‑CAL I, and similar experiments to disappear for ε≲10⁻⁴. For very large couplings (≥10⁻¹ GeV⁻¹) the aγ mode overwhelms all visible channels for m_{γ′}≳0.1 GeV, allowing ε as large as O(10⁻²) for m_{γ′}≳10 GeV. However, BaBar mono‑photon searches constrain g_{aγγ′}≳3×10⁻³ GeV⁻¹, limiting the viable parameter space below ~10 GeV. When g_{aγγ′} is taken to be ∼1 GeV⁻¹, even the LHCb and BaBar limits are essentially lifted, opening a broad region consistent with the muon g‑2 preferred band.

The authors conclude that the inclusion of an ALP dramatically reshapes the dark‑photon landscape. In particular, for heavy dark photons (m_{γ′}>10 GeV) the kinetic‑mixing parameter ε can be as large as a few percent while still evading all current bounds, thereby reviving the dark‑photon explanation of the muon g‑2 anomaly. They suggest that future searches at LHCb, Belle II, and dedicated beam‑dump experiments should target both ε and g_{aγγ′} simultaneously to fully test this scenario.