Search for low-mass hidden-valley dark showers with non-prompt muon pairs in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 41.6 fb$^{-1}$ of 13 TeV proton-proton collision data collected by the CMS experiment in 2018, this study searches for low-mass hidden-valley dark showers via non-prompt muon pairs from Higgs boson decays, setting new upper limits on the branching fraction to dark partons and establishing first constraints on extended dark-shower models with dark photons.

The Gist

The Great Cosmic Hide-and-Seek: Hunting for "Dark" Particles at CERN

Imagine the universe as a giant, bustling city. We can see the buildings, the cars, and the people (this is normal matter). But we know there's a massive, invisible population living in the shadows that we can't see directly, yet we know they are there because they have weight and gravity (this is dark matter).

For decades, physicists have been trying to figure out what this "dark" population looks like. One popular theory suggests that dark matter isn't just one lonely particle, but a whole hidden society with its own rules, its own "dark force," and even its own version of a particle accelerator. This is called the Hidden Valley.

This paper from the CMS experiment at CERN (the giant particle collider in Switzerland) is a report on a massive game of "Hide-and-Seek" designed to find clues about this Hidden Valley.

The Setup: The Higgs Boson as a "Doorway"

Think of the Higgs boson (a famous particle discovered in 2012) as a special, heavy door in our visible city. The theory goes that sometimes, this door doesn't just open to let out normal particles; it opens a secret tunnel into the Hidden Valley.

When this happens, the Higgs decays into "dark partons" (the dark citizens). These dark citizens immediately start crashing into each other, creating a chaotic spray of new dark particles. Physicists call this a "Dark Shower." It's like dropping a bucket of glitter into a dark room; you can't see the glitter directly, but you know it's there because it eventually lands on something you can see.

The Clue: The "Ghostly" Muons

In this Hidden Valley, the dark particles eventually decay (break apart) and turn back into normal particles we can detect. The specific clue this team was looking for is a pair of muons (a type of heavy electron).

Here is the tricky part:

• Normal particles usually appear instantly where the collision happened.
• The dark particles in this theory are "long-lived." They travel a short distance (like a few millimeters to several centimeters) before they break apart and turn into muons.

So, the team was looking for muon pairs that appeared out of nowhere, away from the main collision point. It's like seeing two people appear in a park, holding hands, but they didn't walk in from the street; they just popped into existence a few feet away from the entrance.

The Strategy: The "Data Parking" Trick

The challenge was that these "ghostly" muons are often slow and light. Standard detectors at CERN are like bouncers at a VIP club; they usually only let in the fast, heavy, high-energy particles. They would have ignored these slow, low-mass dark muons.

To solve this, the team used a clever strategy called "Data Parking."

• Normal Mode: The detector records only the "VIPs" (high-energy particles).
• Parking Mode: The team lowered the bouncer's standards. They recorded everything, even the slow, low-energy particles.
• The Catch: They couldn't process all this data immediately (it was too much!). So, they "parked" the raw data on tape storage, like putting a heavy box in a garage. They waited until the LHC was shut down for maintenance, then used the quiet time to unpack and analyze the "parked" data.

This allowed them to look for very light, slow-moving particles that other searches missed.

The Detective Work: AI and Machine Learning

Once they had the data, they had to find the "ghostly" muon pairs in a sea of billions of normal collisions. This is like trying to find a specific needle in a haystack the size of a mountain.

They used Machine Learning (AI) to help. They trained a computer (a "Boosted Decision Tree") to recognize the specific "fingerprint" of a dark shower. The AI learned to spot:

1. Too many muons: Dark showers often produce a spray of particles, not just one or two.
2. Displaced vertices: The muons appearing in the wrong place (away from the center).
3. Specific angles: How the particles are pointing relative to the collision.

The AI became an expert detective, filtering out the billions of boring, normal events to highlight the few that looked suspicious.

The Results: No Ghosts Found (Yet)

After analyzing 41.6 "inverse femtobarns" of data (a fancy way of saying a massive amount of collisions), the team found no significant evidence of these dark showers.

