Probing displaced (dark)photons from low reheating freeze-in at the LHC

This paper proposes a low-reheating freeze-in dark matter model featuring a stable dark photon and a long-lived pseudo-scalar mediator, demonstrating that LHC searches for displaced photons from Higgs decays can effectively constrain the model's parameter space and exclude thermalized mediators consistent with observed relic abundance.

The Gist

The Big Picture: A Hidden World and a "Ghostly" Messenger

Imagine the universe is a massive, bustling city (the Standard Model). We know almost everything about the people living there: the buildings, the traffic, the laws of physics. But we also know there is a huge, invisible population hiding in the shadows called Dark Matter. We can't see them, but we know they are there because their gravity holds the city together.

This paper proposes a new theory about how this invisible population was born and how we might finally catch a glimpse of them at the Large Hadron Collider (LHC), the world's biggest particle accelerator.

The Cast of Characters

The authors introduce three new characters to their story:

1. The Dark Photon (The Invisible Ghost): This is the candidate for Dark Matter. It's a particle that has mass but doesn't interact with light or normal matter. It's like a ghost that walks through walls.
2. The Pseudo-Scalar (The Messenger): This is a special particle that acts as a bridge between our visible city and the invisible dark world. It's "long-lived," meaning it doesn't die immediately after being created. It travels a bit before disappearing.
3. The Higgs Boson (The Factory): In the Standard Model, the Higgs is a particle that gives others mass. In this story, the Higgs acts like a factory that occasionally produces pairs of these "Messenger" particles.

The Story of the "Low Reheating" Universe

Usually, scientists think the universe started very hot and dense, like a boiling pot of soup. As it cooled, particles formed. This paper suggests a different scenario: Low Reheating.

Imagine the universe didn't get as hot as we thought. It was more like a lukewarm bath.

• The Problem: In a lukewarm bath, it's very hard to cook a steak (create heavy particles). The energy just isn't there.
• The Solution: Because the universe was "cool," the particles couldn't be created easily. This actually helps the Dark Matter! If the universe were too hot, we would have made too much Dark Matter, and the universe would have collapsed. The "cool" temperature acts like a dimmer switch, keeping the production of Dark Matter just right.

The "Freeze-In" Mechanism

How did the Dark Matter get there if the universe was so cool?
Think of a crowded room where everyone is trying to sneak a cookie (Dark Matter) onto a plate.

• Thermal Equilibrium (The Old Way): Everyone is running around, grabbing cookies, and eating them until the plate is full and empty. This is too chaotic and creates too many cookies.
• Freeze-In (The New Way): The room is so cold and quiet that people barely move. A few cookies are slowly, very slowly, placed on the plate by a few people sneaking in. They never reach a "full" state; they just "freeze in" at a low, steady number. This paper argues that Dark Matter was created this way: slowly and quietly, never reaching a high-energy state.

The Detective Work at the LHC

So, how do we find these invisible ghosts? We can't see them directly. But we can see the Messenger.

1. The Setup: At the LHC, scientists smash protons together to create Higgs bosons.
2. The Decay: Sometimes, a Higgs boson decays into two Messengers.
3. The Travel: Because the Messenger is "long-lived," it doesn't vanish instantly. It travels a few meters inside the detector (like a slow-moving snail) before it decays.
4. The Clue: When the Messenger finally dies, it splits into two things:
   • A Dark Photon (The Ghost): It flies away invisibly, taking energy with it.
   • A Visible Photon (The Flash): A burst of light that hits the detector.

The "Non-Pointing" Trick:
Normally, when a particle decays, the light it emits points straight back to the center of the collision (the primary vertex). But because our Messenger traveled a few meters before dying, the light it emits points to a spot away from the center.

• Analogy: Imagine throwing a ball from a moving car. If you drop it immediately, it lands near the car. If you wait until the car drives 100 meters down the road before dropping it, the ball lands far away from the car.
• The LHC detectors look for these "misplaced" flashes of light. If they see a flash of light that doesn't point back to where the collision happened, plus a missing chunk of energy (the ghost), they have found a clue.

