From WIMP to FIMP during reheating: collider vs non-collider probes for p-wave annihilation

This paper investigates how collider and non-collider probes can constrain the reheating temperature, dark matter mass, and interaction scale of a scenario where dark matter transitions from WIMP to FIMP production via p-wave suppressed interactions, demonstrating that collider experiments are uniquely powerful in constraining derivative operators that are weakly limited by astrophysical observations.

The Gist

The Big Picture: The Missing Chapter of the Universe's Story

Imagine the history of the Universe as a massive book. We know the very first page (the Big Bang/Inflation) and we know the last few pages (the formation of stars, galaxies, and us). But there is a huge, mysterious gap in the middle—a chapter called Reheating.

After the Big Bang, the Universe was cold and empty. Then, something happened that "reheated" it, filling it with hot soup of particles. This is the "Reheating" era. The paper asks: Can we figure out what happened in this missing chapter by looking at Dark Matter?

Dark Matter is the invisible glue holding galaxies together. We know it's there, but we don't know what it is. The authors propose that Dark Matter might have been created during this Reheating phase, not before or after.

The Two Types of Dark Matter Characters

The paper looks at two different "personalities" of Dark Matter, using a cooking analogy:

1. The WIMP (Weakly Interacting Massive Particle): Think of this as a popular chef in a kitchen. It interacts so much with the other ingredients (normal matter) that it gets into a "thermal equilibrium." It's constantly cooking, tasting, and adjusting until the heat drops, and then it freezes into a specific amount. This is the traditional theory.
2. The FIMP (Feebly Interacting Massive Particle): Think of this as a ghost in the kitchen. It barely touches anything. It doesn't mix with the soup. Instead, it slowly leaks into the pot from the outside, accumulating just enough to fill the bowl. It never really "cooks" with the other ingredients. This is the newer, more elusive theory.

The paper investigates the transition between these two personalities.

The "P-Wave" Problem: The Bouncers at the Door

The authors focus on a specific type of interaction called "p-wave suppression."

• The Analogy: Imagine a nightclub (the early Universe). Usually, if you want to get in, you just walk through the door (s-wave). But for these specific Dark Matter particles, the bouncer (physics) has a rule: "You can only enter if you are dancing."
• The Catch: In the early Universe, particles were moving fast (dancing), so they could get in. But today, the Universe is cold and quiet. The particles are standing still (not dancing). Because they aren't moving fast enough to "dance," they can't interact with normal matter.
• The Result: This makes them very hard to catch with standard telescopes or detectors that look for slow-moving particles. It's like trying to catch a fish that only bites when the water is boiling; once the water cools, the fish stops biting.

The Detective Work: How Do We Find Them?

Since these "ghosts" are hard to catch in space (because they aren't "dancing" anymore), the authors ask: Can we catch them in a lab?

They use a "Detective Board" approach, connecting clues from three different types of investigations:

1. The "Cosmic Thermometer" (Reheating Temperature)

The paper argues that the amount of Dark Matter we see today depends on how hot the Universe got during Reheating.

• The Analogy: If you bake a cake, the final texture depends on the oven temperature. If the oven was too cool, you get a raw cake; too hot, and it burns.
• The Finding: By measuring how much Dark Matter exists, we can work backward to figure out the "oven temperature" of the early Universe. The paper shows that if Dark Matter is a "FIMP" (the ghost), the Universe must have been reheated to a specific temperature range to get the right amount of "cake."

2. The "Invisible Decay" Clues (Mesons and Z-Bosons)

The authors look at particles that shouldn't exist if Dark Matter is real.

• The Analogy: Imagine a magician pulling a rabbit out of a hat. If you see the hat shake and a rabbit disappears, you know something weird happened.
• The Science: They look at particles like Kaons (a type of subatomic particle) and the Z-boson. Sometimes, these particles decay (break apart) into things we can't see. If they are decaying into Dark Matter, the "invisible" part of the decay will be bigger than expected.
• The Result: Experiments at places like CERN (LHC) and older experiments (LEP) have set strict limits. If the Dark Matter interacts too strongly, we would have seen these "missing" decays by now. The paper finds that for these specific "p-wave" particles, the interaction must be very weak, or we would have seen it.