• The Verdict: The "Hidden Valley" door didn't seem to open in the way they predicted for the masses they tested.
• The Silver Lining: Even though they didn't find the particles, they set strict limits. They proved that if these dark particles do exist, they must be even rarer or behave differently than their current best guesses. They ruled out a huge range of possibilities, narrowing the search for future scientists.

Why This Matters

This search is unique because it looked at very low masses (lighter than a proton) and short distances (millimeters), a region that previous experiments had largely ignored.

Think of it like searching for a lost key. Previous searches looked under the streetlights (high energy, heavy particles). This team looked in the dark corners of the alleyway (low energy, light particles). Even though they didn't find the key, they proved the key isn't in those specific dark corners, which helps us know exactly where not to look next.

In short: The CMS team used a clever data-saving trick and super-smart AI to hunt for invisible dark particles that might be hiding in plain sight. They didn't find them this time, but they tightened the net, making the search for the universe's dark secrets more precise than ever before.

Technical Summary

1. Problem and Motivation

The Standard Model (SM) of particle physics does not account for dark matter, which constitutes approximately 27% of the universe's energy content. A class of theories known as Hidden Valley (HV) models proposes a "dark sector" with its own non-Abelian gauge group (Dark QCD). In these models:

• The SM Higgs boson can decay into dark partons ($\psi\bar{\psi}$).
• These dark partons undergo hadronization via Dark QCD to form dark hadrons (e.g., dark mesons like $\tilde{\omega}$, $\tilde{\eta}$, or dark pions $\tilde{\pi}$).
• These dark hadrons can be long-lived and decay back into SM particles, specifically muons, creating displaced vertices (non-prompt decays) distinct from the primary interaction point.

Previous searches at the LHC were limited by:

• High mass thresholds (typically $>10$ GeV).
• Focus on specific topologies (e.g., emerging jets) or specific decay lengths.
• Lack of sensitivity to low-mass dark showers where the dark mesons decay into muon pairs with significant displacement.

This analysis aims to probe low-mass dark showers (0.3–20 GeV) with long-lived particles decaying into non-prompt muon pairs, a signature previously unexplored in this mass and lifetime regime.

2. Methodology

Data Set and Trigger Strategy

• Data Source: Proton-proton collisions at $\sqrt{s} = 13$ TeV collected by the CMS experiment in 2018.
• Integrated Luminosity: 41.6 fb$^{-1}$.
• Trigger Strategy: The analysis utilizes the "B-parking" data set. Unlike standard triggers, B-parking lowers the transverse momentum ($p_T$) thresholds for muons (down to 7–12 GeV) and requires a significant impact parameter ($IP_{sig} > 3-6$). This strategy enriches the sample with displaced muons (from B-hadron decays) and allows the collection of low-mass, long-lived signals that would otherwise be discarded due to high trigger rates.
• Event Selection:
  • Events must contain at least one reconstructed muon satisfying $p_T > 9$ GeV, $|IP_{sig}| > 6$, and $|\eta| < 1.5$.
  • At least one secondary vertex (SV) formed by a pair of oppositely charged muons is required.
  • The SV reconstruction algorithm is modified to extend the search range for transverse displacement ($l_{xy}$) up to ~15 cm.

Signal Models

The search targets three specific benchmark models:

1. Vector Portal Model: The Higgs decays to dark partons, forming dark vector mesons ($\tilde{\omega}$) and pseudoscalars ($\tilde{\eta}$). The $\tilde{\omega}$ decays displaced into SM fermions (including $\mu^+\mu^-$).
2. Scenario A (Pointing): An extended HV model with two dark flavors. A dark pion ($\tilde{\pi}_3$) decays promptly to two dark photons ($A'$), which then decay displaced into muons. The vector sum of the dimuon momenta points back to the beam axis.
3. Scenario B1 (Non-pointing): Similar to Scenario A, but the $\tilde{\pi}_3$ itself is long-lived and decays displaced to two dark photons ($A'$), which then decay promptly to muons. The dimuon vertices do not point back to the beam axis.

