Search for soft unclustered energy patterns containing muons in the final state in $pp$ collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

Using 140 fb$^{-1}$ of 13 TeV proton-proton collision data collected by the ATLAS detector, this study searches for soft unclustered energy patterns (SUEPs) containing muons in Hidden Valley scenarios, finding no significant excess over Standard Model expectations and setting exclusion limits on the production cross section and branching fraction for scalar mediators with masses ranging from 125 to 750 GeV.

The Gist

The Search for the "Soft Unclustered Energy Pattern" (SUEP)

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. Usually, when scientists smash protons together, they expect the debris to fly out in specific, predictable ways—like two cars crashing and sending pieces flying in distinct, high-speed jets.

But what if, instead of a crash, the collision created a gentle, expanding cloud of thousands of tiny, slow-moving particles? This is the idea behind a "Soft Unclustered Energy Pattern" (SUEP).

This paper is a report from the ATLAS experiment at CERN, where scientists looked for this specific type of "cloud" in 140 trillion proton collisions. Here is the breakdown of what they did and what they found, using simple analogies.

1. The Theory: The Hidden "Dark Party"

The scientists are looking for evidence of a "Hidden Valley."

• The Analogy: Imagine the Standard Model of physics as a bustling, noisy city. The "Hidden Valley" is a secret, parallel neighborhood right next door that we can't see directly.
• The Connection: Sometimes, a "messenger" (called a scalar mediator) is created in the city. This messenger travels into the secret neighborhood and throws a party.
• The Party: In this hidden neighborhood, the rules are different. Instead of a few loud guests (high-energy particles), the party produces a massive crowd of hundreds of quiet, low-energy guests (soft particles).
• The Exit: Eventually, these quiet guests escape the secret neighborhood and re-enter our visible city. If they do, they arrive as a sudden, isotropic (equal in all directions) burst of many low-energy particles.

2. The Challenge: Finding a Needle in a Haystack

The problem is that these "quiet guests" are very hard to spot.

• The Trigger Problem: The ATLAS detector is like a security camera system designed to catch fast, loud events (like a speeding car). It often ignores slow, quiet things.
• The Background Noise: The real world is full of "noise." When protons collide, they often produce heavy particles (like top quarks) that decay into muons (a type of particle similar to an electron but heavier). These muons usually come in pairs or small groups and fly in specific directions.
• The Strategy: The team decided to look for a very specific signature: a large group of muons that are:
  1. Soft: Moving slowly (low energy).
  2. Prompt: Appearing immediately (not delayed).
  3. Isotropic: Spread out evenly in a circle, like a dandelion puff, rather than flying in a straight line like a jet.

3. The Investigation: How They Searched

The scientists analyzed data from 2015 to 2018 (140 fb⁻¹ of data). They used a clever two-step filter to separate the "signal" (the SUEP) from the "noise" (standard background):

• Step 1: The Muon Count. They looked for events with at least 5 muons.
• Step 2: The Shape Check (Sphericity).
  • Background Noise: Usually, background muons come from heavy particles decaying. They tend to clump together or fly in two opposite directions (like a jet engine).
  • The Signal: A SUEP event would look like a perfect sphere of muons, spread evenly in all directions.
• Step 3: The Track Count. They also counted the total number of charged tracks (paths left by particles). A SUEP event should have a lot of tracks because of the high number of particles, whereas background events usually have fewer.

They used a statistical method called the ABCD method. Think of it like a game of "Hot and Cold." They defined four zones based on how "spherical" the event was and how many tracks it had. They used three zones to learn what the background noise looks like, and then checked the fourth zone (the "Signal Region") to see if there were any unexpected guests.

4. The Results: No New Particles Found

After crunching the numbers, the result was clear: No significant excess was found.

• The Outcome: The number of events they saw in the "Signal Region" matched exactly what they expected from standard background noise. There was no "dandelion puff" of hidden valley particles.
• The Limits: Even though they didn't find it, they set strict limits on how heavy the "messenger" particle could be and how likely it is to decay into this hidden state.
  • If the messenger is heavy (750 GeV), the chance of it turning into a SUEP is less than 0.05% (very rare).
  • If the messenger is the Higgs boson (125 GeV), the chance of it decaying into this hidden state is less than 0.2%.

5. Conclusion

The ATLAS team successfully cast a wide net for a very exotic type of physics event. They proved that if these "Soft Unclustered Energy Patterns" exist, they are even rarer than previously thought, or they don't exist in the specific mass ranges they tested.

In short: They looked for a quiet, spherical cloud of particles in a noisy, chaotic collision. They didn't find the cloud, but they successfully mapped out exactly where it isn't, helping to narrow down the search for new physics in the future.

