Search for soft unclustered energy patterns produced in association with a W or Z boson in proton-proton collisions at $\sqrt{s}$ = 13 TeV

This paper presents a search for a Higgs boson decaying into soft unclustered energy patterns (SUEP) produced in association with a W or Z boson using 138 fb$^{-1}$ of 13 TeV proton-proton collision data, finding no significant excess over the Standard Model background and setting limits on the production cross section.

The Gist

The Big Picture: Hunting for a "Ghost Party"

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. It smashes protons together at nearly the speed of light to see what happens. Usually, when these particles smash, they create a predictable spray of debris, like shrapnel from a grenade. Physicists have a "rulebook" (the Standard Model) that predicts exactly what that shrapnel should look like.

But for decades, the rulebook has been missing a few pages. It doesn't explain things like Dark Matter or why gravity is so weak compared to other forces. Scientists suspect there might be a "Hidden Valley"—a secret world of particles that don't interact with our normal world very much.

This paper is about a specific search for a strange signature from this Hidden Valley, called a SUEP (Soft Unclustered Energy Pattern).

The Analogy: The "Confetti Bomb" vs. The "Fireworks"

To understand what they are looking for, imagine two different ways a party could end:

1. The Standard Model (Fireworks): When a normal particle decays, it's like a firework. It shoots out a few distinct, high-speed sparks in specific directions. You can easily track where they went.
2. The Hidden Valley (The Confetti Bomb): The theory suggests that if a Higgs boson (a famous particle found in 2012) decays into this "Hidden Valley," it doesn't shoot out sparks. Instead, it releases a massive cloud of tiny, slow-moving particles.
   • Imagine a piñata filled with thousands of tiny, lightweight pieces of confetti. When it breaks, the confetti doesn't fly in a stream; it puffs out in a soft, spherical cloud that drifts slowly.
   • In physics terms, this is a SUEP: a "soft" (low energy), "unclustered" (not grouped into tight jets), and "pattern" (spherically distributed) burst of energy.

The Strategy: Catching the "Bouncer"

The problem with looking for a SUEP is that it's very quiet. It's a soft cloud of slow particles that looks a lot like background noise (like static on a radio). If you just look for the cloud, you'll never find it because the background noise is too loud.

So, the CMS team (the scientists at CERN) used a clever trick. They didn't look for the cloud alone. They looked for the cloud only if it was accompanied by a "Bouncer."

• The Bouncer: A W or Z boson. These are heavy, well-known particles that decay into high-energy electrons or muons (charged particles).
• The Scenario: They are looking for a collision where a Higgs boson is created alongside a W or Z boson.
  • The W or Z boson acts as a loud, bright flare in the sky. It says, "Hey! Something interesting happened here!"
  • Because the W or Z is so distinct, the scientists can use it to "trigger" their cameras. Once the camera is focused on that loud flare, they can look closely at the rest of the event to see if there is a quiet, soft cloud of confetti (the SUEP) drifting away from it.

The Search: Sifting Through the Noise

The team analyzed data from 2016 to 2018, which is like looking at 138 billion billion proton collisions. They set up a very specific filter:

1. Spot the Bouncer: Find an event with a high-energy electron or muon (from the W or Z).
2. Look for the Cloud: Check if there is a large, spherical cluster of low-energy particles nearby.
3. The "ABCD" Method: To be sure they weren't just seeing random noise, they used a statistical trick called the "ABCD method." Imagine dividing a room into four corners. If you know how many people are in three corners, you can mathematically predict how many should be in the fourth. They did this with different variables to predict exactly how much "background noise" (standard particle collisions) should look like a SUEP.

The Result: Silence is Golden (for now)

After sifting through all that data, the result was: Nothing.

They did not find any evidence of the "Confetti Bomb." The number of events they saw matched the predictions of the Standard Model perfectly. There was no extra "ghost party" happening.

What does this mean?

• No New Physics (Yet): They didn't find the Hidden Valley particles in this specific way.
• Better Rules: By not finding it, they have set new, stricter limits. They can now say, "If these Hidden Valley particles exist, they must be even rarer or behave differently than we thought."
• A New Tool: Even though they didn't find the particle, they developed a new way of looking for it. They proved that looking for a "soft cloud" alongside a "loud bouncer" is a valid strategy. This opens the door for future experiments to try again with even more sensitive equipment.

