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Reheating the FCC: Probing Early Matter Domination with Long-Lived Particles

This paper investigates how a GeV-scale Higgs-portal scalar can drive an early matter-dominated era and links the resulting reheating temperature to long-lived particle signatures, demonstrating that FCC-hh displaced-decay searches can probe transition temperatures up to the electroweak scale.

Original authors: Nicolás Bernal, Giovanna Cottin, Kuldeep Deka, Manuel López

Published 2026-07-24

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CC BY 4.0

Original authors: Nicolás Bernal, Giovanna Cottin, Kuldeep Deka, Manuel López

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Universe as a giant, expanding balloon. We know a lot about what happened after the balloon got big enough to form stars and planets, but the very first moments—right after the "Big Bang"—are a bit of a mystery. Scientists have a standard story: the early Universe was a super-hot soup of energy that quickly cooled down into a sea of light particles called radiation. But what if there was a hidden chapter in that story? What if, for a brief moment, the Universe was dominated not by light, but by heavy, slow-moving particles that acted like invisible matter? This is the idea of an "early matter-dominated era." It's a bit like a traffic jam in the cosmic highway before the cars (radiation) finally started flowing freely again.

The key to solving this mystery lies in a special kind of particle called a "Long-Lived Particle" (LLP). Think of these as cosmic ghosts. They are created, but they don't die immediately like normal particles; instead, they hang around for a surprisingly long time before decaying (turning into other particles). If such a ghost existed in the early Universe, it could have been the heavy traffic jam that dominated the cosmos before eventually vanishing, allowing the Universe to heat up and start the era of radiation we know today. The temperature at which this transition happened is a crucial clue to understanding our cosmic origins.

Now, here is the twist: these same "ghost" particles might be hiding in plain sight at our biggest particle smashers, like the Large Hadron Collider (LHC). If they are long-lived, they might travel a few meters inside the detector before popping into existence, leaving a "displaced decay"—a spot where a particle appears out of nowhere, far from where it was created. This paper, titled "Reheating the FCC: Probing Early Matter Domination with Long-Lived Particles," is a detective story connecting the dots between these cosmic ghosts and the machines we build to find them.

The authors, Nicolás Bernal and his team, focus on a specific type of ghost: a scalar particle (let's call it $\phi$ ) that is connected to the famous Higgs boson through a tiny, weak link called "mixing." Because this link is so weak, the particle is hard to make and takes a long time to decay, making it a perfect candidate for an LLP. The team asks a big question: If we could spot this particle at a future, super-powerful collider called the Future Circular Collider (FCC-hh), what would that tell us about the early Universe?

They found that the FCC-hh, a proposed machine that would smash protons together at a staggering 100 TeV (compared to the LHC's 14 TeV), could be the perfect hunting ground. While the current LHC is like a flashlight trying to find a firefly in a storm, the FCC-hh would be a high-powered spotlight. The researchers simulated how often these particles would be created and how far they would travel before decaying. They discovered that for particles with masses between 3 and 15 GeV (a few times heavier than a proton), the FCC-hh could detect them if they live long enough to travel a few meters to a few hundred meters inside the detector.

Crucially, the paper shows that finding these particles isn't just about spotting new physics; it's about reading the history book of the Universe. By measuring how long the particle lives and how heavy it is, scientists could calculate the temperature of the Universe at the moment the "traffic jam" of heavy particles ended and the "flow" of radiation began. The team found that the FCC-hh could probe transition temperatures ranging from the GeV scale (around a few billion degrees) all the way up to the electroweak scale (a trillion degrees). This would allow us to test if the Universe went through a quiet, matter-dominated phase before the Big Bang Nucleosynthesis (the time when the first atomic nuclei formed).

However, the paper also rules out some hopes. The authors show that the current LHC is likely too weak to see these specific particles because the "mixing" is too small, making the production rate too low and the decay products too soft (low energy) for current detectors to catch. They also note that if the particle decays too quickly or is too heavy, it won't leave the "displaced" signature needed to be spotted.

In short, this paper suggests that the next generation of colliders could do double duty: acting as a microscope for new particles and a time machine for the early Universe. If the FCC-hh is built and finds these long-lived Higgs-portal particles, it would confirm that the Universe once had a hidden, matter-dominated chapter, effectively "reheating" the cosmos in a way we can now measure. It's a beautiful link between the tiniest particles and the grandest history of our existence.

Technical Summary: Reheating the FCC: Probing Early Matter Domination with Long-Lived Particles

Problem Statement
The thermal history of the Universe prior to Big-Bang Nucleosynthesis (BBN) is weakly constrained. While standard cosmology assumes an early radiation-dominated era, many extensions of the Standard Model (SM) predict an early matter-dominated epoch driven by a non-relativistic field or long-lived particle (LLP), denoted here as $\phi$ . The transition from this matter-dominated era to the standard radiation-dominated era occurs at a temperature $T_{rh}$ . In minimal scenarios, $\phi$ is identified with the inflaton or reheaton; in broader contexts, it could be a modulus-like field. A critical challenge is linking the cosmological parameter $T_{rh}$ to observable collider signatures. If $\phi$ has feeble couplings to the SM, it becomes an LLP with a macroscopic lifetime, potentially producing displaced decay vertices. However, existing LHC searches are often optimized for heavier particles or specific kinematic regimes, leaving a gap in sensitivity for GeV-scale scalars with soft decay products. Furthermore, the relationship between the particle's lifetime and $T_{rh}$ is modified by finite-temperature effects in the early Universe plasma, which are often neglected in simple vacuum decay estimates.