What the Paper Found

The authors did the math to see if this story makes sense:

1. Cosmology Check: They checked if this "cool universe" scenario fits with what we know about the early universe (like how the first elements formed). They found a "sweet spot" where the temperature was just right to create the exact amount of Dark Matter we see today.
2. The LHC Check: They simulated what the LHC would see if this theory were true. They found that current searches for "misplaced" photons are already powerful enough to test this idea.
3. The Result: They discovered that if the Messenger particle gets too "hot" (interacts too strongly with normal matter), it would have been created too early in the universe, breaking the "cool universe" story. The LHC data is already telling us that the Messenger must be very quiet and elusive.

The Conclusion

This paper connects two very different worlds: the history of the entire universe and the tiny experiments happening in a machine in Switzerland.

It suggests that Dark Matter might be a "ghost" that was born in a "cool" early universe, produced slowly by a "Messenger" particle. The best way to catch this ghost is to look for a flash of light that arrives late and points in the wrong direction at the LHC. The authors show that we are already looking in the right place, and the data is starting to tell us exactly how this hidden world works.

Technical Summary

Technical Summary: Probing Displaced (Dark) Photons from Low Reheating Freeze-in at the LHC

Problem Statement
The nature of dark matter (DM) and the thermal history of the early Universe remain open questions. While Big Bang Nucleosynthesis (BBN) constrains the Universe's history at temperatures above a few MeV, earlier epochs, particularly those involving low reheating temperatures ($T_{RH}$), remain largely unconstrained. Traditional freeze-in DM models assume high $T_{RH}$, requiring extremely small couplings that render them inaccessible to current experiments. However, scenarios with low $T_{RH}$ (potentially as low as $\mathcal{O}(4)$ MeV) allow for larger couplings, making them testable. A specific gap exists in models where a long-lived particle (LLP) mediator couples to both DM and the Standard Model (SM) without thermalizing, specifically in the context of displaced photon signatures at the Large Hadron Collider (LHC). Previous studies have not fully detailed the interplay between a non-thermalized mediator, low $T_{RH}$ freeze-in, and LHC constraints on displaced photons.

Methodology
The authors propose an extension of the Standard Model (SM) featuring a dark sector with a $U(1)'$ gauge symmetry. The model includes:

1. A stable dark vector boson ($A'_\mu$, denoted $\gamma'$) acting as the DM candidate.
2. A real pseudo-scalar field ($\phi$) acting as a mediator.
   Both fields are odd under a $Z_2$ symmetry, which forbids kinetic mixing between the dark photon and the SM hypercharge.

The interaction Lagrangian includes:

• A Higgs portal coupling ($\lambda_{HS} \phi^2 |H|^2$) connecting the pseudo-scalar to the SM.
• A dimension-five operator ($g_D \phi F'_{\mu\nu} \tilde{B}^{\mu\nu}$) connecting the pseudo-scalar to both the dark photon and the visible photon (via the SM hypercharge field strength).

The study focuses on the parameter space where $m_{\gamma'} < m_\phi < m_h/2$. In this regime, the Higgs boson can decay into pairs of pseudo-scalars ($h \to \phi\phi$), which subsequently decay into a dark photon and a visible photon ($\phi \to \gamma \gamma'$). If the decay length $c\tau_\phi$ is macroscopic (cm to m scale), this produces a "non-pointing" photon signature.