3. The "Missing Energy" Hunt (Colliders)

This is the most exciting part. The authors suggest that giant particle smashers (like the Large Hadron Collider) are actually the best place to find these ghosts.

• The Analogy: Imagine two cars crashing. If a passenger jumps out of the car and runs away into the fog, you can't see them. But you can see the car skid sideways because of the missing weight.
• The Science: When protons collide, if Dark Matter is created, it flies out of the detector unseen. The detector sees a "kick" (missing energy) in the opposite direction of a visible particle (like a jet of gas or a photon).
• The Twist: Because these particles are "p-wave" (they need to be moving fast to interact), the high energy of the collider is perfect for making them. The paper shows that while space telescopes might miss them, the LHC and future colliders (like the FCC) could catch them if they exist.

The Main Takeaways

1. Space is quiet, but the Lab is loud: Because these Dark Matter particles are "p-wave" suppressed, they are very hard to detect in the cold, slow Universe today (via direct detection or looking at the Cosmic Microwave Background). However, they are much easier to spot in the high-energy, fast-moving environment of a particle collider.
2. The "Ghost" is hard to pin down: The paper maps out exactly where this Dark Matter could exist. It turns out that if the interaction is too strong, we would have seen it in past experiments (like the decay of Kaons or the Z-boson). If it's too weak, we can't make enough of it to explain the Universe.
3. A Bridge to the Past: By finding (or ruling out) these particles in a collider, we aren't just finding a new particle; we are effectively reading the "missing chapter" of the Universe's history. We can determine exactly how hot the Universe was right after the Big Bang.

Summary in One Sentence

This paper argues that while "ghost-like" Dark Matter is too shy to be caught by looking at the stars, it might be caught by smashing particles together at high speeds, and doing so would tell us exactly how hot the Universe was in its very first moments.

Technical Summary

Technical Summary: From WIMP to FIMP during reheating: collider vs non-collider probes for p-wave annihilation

Problem Statement
The cosmological interval between the end of inflation and the onset of Big Bang Nucleosynthesis (BBN), known as the reheating epoch, remains poorly understood due to a lack of direct observational guidance. While the canonical Weakly Interacting Massive Particle (WIMP) paradigm has faced increasing pressure from null results in direct and indirect searches, the Feebly Interacting Massive Particle (FIMP) paradigm offers a compelling alternative where Dark Matter (DM) never reaches thermal equilibrium. This paper investigates the transition between WIMP and FIMP production mechanisms specifically during the reheating epoch. A critical challenge in this regime is that many viable DM models involve $p$-wave suppressed annihilation operators. Such operators are naturally suppressed in the current cold Universe, rendering them effectively invisible to standard astrophysical indirect detection searches (e.g., CMB constraints, gamma-ray observations) and often weakly constrained by direct detection. The authors ask whether this "apparent freedom" is deceptive and if these models can be rigorously tested through a combination of collider observables and complementary non-collider probes.

Methodology
The study employs an Effective Field Theory (EFT) framework to characterize interactions between the Dark Sector and the Standard Model (SM). The authors focus on two representative dimension-6 operators that induce $p$-wave suppressed DM annihilation at leading order:

1. $O_{f\Phi}$: $(\bar{f}\gamma_\mu f)(\Phi^\dagger i \overleftrightarrow{\partial}^\mu \Phi)$, coupling a complex scalar DM field $\Phi$ to SM fermions $f$.
2. $O_{D\Phi}$: $(H^\dagger \overleftrightarrow{D}_\mu H)(\Phi^\dagger i \overleftrightarrow{\partial}^\mu \Phi)$, coupling $\Phi$ to the SM Higgs doublet $H$.

The cosmological background is modeled via perturbative reheating, where the inflaton condensate decays or scatters into SM particles (specifically Higgs-like bosons), generating a thermal bath. The evolution of the inflaton energy density and the resulting radiation temperature $T$ depends on the inflaton potential parameter $n$ (where $V(\phi) \propto \phi^n$) and the reheating channel (decay vs. scattering).

The authors solve the Boltzmann equations for DM number density during reheating to determine the relic abundance for both freeze-out (WIMP) and freeze-in (FIMP) scenarios. They systematically map the parameter space defined by the DM mass ($m_\Phi$), the new physics scale ($\Lambda_{NP}$), and the reheating temperature ($T_{rh}$).