Summary

Think of this paper as a detective story where the detectives set up a trap for a ghost. They knew the ghost only appeared when a specific celebrity (the W/Z boson) was in the room. They watched thousands of parties, waiting for the celebrity to show up and the ghost to appear. The celebrity showed up, but the ghost didn't. The detectives concluded, "The ghost isn't here, or if it is, it's much harder to catch than we thought." They have now updated their "Wanted" poster with stricter rules for the next time they look.

Technical Summary

1. Problem and Motivation

• The Search for BSM Physics: Despite extensive searches at the LHC, no direct evidence for Beyond the Standard Model (BSM) physics has been found. Many minimal BSM models are ruled out, necessitating the exploration of unconventional signatures that may have evaded previous triggers and selection criteria.
• Hidden Valley (HV) Models: The paper focuses on HV models, which introduce a "dark sector" with a non-Abelian gauge group (dark QCD). These models predict signatures such as "emerging jets" or "semivisible jets."
• Soft Unclustered Energy Patterns (SUEP): A specific signature arises when the dark QCD coupling is strong over a broad energy range. This leads to the production of low-momentum particles that are spherically distributed in the rest frame of the initiating particle, rather than collimated into jets. This is termed a SUEP.
• The Specific Hypothesis: Previous CMS searches focused on SUEPs produced via gluon fusion ($gg \to H \to \text{SUEP}$). This paper investigates a different production mode: Vector Boson Fusion (VBF) or associated production where a 125 GeV Higgs boson ($H$) is produced in association with a massive vector boson ($W$ or $Z$), denoted as $VH$. The Higgs decays into a SUEP, while the $V$ boson decays leptonically ($V \to \ell\nu$ or $\ell^+\ell^-$).
• Trigger Advantage: Using leptonic decays of the $W/Z$ boson allows for efficient triggering on high-$p_T$ leptons, significantly reducing the overwhelming multijet background that plagued previous gluon-fusion searches, although it introduces challenges in separating signal from Drell-Yan (DY), $W$+jets, and $t\bar{t}$ backgrounds.

2. Methodology

Data and Simulation

• Dataset: Proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the CMS detector between 2016 and 2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Signal Simulation: Simulated using PYTHIA 8.240. The Higgs boson ($m_H = 125$ GeV) decays into dark mesons ($\phi_D$), which decay into dark photons ($A'$), which then mix kinetically with SM photons to decay into visible SM particles ($e, \mu, \pi, K$).
  • Parameters Varied: Dark meson mass ($m_{\phi_D} \in [1, 8]$ GeV), Boltzmann temperature ($T_D$), and dark photon mass ($m_{A'}$).
  • Decay Modes: Models include dominantly leptonic ($m_{A'} = 0.5$ GeV), dominantly hadronic ($m_{A'} = 0.7$ GeV), and fully hadronic ($m_{A'} = 1.0$ GeV, $A' \to \pi^+\pi^-$) scenarios.
• Background Simulation: Standard Model (SM) processes (DY, $W$, $t\bar{t}$, multijets) simulated using MADGRAPH5_aMC@NLO and POWHEG at NLO, with parton showering via PYTHIA (CP5 tune).

Object Reconstruction and Selection

• Leptons: Electrons ($p_T > 15$ GeV, $|\eta| < 2.5$) and Muons ($p_T > 10$ GeV, $|\eta| < 2.4$) are selected using MVA discriminants.
  • WH Channel: Exactly one tight lepton + SUEP candidate.
  • ZH Channel: Exactly two loose, same-flavor, opposite-charge leptons + SUEP candidate.
• SUEP Reconstruction:
  • Charged PF candidates with $p_T > 1.0$ GeV and $|\eta| < 2.5$ originating from the primary vertex are clustered using the anti-$k_T$ algorithm with a large radius parameter $R = 1.5$.
  • The cluster with the highest $p_T$ is defined as the SUEP candidate, requiring $p_T > 60$ GeV.
  • Overlap with selected leptons ($\Delta R < 0.4$) is vetoed to avoid contamination from the $V$ boson decay.
• Event Selection Cuts:
  • WH: $p_T^{\text{miss}} > 30$ GeV, $p_T^W > 60$ GeV, $30 < m_T^W < 130$ GeV. Ratio $p_T^W / p_T^{\text{SUEP}} < 3$. Azimuthal separation $\Delta\phi > 1.5$. Boosted sphericity $S_{\text{SUEP}}^{\text{boosted}} > 0.3$. $b$-jet veto.
  • ZH: Leading jet overlapping the SUEP must have $p_T > 25$ GeV. $p_T^Z > 25$ GeV, $60 < m_{\ell\ell} < 120$ GeV. $b$-jet veto.