The methodology involves:

1. Cosmological Evolution: Solving coupled Boltzmann equations for the yields of $\gamma'$ and $\phi$ in a low reheating scenario ($T_{RH} \sim \mathcal{O}(1\text{--}5)$ GeV). The analysis considers two production regimes: non-thermal $\phi$ (freeze-in via Higgs portal followed by decay) and thermalized $\phi$ (freeze-out followed by decay, acting as a super-WIMP).
2. Collider Phenomenology: Reinterpreting ATLAS Run 2 data (139 fb$^{-1}$ at $\sqrt{s}=13$ TeV) searching for displaced photons. The authors simulate signal events for $pp \to h \to \phi\phi \to (\gamma\gamma')(\gamma\gamma')$ using MadGraph5_aMC@NLO, Pythia, and Delphes. They refine the calculation of the non-pointing variable $|\Delta z_\gamma|$ and apply specific selection cuts (lepton triggers, photon isolation, missing transverse energy, and displacement/time-delay cuts).
3. Constraint Synthesis: Combining limits from displaced photon searches, Higgs invisible decays, and Higgs decays to undetected particles to constrain the parameter space ($m_\phi, g_D, \lambda_{HS}, T_{RH}$).

Key Contributions

• Model Construction: The paper establishes a consistent DM scenario where the dark photon relic abundance is generated via freeze-in at low reheating temperatures, mediated by a pseudo-scalar that does not necessarily thermalize.
• Cosmological Dynamics: The authors map the yield evolution of the dark sector, identifying regions where the mediator $\phi$ thermalizes (leading to super-WIMP production) versus regions where it remains non-thermal. They demonstrate that for the correct relic abundance, a "golden window" of $T_{RH} \sim 3$ GeV is required to avoid overproduction.
• Collider Recasting: The study provides a detailed recast of the ATLAS displaced photon search, improving the simulation of the non-pointing variable and muon isolation. It derives explicit bounds on the Higgs portal coupling $\lambda_{HS}$ as a function of the dark photon portal coupling $g_D$ and the mediator mass $m_\phi$.
• Exclusion of Thermal Scenarios: A primary result is the exclusion of the parameter space where the mediator $\phi$ thermalizes in the early Universe. The collider constraints on $\lambda_{HS}$ are found to be significantly lower than the values required for thermalization, effectively ruling out the super-WIMP scenario for the proposed mass range.

Results

• Parameter Space Viability: The viable parameter space for the dark photon DM candidate is identified for $m_{\gamma'} \in [1, 5]$ GeV, $m_\phi \lesssim m_h/2$, and $T_{RH} \approx 3$ GeV.
• Collider Sensitivity: Displaced photon searches are most sensitive to mediator decay lengths of $c\tau_\phi \approx 2$ m. For $m_\phi = 60$ GeV, the search can probe Higgs branching ratios to $\phi\phi$ as low as $\sim 0.5\%$.
• Coupling Constraints: The analysis places stringent upper limits on the Higgs portal coupling $\lambda_{HS}$. For the target parameter space ($g_D \sim 10^{-11} - 10^{-9}$ GeV$^{-1}$), $\lambda_{HS}$ is constrained to be $\lesssim \mathcal{O}(10^{-3})$.
• Thermalization Ruled Out: Since thermalization of the mediator requires $\lambda_{HS} \sim \mathcal{O}(10^{-1})$, the collider bounds completely exclude the possibility of a thermalized mediator in this model. This reinforces a purely non-thermal freeze-in picture.
• BBN and Structure Formation: The model satisfies BBN constraints (requiring decay before $T \sim 10$ keV to avoid photodisintegration) and structure formation constraints (ensuring dark photons are non-relativistic by matter-radiation equality) within the identified parameter space.

Significance
The paper claims to bridge the gap between low-reheating cosmological scenarios and LHC phenomenology. It demonstrates that models featuring long-lived mediators coupling to both dark and visible photons can be rigorously tested using existing displaced photon data. The significance lies in the ability of current LHC searches to rule out specific thermal histories (thermalized mediators) for DM models that would otherwise be viable based on cosmological considerations alone. By identifying a well-defined target region ($T_{RH} \sim 3$ GeV, non-thermal mediator), the work provides a concrete motivation for dedicated experimental searches targeting displaced photon signatures arising from well-motivated dark sector models.