To constrain this parameter space, the authors perform a comprehensive analysis of:

• Non-collider constraints: Direct detection (DM-nucleon and DM-electron scattering), indirect detection (CMB energy injection, cosmic rays, supernova cooling bounds), and inflationary gravitational waves (GWs).
• Collider constraints: Invisible meson decays (vector and pseudoscalar), $K^0-\bar{K}^0$ oscillations, LEP constraints (Z-pole invisible width, mono-$\gamma$), and LHC searches (mono-jet, mono-Higgs). They also project sensitivities for the High-Luminosity LHC (HL-LHC) and the Future Circular Collider (FCC-ee) at 160 GeV and 365 GeV.

Key Contributions and Results
The analysis reveals that while $p$-wave suppressed operators evade traditional astrophysical constraints, they are subject to stringent bounds from low-energy flavor physics and high-energy colliders.

1. Supremacy of Collider and Flavor Constraints: For the operator $O_{f\Phi}$, flavor-changing neutral current (FCNC) processes such as $K_L \to \pi^0 + \text{inv}$ and $B^0 \to \pi^0 + \text{inv}$, along with $K^0-\bar{K}^0$ mixing, impose lower bounds on $\Lambda_{NP}$ reaching up to $\sim 50$ TeV for light DM masses. For $O_{D\Phi}$, the invisible decay width of the Z boson ($Z \to \Phi\Phi^\dagger$) at LEP provides a strong bound ($\Lambda_{NP} \lesssim 1$ TeV excluded) for $m_\Phi < m_Z/2$.
2. WIMP vs. FIMP Transition: The study delineates the transition region where increasing $\Lambda_{NP}$ shifts the production mechanism from freeze-out to freeze-in. The authors find that for a fixed DM mass, reproducing the observed relic abundance in the freeze-in regime requires larger $\Lambda_{NP}$ as $T_{rh}$ increases (UV freeze-in nature).
3. Impact of Reheating Dynamics: The equation of state parameter $n$ significantly affects the viable parameter space. For $n=6$, the faster Hubble expansion leads to earlier freeze-out and stronger entropy dilution, requiring larger $\Lambda_{NP}$ for freeze-out but smaller $\Lambda_{NP}$ for freeze-in compared to the $n=4$ case.
4. Collider Reach:
   • LHC/HL-LHC: Mono-jet searches at the HL-LHC can probe $\Lambda_{NP}$ up to $\sim 2$ TeV for $O_{f\Phi}$. However, for $O_{D\Phi}$, the viable parameter space consistent with relic density is largely excluded by existing LEP and direct detection limits, leaving little room for HL-LHC discovery unless the model is UV-completed.
   • Mono-Higgs: The mono-Higgs channel ($h + \not{E}_T$) at the LHC provides a significantly stronger constraint on $O_{D\Phi}$ than mono-jet searches, probing $\Lambda_{NP} \sim 1$ TeV.
   • FCC-ee: Future lepton colliders offer complementary sensitivity. At $\sqrt{s}=160$ GeV, FCC-ee is sensitive to $O_{D\Phi}$ via mono-$\gamma$ searches, while at $\sqrt{s}=365$ GeV, sensitivity to $O_{f\Phi}$ is enhanced due to the contact interaction nature of the operator.
5. Gravitational Waves: The paper notes that a stiff equation of state ($n > 4$) during reheating generates a blue-tilted primordial gravitational wave spectrum. Future detectors (e.g., BBO, DECIGO, µARES) could probe the reheating temperature and $n$ values consistent with the DM production scenarios, offering a complementary cosmological probe.

Significance
The authors claim that this work constitutes the first investigation of the WIMP–FIMP transition in a generic reheating background using effective DM-SM interactions. The primary significance lies in demonstrating that terrestrial and astrophysical searches for new physics can serve as indirect probes of the pre-BBN Universe. Specifically, the study shows that "invisible" $p$-wave suppressed interactions are not immune to experimental scrutiny; rather, they are tightly constrained by flavor physics and collider data. Consequently, the allowed parameter space for DM production during reheating is significantly restricted, and future experiments (HL-LHC, FCC-ee, next-generation direct detection) have the potential to reconstruct aspects of the Universe's thermal history, including the reheating temperature and the nature of the inflaton potential.