Quirk SUEP

Technical Summary: Soft-unclustered-energy patterns from quirks

Problem and Motivation
The search for physics beyond the Standard Model (SM) at the LHC often overlooks signatures involving Soft-Unclustered-Energy Patterns (SUEPs) composed of low-transverse-momentum ($p_T \lesssim \text{GeV}$) particles. These signatures are challenging to detect because they are obscured by large non-perturbative backgrounds and difficult to trigger on online. The authors propose a strategy to search for such phenomena in the low-$p_T$ tracks accompanying TeV-scale resonances. This approach leverages the resonance to satisfy high-$p_T$ trigger requirements while using the resonance sidebands to estimate backgrounds without relying solely on simulation. The specific motivation is a class of "Hidden Valley" models featuring "dark QCD," where heavy dark quarks (quirks) are produced and subsequently de-excite via the emission of numerous soft SM particles before annihilating.

Signal Model: Microscopic Quirks
The paper develops a benchmark model based on "quirks"—dark quarks with masses ($m_{q'}$) much larger than the dark confinement scale ($\Lambda'$). In this scenario, a pair-produced quirk-antiquirk pair is connected by a color string that cannot break due to the absence of light dark quark flavors. Instead, the pair oscillates, radiating energy until they reach a ground state and annihilate.

• De-excitation: The model assumes the quirks carry SM QCD charge. During de-excitation, they emit SM pions isotropically in their rest frame. The emission is modeled as a thermal process with a Hagedorn temperature ($T_H \approx 150$ MeV), resulting in $\mathcal{O}(10^3)$ soft pions per event.
• Annihilation: Once de-excited, the quirkonium annihilates into a pair of high-$p_T$ SM jets (dijets).
• Parameters: The model is defined by the quirk mass ($m_{q'}$), the dark confinement scale ($\Lambda'$), and a parameter $E_{\text{frac}}$ representing the fraction of internal energy converted into pions (ranging from 0.2 to 1.0). The study focuses on the "microscopic" regime where the string length is smaller than the inverse SM confinement scale, ensuring prompt de-excitation and annihilation.

Methodology and Simulation
The authors simulate signal and background events for 13 TeV proton-proton collisions corresponding to an integrated luminosity of $140 \text{ fb}^{-1}$.

• Simulation Tools: Signal generation uses a semi-analytical hybrid approach combining MG5_aMCatNLO for quirk production and Pythia 8 for hadronization. The pion emission is treated as isotropic thermal radiation. Background dijet events are generated at leading order.
• Detector Simulation: Events are processed through a simplified Delphes 3.5 simulation. Selection criteria mimic ATLAS dijet searches but with an increased jet radius ($R=1.0$) to improve mass resolution, accepting tracks with $p_T > 0.5$ GeV.
• Selection Strategies: Three strategies are evaluated to enhance sensitivity over inclusive resonance searches:
  1. Cut-based: A simple rectangular cut on the number of tracks ($N_{\text{tracks}}$), identified as the most powerful discriminant.
  2. Supervised Learning: A neural network trained on signal and background distributions using observables including $N_{\text{tracks}}$, polar angle, transverse sphericity, and average track separation.
  3. Weakly Supervised Anomaly Detection: The CATHODE framework is employed to find anomalies in the track distributions within the dijet signal region, using sidebands to estimate the background density via normalizing flows.

Key Results

• Discriminating Power: The number of soft tracks is the dominant observable. For high $E_{\text{frac}}$ (high pion multiplicity), the signal exhibits a significantly higher track count and greater isotropy compared to the QCD background.
• Discovery Potential:
  • For the nominal benchmark model ($\mu=1$), a $5\sigma$ discovery is nearly achievable for a quirk mass of 750 GeV using inclusive searches alone.
  • For higher masses (1.0 and 1.5 TeV), the inclusion of track-based selection strategies significantly improves sensitivity.
  • The supervised classifier achieves the best performance, requiring the lowest signal strength for discovery. However, it remains robust even when trained on a model with a different $E_{\text{frac}}$ than the test signal.
  • The simple track multiplicity cut performs comparably to the supervised classifier for high $E_{\text{frac}}$ and offers a model-independent alternative.
  • CATHODE (anomaly detection) yields sensitivity similar to the simple track cut. The authors note that for the low signal strengths required for discovery in this specific model, the anomaly detector relies almost exclusively on the track multiplicity observable rather than more subtle kinematic features.
• Exclusion Limits:
  • Using a supervised classifier, quirk masses up to $\approx 1450$ GeV can be excluded for $E_{\text{frac}} = 0.2$.
  • For $E_{\text{frac}} = 1.0$, the entire probed phase space ($m_{q'} < 1500$ GeV, $\Lambda' < 200$ GeV) can be excluded using either the supervised classifier or a tight track multiplicity cut.
  • Anomaly detection methods (CATHODE/IAD) do not significantly improve exclusion limits over inclusive searches for the lower signal strengths typical of exclusion, as statistical fluctuations make distinguishing $S+B$ from $B$ difficult.

Significance and Claims
The paper claims to demonstrate that searching for TeV-scale resonances accompanied by anomalies in low-$p_T$ track distributions is a viable and powerful strategy for discovering de-excited bound states and dark showers. The authors emphasize that:

1. Enhanced Reach: Utilizing soft track information extends the reach of standard dijet searches, particularly for models with high track multiplicity.
2. Model Independence: A simple cut on track multiplicity offers a relatively model-independent way to enhance sensitivity without assuming specific angular or kinematic properties of the new tracks.
3. Robustness: Supervised classifiers remain effective even with mismodeled signal parameters (e.g., incorrect $E_{\text{frac}}$), though their performance relies on the specific signal characteristics.
4. Unexplored Phase Space: The proposed phenomenology covers a parameter space (resonances with soft, isotropic track anomalies) that has not been probed at the LHC to date.

The authors conclude that while anomaly detection methods like CATHODE are valuable for maintaining low model dependence, the dominance of the track multiplicity observable in this specific benchmark model means that simpler selection strategies are highly effective. They suggest future work could explore varying the resonance type (e.g., dileptons) or the radiation spectrum.