Machine Learning (BDT)

To distinguish the signal from the dominant QCD background (heavy-flavor decays and random track combinations), an event-level Boosted Decision Tree (BDT) using the XGBoost algorithm is employed.

• Input Variables: Up to 390 features, including muon multiplicity, transverse impact parameters ($d_{xy}$), secondary vertex kinematics ($\chi^2$, displacement, pointing angle), and jet variables (excluded to maintain model independence).
• Performance: The BDT achieves a signal efficiency of 30–60% while suppressing the background by a factor of $10^4$ to $10^5$.
• Key Discriminators: Muon multiplicity (signal events have higher multiplicity due to dark showers) and the quality of the vertex fit ($\chi^2$).

Statistical Analysis

• Categorization: Events are categorized by the number of vertices (single vs. multi-vertex), transverse displacement ($l_{xy}$ bins: $<1$ cm, 1–10 cm, $>10$ cm), and pointing angle.
• Fitting: A sliding window fit is performed on the dimuon invariant mass spectrum.
  • Signal: Modeled with a Voigtian function (convolution of Gaussian and Breit-Wigner).
  • Background: Modeled using an envelope of functions (polynomial, exponential, power law) fitted to data sidebands.
• Limits: Upper limits on the branching fraction $B(H \to \text{dark partons})$ are set at 95% confidence level (CL) using the $CL_s$ criterion.

3. Key Contributions

• First Search of its Kind: This is the first LHC search specifically targeting hidden-valley dark showers where dark-sector particles decay into pairs of muons in the low-mass regime (0.3–20 GeV).
• Extended Parameter Space: The analysis probes mean proper decay lengths ($c\tau$) from 0.1 mm to 500 mm, covering a region of short-to-medium lifetimes that was previously inaccessible to muon-detector-only searches.
• Low Mass Sensitivity: By utilizing the B-parking trigger and tracker-based reconstruction, the search extends sensitivity to dark meson masses as low as 0.3 GeV and dark photon masses down to 0.33 GeV.
• Novel Topologies: It is the first to set limits on Scenario A and B1 models, which involve extended dark sectors with two dark flavors and complex decay chains involving dark photons.

4. Results

• Observation: No significant excess of events was observed above the Standard Model expectation across the entire mass and lifetime range.
• Upper Limits:
  • Vector Portal Model: Upper limits on the branching fraction $B(H \to \psi\bar{\psi})$ reach as low as $10^{-4}$ at 95% CL. These limits improve upon previous results by up to two orders of magnitude for decay lengths between 100–500 mm and masses down to 0.3 GeV.
  • Scenario A & B1: First-ever constraints are set for these models. Limits on the branching fraction are in the range of $10^{-2}$ to $10^{-4}$, depending on the mass and lifetime.
• Mass Coverage: The search effectively covers the dimuon mass range of 0.3 to 20 GeV, masking known SM resonances (e.g., $J/\psi$, $\Upsilon$) to avoid false positives.

5. Significance

This work significantly advances the search for dark matter and hidden sectors at the LHC by:

1. Complementing Existing Searches: It fills the "gap" in sensitivity for short-to-medium lifetimes ($c\tau < 500$ mm) and low masses ($< 10$ GeV) that muon-detector-only searches miss.
2. Validating HV Models: It provides the most stringent constraints to date on vector portal models with dark $\tilde{\omega}$ mesons and establishes the first exclusion limits for extended HV models with dark photons.
3. Demonstrating Data Parking Utility: The success of the B-parking strategy highlights the importance of specialized trigger strategies in uncovering rare, low-mass, displaced signatures that standard triggers would discard.

In summary, this analysis sets the new benchmark for low-mass, long-lived particle searches in the dimuon channel, ruling out significant portions of the parameter space for hidden-valley theories and guiding future theoretical and experimental efforts in the dark sector.