Technical Summary

Technical Summary: Search for Soft Unclustered Energy Patterns Containing Muons in $pp$ Collisions at $\sqrt{s}=13$ TeV

Problem and Motivation
Hidden Valley (HV) models propose a hidden sector connected to the Standard Model (SM) via weak portal interactions. While many searches target hidden sectors that produce jet-like signatures (e.g., semi-visible or emerging jets), scenarios where the hidden sector remains strongly coupled well above its hadronization scale can produce "Soft Unclustered Energy Patterns" (SUEPs). These signatures consist of high-multiplicity, low-momentum particles distributed approximately isotropically in the center-of-mass frame. Such events are challenging to trigger on and reconstruct due to the absence of hard or collimated objects. Previous searches by the CMS Collaboration targeted SUEPs using high-transverse-momentum initial-state radiation or associated production with vector bosons, but these approaches were primarily sensitive to large mediator masses or required very high particle multiplicities, limiting coverage for scenarios with lower multiplicities and specific dark-photon mass ranges. This paper presents a complementary search targeting final states with a high multiplicity of prompt muons, extending sensitivity to SUEP scenarios with moderate particle multiplicities and sizable muon fractions.

Methodology
The analysis utilizes 140 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=13$ TeV collected by the ATLAS detector during 2015–2018. The search targets the gluon–gluon fusion production of a scalar mediator $S$ (either the SM Higgs boson or a heavier scalar) decaying into a quasi-conformal hidden sector. The hidden sector particles shower and hadronize into dark mesons ($\phi$), which decay promptly into dark photons ($A'$), subsequently decaying into SM particles (electrons, muons, and hadrons).

• Event Selection: Events are selected using multi-muon triggers (requiring $\ge 3$ muons with $p_T > 6$ GeV in 2015–2016, or $\ge 4$ muons with $p_T > 4$ GeV in 2017–2018). Offline selection requires:
  • At least 5 prompt muons ($N_\mu \ge 5$).
  • Average muon transverse momentum $\langle p_T^\mu \rangle < 10$ GeV to suppress backgrounds from heavy particle decays (e.g., $Z$, $t\bar{t}$).
  • Transverse impact-parameter significance of the highest-$p_T$ muon $d_0^{sig}(\mu_1) < 3$ to ensure promptness.
• Discriminating Observables: Two key observables are used to distinguish signal from the dominant QCD multijet background:
  1. Muon Sphericity ($S_\mu$): Calculated in the rest frame of the muon system to characterize the isotropic distribution of signal muons. Signal events are expected to have high sphericity ($S_\mu > 0.6$), while background events tend to be more collimated.
  2. Corrected Track Multiplicity ($N_{tracks}$): The number of charged-particle tracks associated with the primary vertex, corrected for pile-up contributions using a data-driven method based on the longitudinal position of the primary vertex and the instantaneous luminosity.
• Background Estimation: The background is estimated using a data-driven, likelihood-based ABCD method. The method exploits the weak correlation between $N_{tracks}$ and $S_\mu$ in the validation regions (defined by varying muon multiplicity and impact parameter significance). The background prediction is constrained by maximum-likelihood fits to data in control regions, with systematic uncertainties accounting for residual correlations and modeling variations.

Key Contributions

• Novel Trigger Strategy: The analysis demonstrates the effectiveness of multi-muon triggers for SUEP searches, allowing sensitivity to scenarios with moderate particle multiplicities that were previously inaccessible to calorimeter-based triggers.
• Data-Driven Background Modeling: The implementation of a robust ABCD method using $N_{tracks}$ and $S_\mu$ allows for a fully data-driven background prediction without reliance on simulated background samples for the dominant QCD multijet component.
• Comprehensive Parameter Scan: The study explores a wide range of model parameters, including mediator masses ($m_S = 125, 400, 750$ GeV), dark-meson masses ($m_\phi = 1.5, 3, 5$ GeV), Hagedorn temperatures ($T$), and dark-photon masses ($m_{A'} = 0.3, 0.5, 0.7$ GeV).

Results
No significant excess over the Standard Model expectation is observed in the search region. The results are interpreted as 95% confidence level (CL) upper limits on the product of the mediator production cross section and the branching fraction for its decay into a SUEP ($\sigma_S \times \mathcal{B}(S \to \text{SUEP})$).

• Exclusion Limits: The observed limits reach:
  • $\sim 0.05$ fb for $m_S = 750$ GeV.
  • $\sim 0.4$ fb for $m_S = 400$ GeV.
  • $\sim 70$ fb for $m_S = 125$ GeV.
• Higgs Branching Fraction: For the case where the mediator is the SM Higgs boson ($m_S = 125$ GeV), the upper limit on the branching fraction $\mathcal{B}(H \to \text{SUEP})$ is approximately 0.2% (specifically $\sim 0.3\%$ for $m_\phi = T = 3, 5$ GeV and $m_{A'} = 0.5$ GeV). This represents a significant improvement over previous limits for similar model parameters.
• Sensitivity: The strongest limits are generally obtained for $m_\phi = T = 3$ GeV. Sensitivity decreases for lower values due to reduced trigger efficiency for softer particles and for higher values due to reduced particle multiplicity.

Significance
This search extends the sensitivity to SUEP scenarios beyond previous LHC results, particularly in regions of parameter space characterized by moderate particle multiplicities and sizable muon fractions in the final state. By utilizing multi-muon triggers and a data-driven background estimation technique, the analysis provides a complementary approach to existing searches targeting primarily hadronic final states. The results constrain a broad range of Hidden Valley models and demonstrate the capability of the ATLAS detector to probe unconventional, soft, and isotropic signatures. The paper claims that these limits are one to four orders of magnitude more stringent than previous results for specific benchmark scenarios, significantly improving the constraints on the branching fraction of the Higgs boson to hidden sector decays.