Hiding a Light Vector Boson from Terrestrial Experiments: A Chargephobic Dark Photon

1. Problem Statement

Light vector bosons are prime candidates for mediating interactions between the Standard Model (SM) and the dark sector. The two most studied scenarios are the Dark Photon ($A'$), which couples to the electromagnetic current ($J_{EM}$), and the $B-L$ boson, which couples to the difference between baryon and lepton numbers.

However, these models are subject to a vast array of constraints from terrestrial experiments (beam dumps, colliders, precision tests), astrophysics (supernova cooling), and cosmology ($\Delta N_{eff}$). The authors investigate a generalized model where a light vector boson $X_\mu$ couples to an arbitrary linear combination of the electromagnetic current and the $B-L$ current. The central question is: Is there a specific mixing angle where the vector boson evades the stringent constraints from terrestrial experiments that rely on couplings to charged leptons and protons?

2. Methodology

The authors employ a comprehensive phenomenological analysis within a low-energy effective field theory framework.

• Model Definition: The interaction Lagrangian is defined as a linear combination of currents:
  $$\mathcal{L}_{int} = g_X (\cos\phi J_{EM}^\mu + \sin\phi J_{B-L}^\mu) X_\mu$$
  where $\phi$ is the "dark mixing angle." The couplings to fermions ($x_f$) are derived as $x_f = Q_f \cos\phi + q_f \sin\phi$.
• The "Chargephobic" Limit: The authors focus on the specific angle $\phi = 3\pi/4$. At this angle, the couplings to the electron ($e$) and proton ($p$) vanish exactly at tree level ($x_e = 0, x_p = 0$). Consequently, the boson couples to neutrons ($n$) and neutrinos ($\nu$) but not to charged leptons or protons.
• Renormalization Group Evolution (RGE): The authors acknowledge that the mixing angle $\phi$ is not static; it runs with energy scale due to loop corrections. They calculate the RGEs for the couplings to determine how the "chargephobic" condition ($x_e \approx 0$) is maintained or broken at higher energies (relevant for colliders).
• Production and Decay Calculations:
  • Production: They generalize production mechanisms (Bremsstrahlung, Drell-Yan, Meson decays, Vector Meson Dominance) to include the $\phi$ dependence.
  • Decay: They calculate partial decay widths into SM fermions and hadrons, utilizing Vector Meson Dominance (VMD) for the hadronic sector below 2 GeV.
• Constraint Derivation:
  • Cosmology: They perform a full non-equilibrium evolution of the early universe (solving Boltzmann equations for $X$, $\nu$, $e$, and $\gamma$) to determine constraints on $\Delta N_{eff}$ and Big Bang Nucleosynthesis (BBN).
  • Astrophysics: They model Proto-Neutron Star (PNS) cooling using the Garching supernova simulations (SFHo and LS220 equations of state). They calculate the luminosity of $X$ emission via nucleon-nucleon bremsstrahlung and its absorption/re-emission, applying the Raffelt criterion.
  • Terrestrial Experiments: They recast constraints from beam dumps, colliders (LHCb, CMS, BaBar, KLOE), and neutrino experiments (COHERENT, CONUS+, TEXONO) using scaling factors based on the modified couplings and branching ratios.

3. Key Contributions

1. Identification of the Chargephobic Vector Boson: The paper rigorously defines and analyzes the "chargephobic" limit ($\phi = 3\pi/4$), demonstrating that it is the most weakly constrained anomaly-free vector boson coupling to flavor-independent currents.
2. Suppression of Terrestrial Constraints: The authors show that because most beam dump and collider experiments rely on $X \to e^+e^-$ or $X \to \mu^+\mu^-$ decays and production via electron/proton beams, these constraints effectively vanish for the chargephobic case.
3. Survival of Neutrino and Neutron Constraints: The paper establishes that constraints from neutrino-nucleus scattering (CE$\nu$NS), supernova cooling, and $\Delta N_{eff}$ remain robust because the chargephobic boson retains non-zero couplings to neutrons and neutrinos.
4. Resolution of B-L Tensions: The authors provide a refined calculation for $B-L$ vector boson constraints from SN1987A, resolving discrepancies in previous literature by including finite temperature effects and proper treatment of in-medium photon mixing.
5. Future Projections: They highlight that future experiments like SHiP (which can detect hadronic decays) and REDTOP are uniquely capable of probing the chargephobic parameter space, as they do not rely solely on leptonic decays.

4. Key Results

• Parameter Space Survival: For the chargephobic case ($\phi = 3\pi/4$), the vast majority of exclusion regions from terrestrial experiments (beam dumps, fixed targets, and most collider searches) disappear. The allowed parameter space is significantly larger compared to the Dark Photon or $B-L$ cases.
• Dominant Constraints:
  • Supernova (SN1987A): Remains a strong constraint for $m_X \lesssim 100$ MeV due to $X$ emission via neutron bremsstrahlung. Unlike the Dark Photon, $X$ decays almost exclusively to neutrinos, preventing the "fireball" constraints that apply to $e^+e^-$ decays.
  • Cosmology ($\Delta N_{eff}$): Provides strong constraints for small masses ($m_X \lesssim 10$ MeV) and couplings. The chargephobic boson heats the neutrino bath, increasing $N_{eff}$.
  • Neutrino Experiments (COHERENT/CONUS+): These provide the strongest terrestrial constraints. Since the boson couples to neutrons, it enhances Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS) rates.
• RGE Effects: While the tree-level coupling to electrons is zero, RGE running induces a small coupling ($x_e \sim \mathcal{O}(10^{-2})$) at high energies ($m_X \gtrsim 1$ GeV). This re-activates constraints from LHCb and CMS, but only in the high-mass region ($m_X > 1$ GeV).
• Branching Fractions: In the chargephobic limit, the branching fraction to charged leptons is negligible. For $m_X > 2m_\pi$, the dominant decay mode becomes hadronic ($X \to \pi^+\pi^-$), which is crucial for future detection strategies.
• Comparison with Other Models: The chargephobic model is found to be less constrained than $B-3L_\tau$ (which is heavily constrained by neutrino oscillation NSI) and Baryon Number models (constrained by anomalous processes).

5. Significance

This paper fundamentally shifts the landscape of light vector boson searches. It demonstrates that relying on charged lepton couplings is a "disaster" for experimental sensitivity if the new physics is chargephobic.

• Model Independence: It provides a model-independent framework showing that a significant portion of the parameter space for light vector bosons has been overlooked because it was assumed that couplings to electrons/protons were necessary for detection.
• Experimental Guidance: The results strongly motivate the development of experiments capable of detecting hadronic decays (like SHiP and REDTOP) and neutrino scattering (like future CE$\nu$NS detectors) rather than just electromagnetic showers.
• Astrophysical Robustness: It reinforces the importance of astrophysical and cosmological bounds as the primary "model-independent" constraints for light mediators that evade terrestrial detection.

In conclusion, the "Chargephobic Dark Photon" represents a viable, minimally constrained extension of the Standard Model that requires a paradigm shift in experimental search strategies, moving away from purely leptonic signatures toward hadronic and neutrino-based detection channels.