Methodology
The authors investigate a minimal Higgs-portal model where the SM is extended by a real singlet scalar $\tilde{\phi}$ that mixes with the Higgs doublet $\Phi$ via a trilinear interaction. After electroweak symmetry breaking (EWSB), the mass eigenstates are the SM-like Higgs boson $h$ and the lighter scalar $\phi$ , mixed by an angle $\theta$ .

Cosmological Modeling:
- The study assumes $\phi$ dominates the early Universe energy density. The transition to radiation domination occurs when $\phi$ decays into SM states.
- Crucially, the authors incorporate finite-temperature suppression of the decay width. In the early Universe, $\phi$ decays into a thermal plasma of SM fermions. The decay width $\Gamma_\phi(T)$ is modified by Pauli blocking and inverse decays, described by the relation:
  $\Gamma_\phi(T) = \Gamma^{(0)}_\phi \tanh\left(\frac{m_\phi}{4T}\right)$
  where $\Gamma^{(0)}_\phi$ is the vacuum decay width. This suppression lowers the effective decay rate at temperatures $T \gtrsim m_\phi/4$ , altering the calculation of the reheating temperature $T_{rh}$ .
- $T_{rh}$ is determined by solving the condition $H(T_{rh}) = \Gamma_\phi(T_{rh})$ , linking $T_{rh}$ to the scalar mass $m_\phi$ and mixing angle $\sin\theta$ .
Collider Phenomenology:
- The production of $\phi$ at hadron colliders occurs primarily via gluon-gluon fusion (ggF), with a cross-section suppressed by $\sin^2\theta$ .
- The authors simulate production and decay at the LHC ( $\sqrt{s}=14$ TeV) and the Future Circular Collider in hadron-hadron mode (FCC-hh, $\sqrt{s}=100$ TeV, $\mathcal{L}=20$ ab $^{-1}$ ).
- They evaluate the sensitivity of three detector concepts for FCC-hh:
  - Central Tracker: An ATLAS-like cylindrical detector near the interaction point (IP).
  - Forward Tracker: Displaced 10 m from the IP along the beam pipe.
  - FOREHUNT: A dedicated forward detector located 50 m from the IP.
- The analysis uses the Displaced Decay Counter (DDC) program to calculate acceptance efficiencies based on the proper decay length $c\tau$ and the kinematics of the events.

Key Contributions and Results

Thermal Correction Impact: The inclusion of the finite-temperature suppression factor significantly changes the mapping between the particle's lifetime and the reheating temperature. Compared to vacuum estimates, the thermal suppression leads to a lower $T_{rh}$ for a given set of parameters ( $m_\phi, \sin\theta$ ).
LHC Limitations: The study concludes that the LHC has limited sensitivity to this specific GeV-scale Higgs-portal scenario. The small mixing angles required for long lifetimes suppress the production cross-section below detectable levels. Additionally, existing ATLAS displaced vertex searches impose cuts (e.g., invariant mass $>10$ GeV, specific transverse/longitudinal displacement ranges) that exclude the soft, low-mass signals predicted by this model.
FCC-hh Sensitivity: The FCC-hh offers a transformative reach due to its higher center-of-mass energy and integrated luminosity. The authors project that FCC-hh displaced-decay searches can probe the parameter space:
$3 \text{ GeV} \lesssim m_\phi \lesssim 15 \text{ GeV}$
$6 \times 10^{-6} \lesssim \sin\theta \lesssim 3 \times 10^{-3}$
The Central tracker provides the highest sensitivity due to its large geometric acceptance, while the Forward tracker and FOREHUNT extend the reach to smaller mixing angles (longer lifetimes).
Mapping Cosmology to Colliders: By overlaying the collider sensitivity contours with the theoretical $T_{rh}$ contours, the authors demonstrate that FCC-hh can probe transition temperatures ranging from the GeV scale up to the electroweak scale ( $T_{rh} \lesssim T_{EW}$ ). This covers the region where the broken-phase Higgs-portal description remains valid and where the transition occurs safely before BBN.

Significance and Claims
The paper claims to establish a direct link between displaced-decay signatures at future colliders and the expansion history of the Universe before BBN.

Minimal Interpretation: In the context of ordinary cosmic reheating, the FCC-hh could test low-temperature Higgs-portal reheating scenarios.
General Interpretation: More broadly, the results demonstrate that LLP searches can probe the end of any early matter-dominated epoch driven by a long-lived component, regardless of whether that component is the inflaton or a generic modulus-like field.
Methodological Value: The work highlights the necessity of including finite-temperature effects when translating collider-accessible lifetimes into early-Universe cosmological parameters, showing that vacuum approximations can lead to incorrect estimates of the reheating temperature.

The authors conclude that while the LHC is insufficient for this specific parameter space, the FCC-hh, with its dedicated forward and central tracking capabilities, offers a unique and robust probe of non-standard thermal histories in the early Universe.

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