Background Estimation: Extended ABCD Method

• Strategy: An extended ABCD method is used to estimate SM backgrounds directly from data, minimizing reliance on simulation.
• Variables: Two uncorrelated (or weakly correlated) variables define the regions:
  1. SUEP Constituent Multiplicity ($n_{\text{SUEP}}^{\text{constituent}}$): High multiplicity is a signal feature.
  2. Discriminating Variable:
     • WH Channel: Boosted Sphericity ($S_{\text{SUEP}}^{\text{boosted}}$).
     • ZH Channel: Transverse momentum of the leading overlapping jet ($p_T^{j1}$).
• Regions: The plane is divided into 9 subregions (A–I). Regions A–H are Signal-Depleted Regions (SDRs) used to predict the background in Region I (Signal-Enriched Region, SER).
• Validation: Validation regions (PR-WH, PR-ZH) using photon triggers (where the photon acts as a proxy for $W/Z$) are used to validate the background estimation closure.

3. Key Contributions

1. First Search in VH Mode: This is the first search for SUEPs specifically in association with a $W$ or $Z$ boson, complementing previous gluon-fusion searches.
2. Novel Trigger Strategy: Demonstrates the effectiveness of using leptonic $V$ boson decays to trigger on SUEP events, bypassing the high-rate QCD background.
3. Advanced Background Estimation: Implementation of an extended ABCD method with 9 subregions to handle the specific kinematic correlations between SUEP multiplicity and event shape variables in the presence of $V$ bosons.
4. Reinterpretation Framework: The analysis provides full statistical models, HEPData entries, and a MADANALYSIS/DELPHES implementation, allowing the community to reinterpret the results for various BSM models without re-running the full simulation chain.

4. Results

• Observation: No significant excess of events over the Standard Model background expectation was observed in either the WH or ZH channels.
• Limits:
  • Upper limits at 95% Confidence Level (CL) were set on the production cross-section times branching fraction: $\sigma_{\text{prod}} \times \mathcal{B}(H \to \text{SUEP}) / \sigma_{\text{prod}}^{\text{SM}}$.
  • The limits are presented as a function of the signal model parameters ($m_{\phi_D}$ and $T_D$).
  • Sensitivity: The analysis is most sensitive to models with lower dark meson masses ($m_{\phi_D}$) and lower temperatures ($T_D$), which produce higher multiplicities of low-momentum particles.
• Improvement: The limits on the production rate of SUEPs via a Higgs mediator improve upon the previous gluon-fusion search (Ref. [14]) by up to two orders of magnitude for specific parameter ranges.
• Benchmark: For a benchmark scenario where $\mathcal{B}(H \to \text{SUEP}) = 0.16$ (consistent with current undetected Higgs limits), the observed limits exclude certain regions of the SUEP parameter space.

5. Significance

• Expanding the Search Landscape: This work proves that searching for "soft" and "unclustered" signatures in association with vector bosons is a viable and highly sensitive strategy for discovering hidden sectors.
• Complementarity: It fills a critical gap in the search for Hidden Valley models, covering production modes that were previously inaccessible due to trigger limitations.
• Model Constraints: The results place stringent constraints on the parameter space of dark QCD models, particularly those predicting SUEP decays of the 125 GeV Higgs boson.
• Open Science: By providing the full statistical model and reinterpretation tools, the collaboration enables other theorists to test alternative models against this dataset, maximizing the scientific return of the LHC Run 2 data.

In summary, this paper represents a significant advancement in the search for exotic Higgs decays, utilizing a novel trigger strategy and robust data-driven background estimation to set the world's most stringent limits on SUEP production in the $VH$ channel.