Bump Hunting Inside Jets with Energy Correlators

This paper proposes a novel "bump hunting" strategy within jets by leveraging the well-understood scaling of energy correlators in perturbative QCD to identify angular resonances caused by new physics, demonstrating the method's effectiveness through projected LHC constraints on a light hadrophilic $Z'$.

The Gist

Imagine the Large Hadron Collider (LHC) as a massive, high-speed car crash zone. When protons smash together, they don't just shatter; they spray out streams of particles called jets. Think of these jets like powerful water hoses spraying out from the collision point.

For decades, physicists have studied these "hoses" to understand the rules of the universe (Quantum Chromodynamics, or QCD). They found that if you look closely at how the water sprays out, it follows a very specific, predictable pattern. It's like a smooth, flowing river that gets narrower and narrower the further you look from the source. This pattern is so reliable that it's like a "fingerprint" of normal physics.

The New Idea: Hunting for "Bumps" in the Spray

This paper proposes a clever new way to look for "new physics"—unknown particles or forces that don't follow the standard rules. The authors suggest that if a new, heavy particle (let's call it a "ghost particle") is created inside one of these jets, it would leave a very specific mark.

Here is the analogy:

• The Normal Jet: Imagine a smooth, continuous waterfall. If you measure the water flow at different angles, it decreases smoothly. This is what we expect from normal physics.
• The New Physics Jet: Now, imagine that hidden inside that waterfall is a small, spinning sprinkler. Even though the main flow is smooth, this sprinkler creates a sudden, sharp bump or a ring of extra water at a specific distance from the center.

The paper calls this "Bump Hunting Inside Jets." Instead of looking for a new particle by seeing it fly across the detector, they look for this "ring of water" (an angular resonance) inside the spray of a single jet.

How It Works: The Energy Correlator

The tool they use is called an Energy Correlator. Think of this as a super-precise camera that doesn't just take a picture of the jet, but measures exactly how much energy is hitting the detector walls at every single angle.

1. The Smooth Background: In normal jets, the energy drops off smoothly as you move away from the center, following a mathematical rule (like a slide).
2. The New Physics Signal: If a new particle (like a light version of a Z boson, called a Z') is created and decays inside the jet, it breaks that smooth slide. Instead of a smooth curve, you get a sharp peak—a "bump"—at a specific angle.
3. The Shape Matters: The paper explains that the shape of this bump tells you what the particle is.
   • If the particle spins one way, the bump looks like a hill.
   • If it spins another way, the bump looks like a double-humped camel.
   • The authors created a "menu" of all possible bump shapes allowed by the laws of physics (specifically, rules about energy and probability). If you see a bump, you can match its shape to the menu to guess what kind of particle made it.

The "Hadrophilic Z'" Test

To prove this idea works, the authors tested it on a specific hypothetical particle called a hadrophilic Z'. "Hadrophilic" just means "loves to talk to normal matter" (quarks).

• They simulated what would happen if these Z' particles were created at the LHC.
• They used their "Energy Correlator camera" to look for the bumps.
• The Result: They found that this method is just as good at finding these particles as the most advanced, complex methods currently used by the CMS experiment at CERN. In fact, it's simpler and more robust because it relies on fundamental math rather than complex computer models that can sometimes be wrong.

Why This Matters

The paper argues that this is a "broadband" search. Just like a radio tuner can pick up many different stations without needing to know exactly what song is playing, this method can spot any new particle that creates a bump, regardless of exactly what that particle is.

They also looked at existing data from the CMS experiment (which was originally used to measure the strength of the strong nuclear force). By re-analyzing that data with their new "bump hunting" technique, they showed they could set strict limits on how heavy or how common these new particles could be.

In Summary

• The Problem: Finding new particles is hard because they are hidden inside messy jets of debris.
• The Solution: Look for a specific "ring" or "bump" in the energy distribution inside the jet, rather than the particle itself.
• The Tool: Energy Correlators, which measure energy flow at different angles.
• The Analogy: Looking for a hidden sprinkler inside a smooth waterfall. The sprinkler creates a distinct ring of water that breaks the smooth flow.
• The Outcome: This method is a powerful, model-independent way to hunt for new physics, capable of matching the sensitivity of current top-tier experiments.

Technical Summary

Technical Summary: Bump Hunting Inside Jets with Energy Correlators

Problem Statement
Jets produced at the Large Hadron Collider (LHC) are information-rich objects encoding both perturbative and non-perturbative Quantum Chromodynamics (QCD) dynamics. While Beyond the Standard Model (BSM) scenarios often predict jet-like signatures with internal structures distinct from QCD, current search strategies frequently rely on machine learning discriminants or specific jet substructure variables. These approaches often suffer from a dependence on accurate modeling of parton showers and hadronization, lacking sharp, first-principles theoretical anchors. Furthermore, while Energy Correlators (ECs) have recently been utilized for precision QCD measurements (such as the determination of the strong coupling constant $\alpha_s$), their potential as a broadband, model-agnostic search tool for new physics remains under-explored. The central problem addressed is how to convert the precise, theoretically understood scaling behavior of ECs in the collinear limit into a sensitive probe for new physics that breaks this scaling.

