Search for Long-Lived Dark Photons from Dark Radiation at the LHC

This paper proposes a novel production mechanism for long-lived dark photons at the LHC via dark radiation from dark matter in $Z$ decays, demonstrating that this channel can dominate over conventional sources and enable dedicated detectors like FASER2, FACET, and MATHUSLA to probe previously inaccessible regions of parameter space consistent with the observed dark matter relic abundance.

The Gist

Imagine the Large Hadron Collider (LHC) as a massive, high-speed particle factory. Usually, when scientists smash protons together, they look for new particles by watching what flies out immediately. But some new particles are "shy" and "long-lived"—they travel a long distance before they finally reveal themselves. These are called Long-Lived Particles (LLPs).

This paper proposes a new, clever way to catch these shy particles, specifically a type called Dark Photons.

The Usual Way vs. The New Way

The Old Way (The "Streetlight" Search):
Traditionally, scientists look for Dark Photons coming from the debris of collisions, like pieces of broken glass (mesons) or sparks from a collision (bremsstrahlung).

• The Problem: This method is like trying to find a specific type of firefly in a forest using only a dim flashlight. If the firefly is too faint (small "kinetic mixing") or too heavy, the flashlight can't see it. The production and the visibility of these particles are tied together; if they are hard to make, they are also hard to see.

The New Way (The "Dark Radiation" Search):
The authors suggest a different source. They propose that the LHC produces a lot of Z bosons (heavy particles). Usually, these Z bosons decay into invisible "Dark Matter" particles (let's call them $\chi$).

• The Twist: As these Dark Matter particles zoom away, they don't just travel silently. They emit a burst of energy, like a runner shedding sweat or a car exhaust pipe emitting smoke. This "sweat" is the Dark Photon.
• The Advantage: This is a game-changer because the "sweat" (Dark Photon) is produced by a mechanism that is completely separate from how easily it can be seen.
  • Analogy: Imagine a factory that makes invisible robots ($\chi$). In the old model, the robots had to carry a tiny, weak flashlight ($\epsilon$) to be seen, so if the flashlight was weak, you couldn't see them. In this new model, the robots are made in huge numbers, and as they run, they naturally emit a bright flare (Dark Photon). Even if the flare's "visibility" is weak, the sheer number of robots running means we get a massive amount of flares to detect.

How It Works (The "Secret Ingredient")

For this to happen, the Dark Matter needs a way to talk to the Standard Model particles. The paper suggests a "messenger" particle: a heavy, colored scalar (let's call it $\Phi$).

• Think of $\Phi$ as a translator. It connects the invisible Dark Matter ($\chi$) to the heavy Top Quark (a known particle).
• Through a complex quantum loop (imagine a roundabout where particles swap places), this translator allows the Z boson to decay into Dark Matter pairs.
• Once the Dark Matter is moving, it radiates the Dark Photon.

Why This Matters for Detectors

The paper looks at three specific detectors designed to catch these long-lived particles: FASER2, FACET, and MATHUSLA. These are like specialized "sweat catchers" placed far away from the main collision point.

• The Result: Because the new "Dark Radiation" method produces so many Dark Photons, these detectors can see things they previously couldn't.
• The Reach: They can detect Dark Photons that are much heavier (up to 30 GeV) and much fainter (smaller kinetic mixing) than current methods allow.
• The Sweet Spot: This is especially true for "Forbidden Dark Matter," a scenario where the Dark Matter is just slightly lighter than the Dark Photon. In this case, the Dark Matter can't easily destroy itself, so it survives long enough to emit that "radiation" we are looking for.

The Bottom Line

The authors are saying: "Stop looking for Dark Photons only in the usual debris. Look for the 'exhaust' they emit when they are born from Z bosons."

By using this new production channel, the LHC's future detectors (FASER2, FACET, MATHUSLA) could potentially discover Dark Photons in regions of the universe that were previously invisible to us, solving a mystery about how Dark Matter interacts with our world. They have mapped out exactly where these detectors should look and how sensitive they need to be to find these hidden particles.

Technical Summary

Technical Summary: Search for Long-Lived Dark Photons from Dark Radiation at the LHC

Problem Statement
Conventional searches for dark photons ($A'$) at the Large Hadron Collider (LHC) rely on production mechanisms such as meson decays and proton bremsstrahlung. In these standard scenarios, both the production rate and the decay width of the dark photon scale with the square of the kinetic mixing parameter ($\epsilon^2$). This correlation limits sensitivity: small $\epsilon$ suppresses production, while large $\epsilon$ leads to prompt decays that escape detection by dedicated long-lived particle (LLP) experiments. Consequently, conventional searches are primarily sensitive to light dark photons ($m_{A'} \lesssim \text{GeV}$) with relatively large kinetic mixing. There is a need to probe regions of parameter space characterized by small $\epsilon$ and heavier dark photon masses, particularly those consistent with the observed dark matter (DM) relic abundance.

Methodology
The authors propose a novel production mechanism where dark photons are generated via "dark radiation" emitted from dark matter fermions ($\chi$) produced in $Z$ boson decays ($Z \to \bar{\chi}\chi$). The framework involves:

1. Model Construction: A dark sector containing a Dirac fermion DM candidate ($\chi$) charged under a broken $U(1)_D$ gauge symmetry, mediated by a dark photon ($A'$). To link the dark sector to the Standard Model (SM), a colored scalar mediator ($\Phi$) is introduced, coupling $\chi$ to the SM right-handed top quark ($t_R$).
2. Effective Interaction: The coupling between the $Z$ boson and the DM pair ($Z\bar{\chi}\chi$) is not tree-level but is generated radiatively at the one-loop level via diagrams involving the top quark and the scalar $\Phi$. This induces an effective vertex parameterized by form factors, dominated by the left-handed vector form factor $F_L$.
3. Production Mechanism: The process proceeds as $pp \to Z \to \bar{\chi}\chi$, followed by final-state radiation $\chi \to \chi A'$. Crucially, the production rate depends on the branching ratio $BR(Z \to \bar{\chi}\chi)$ and the dark radiation probability (governed by the dark gauge coupling $g_D$), while the visible decay of the $A'$ depends solely on the kinetic mixing $\epsilon$. This represents a parametric decoupling between production and decay, unlike conventional models.
4. Constraints and Relic Density: The study incorporates constraints from invisible $Z$ decays, monojet searches, direct detection (accounting for isospin violation), and Cosmic Microwave Background (CMB) observations. The thermal relic abundance is calculated using MicrOMEGAs, specifically focusing on the "forbidden" annihilation regime ($m_{A'} \gtrsim m_\chi$) where annihilation is Boltzmann-suppressed, allowing for larger $g_D$ values to satisfy relic density requirements.
5. Simulation: The authors simulate $10^5$ $Z$ boson events using MADGRAPH5 and MadSpin for $Z \to \bar{\chi}\chi$ decay, and PYTHIA 8 for dark photon radiation. They calculate detection probabilities for FASER2, FACET, and MATHUSLA, incorporating realistic detector geometries and kinematics.

Key Contributions and Results

• Enhanced Production: The study demonstrates that the dark radiation channel can dominate over conventional meson decay and bremsstrahlung sources across wide regions of parameter space, particularly for small $\epsilon$ and $m_{A'}$ well above the GeV scale.
• Detector Sensitivity:
  • FASER2: Projected to probe branching ratios $BR(Z \to \bar{\chi}\chi)$ down to $\sim 3 \times 10^{-5}$ for proper lifetimes $c\tau_{A'} \sim 4$ m. In the $(m_{A'}, \epsilon)$ plane, it can access masses up to $\sim 30$ GeV with $\epsilon \sim 10^{-7}$, significantly surpassing conventional limits restricted to $m_{A'} \lesssim 1$ GeV.
  • FACET: Offers sensitivity to $BR \sim 3 \times 10^{-7}$ and can test masses up to $\sim 40$ GeV with mixings as small as $\epsilon \sim 2 \times 10^{-10}$.
  • MATHUSLA: Due to its large fiducial volume and transverse geometry, it provides the strongest reach, probing $BR \sim 2 \times 10^{-7}$ at $c\tau_{A'} \sim 30$ m. It opens a large new region of parameter space at small $\epsilon$ and heavy $m_{A'}$ that is inaccessible to conventional production models and already excluded by beam-dump experiments for standard scenarios.
• Parameter Space Viability: The analysis identifies viable regions where the DM constitutes the total relic abundance (or a subcomponent), satisfying constraints from the invisible $Z$ width and direct detection. The "forbidden" DM scenario is highlighted as a natural mechanism to accommodate the large dark gauge couplings required to enhance the dark radiation yield.

Significance
The paper claims that this framework provides an efficient probe for long-lived dark photons that is complementary to traditional searches. By decoupling the production mechanism (governed by $Z$ decay and dark sector couplings) from the decay mechanism (governed by $\epsilon$), dedicated LLP detectors can access portions of the dark photon parameter space that are inaccessible in conventional models. Specifically, the authors assert that FASER2, FACET, and MATHUSLA can significantly surpass existing bounds, probing regions consistent with the observed dark matter relic abundance and extending sensitivity to higher masses and smaller kinetic mixings than previously thought possible at the LHC.