Methodology
The authors propose utilizing Energy Correlators (ECs) to detect new physics by identifying "angular resonances" within jets. The methodology is built on the following theoretical and phenomenological framework:

1. Scaling Violation: In the collinear limit ($z \ll 1$, where $z$ is the angular separation), QCD energy correlators exhibit a characteristic power-law scaling governed by perturbative dynamics (specifically DGLAP evolution or light-ray OPE). The paper posits that any new hard scale introduced by BSM dynamics explicitly breaks this scaling.
2. Resonant Signal: The authors consider BSM scenarios where a fraction of jets are initiated by a boosted particle $X$ (mass $m_X$) decaying hadronically. Assuming $X$ couples linearly to a QCD operator and is sufficiently narrow, the energy correlator develops a sharp, resonant excess at a fixed angular scale $z^\star \sim m_X^2/E_J^2$, where $E_J$ is the jet energy.
3. Unitarity and Positivity Constraints: Rather than targeting specific models, the authors classify signals based on the spin $J$ and polarization of the source operator $O$. Using unitarity and energy positivity, they demonstrate that the space of admissible signals is compact and convex. For a spin-1 source, the signal shape is bounded by a single coefficient $c(2)$; for spin-2, it is bounded by $c(2)$ and $c(4)$. This allows for a classification of "shapes" independent of specific model details.
4. Boosted Frame Analysis: While the spin information washes out in the rest frame, the boost to the laboratory frame (characterized by $z^\star$) preserves the dependence on the spin and polarization coefficients. The boost induces a relativistic aberration, mapping the back-to-back decay in the rest frame to a sharp resonance peak at $z' \approx z^\star$ in the lab frame, with a spectral shape determined by the spin.
5. Phenomenological Application: As a proof of principle, the authors apply this framework to a light hadrophilic $Z'$ boson. They analyze two production channels:
   • Associated Production with a Photon ($pp \to Z'\gamma$): Recasting a CMS analysis [45] to compare inclusive Energy Correlators against standard substructure techniques (like soft-drop mass and $N_2$).
   • Associated Production with a Hard Jet ($pp \to Z'j$): Recasting a recent CMS measurement of ECs in dijet events [25] to derive sensitivity limits, incorporating both statistical and systematic uncertainties.

Key Contributions

• Theoretical Classification: The paper provides a complete classification of bilinear QCD singlet operators and their associated "spinning coefficients" ($c(j)$), establishing that unitarity and positivity bound the possible shapes of angular resonances. This converts the search for new physics into "bump hunting" in angular space with a theoretically predicted spectral shape.
• Model-Agnostic Search Strategy: The approach is largely model-independent. It relies on the generic assumption of a boosted resonance decaying hadronically, avoiding the need for specific parton shower modeling or machine training on specific BSM signals.
• Complementary Systematics: The method offers a distinct set of theoretical and experimental systematics compared to conventional jet substructure searches, providing a complementary approach to existing techniques.
• Sensitivity Projections: The authors derive projected LHC sensitivities for a light hadrophilic $Z'$, demonstrating that Energy Correlators can achieve competitive constraints with existing dedicated searches.

Results

• Angular Resonance Shape: Theoretical calculations show that while different spins produce peaks at the same position $z^\star$, they exhibit distinct spectral shapes (Fig. 1). The spin-1 case is bounded by $c(2) \in [-1, 1/2]$, and spin-2 by a triangular region in the $(c(2), c(4))$ plane.
• $Z'$ Search in $Z'\gamma$ Channel: In the recast of the CMS $Z'\gamma$ analysis, the inclusive Energy Correlator (EEC) observable, despite having a background size 10 times larger than the groomed selection used in standard analyses, yields upper limits on the coupling strength $g'_q$ comparable to the CMS recast. Applying a jet mass window to the inclusive EEC further enhances sensitivity by reducing background while preserving the smooth QCD shape (Fig. 3).
• $Z'$ Search in $Z'j$ Channel: Using the CMS dijet EC measurement [25], the authors project limits on the $Z'$ coupling-mass plane. Despite the small jet radius ($R=0.4$) and non-optimized event selection for BSM, the sensitivity is competitive with state-of-the-art searches (Fig. 4). The inclusion of systematic uncertainties (experimental and theoretical) is shown to be significant at current luminosities, but the full shape information of the EEC and three-point correlator (EEEC) ensures that sensitivity improves with luminosity even if systematics remain constant.

Significance and Claims
The paper claims that Energy Correlators offer a robust, theoretically grounded method for searching for new light resonances decaying to QCD. By exploiting the violation of the collinear scaling behavior, this approach transforms the search into a "bump hunt" in angular space where the position of the bump encodes the mass and the shape encodes the spin and polarization.

The authors emphasize that this is a "proof of principle" demonstrating that ECs can reach sensitivity competitive with dedicated searches while maintaining a largely model-agnostic scope. They argue that as the LHC moves toward its high-luminosity phase, repurposing precision jet substructure measurements (like the recent $\alpha_s$ determination) into novel BSM searches is a viable and promising strategy. The work motivates future dedicated experimental and theoretical efforts to explore EC-based BSM searches, including the potential for fully differential three-point correlators and hidden strongly coupled scenarios.