Precision Jet Substructure of Boosted Boson Decays with Energy Correlators

This paper initiates a precision study of boosted jet substructure using energy correlators applied to hadronic Higgs decays, demonstrating that the two-body decay manifests as a distinct angular peak and that infrared scales like the dead-cone effect and confinement transition are resolvable, thereby enabling precision electroweak studies and new physics searches.

The Gist

Imagine you are a detective trying to figure out what happened inside a high-speed crash, but you can't see the crash itself. You only see the debris flying out in a tight, fast-moving spray. This is the challenge physicists face when studying the Higgs boson (a fundamental particle) at the Large Hadron Collider.

When the Higgs boson is created, it often zooms through the detector at nearly the speed of light. Because it's moving so fast, the particles it decays into (breaks apart into) get squished together into a single, narrow cone of debris, looking very much like a standard spray of particles from a common collision. Distinguishing a "Higgs spray" from a "regular spray" is incredibly difficult.

This paper introduces a new, ultra-precise way to look at that spray using a tool called Energy Correlators. Here is the breakdown of their findings using simple analogies:

1. The "Flashlight" Analogy (Energy Correlators)

Instead of just counting how many particles are in the spray, the authors use "Energy Correlators." Imagine shining two flashlights from the center of the spray in different directions. You measure how much light (energy) hits the walls in those two directions simultaneously.

• By scanning the angle between these two flashlights, you can map out the internal structure of the spray with extreme precision.
• This method is like using a high-resolution X-ray to see the bones inside a wrapped gift, rather than just guessing what's inside by shaking it.

2. The "Two-Prong" Signature (The Big Discovery)

The Higgs boson is special because it often decays into exactly two main particles (like a parent splitting into two children).

• At Rest: If the Higgs were standing still, these two children would run away in exactly opposite directions (180 degrees apart).
• In Motion: Because the Higgs is zooming so fast, the two children are forced to run in the same general direction, but they don't run perfectly together. They spread out slightly.

The authors discovered that this specific "two-child" behavior creates a distinct peak in the energy map at a very specific angle.

• The Metaphor: Imagine a firework rocket exploding while flying forward. The sparks don't fly in a perfect circle; they fan out in a specific cone shape. The paper shows that the Higgs leaves a "fingerprint" in this cone shape.
• The Formula: They found that the angle of this peak depends on how fast the Higgs is moving. If you know the speed, you can predict exactly where to look for this peak. It's like knowing that a car traveling at 60 mph will leave skid marks at a specific angle, while a car at 30 mph leaves them at a different angle.

3. Seeing the Invisible Rules (QCD Scales)

The paper also shows that this method is sensitive enough to see the "rules" of the universe that govern how particles stick together (a force called the Strong Force).

• The Dead Cone: For heavy particles (like the bottom quark), there is a "dead zone" right in front of them where they can't emit other particles. It's like a car with a blind spot directly in front of the bumper. The authors show that their energy map clearly reveals this blind spot.
• The Confinement Wall: At very small angles, the particles start to clump together into larger groups (hadrons). The map shows where this "clumping" begins, acting like a ruler that measures the size of the "glue" holding particles together.

4. Why This Matters (The "New Physics" Angle)

The authors argue that because this method is so precise, it can act as a filter.

• The Background Noise: Most particle sprays (from standard collisions) look like a smooth, featureless cone that gets wider and wider as you look closer. They follow a predictable pattern.
• The Signal: The Higgs spray breaks this pattern. It has that specific "two-prong" peak and the specific "dead cone" features.
• The Result: By looking for these specific shapes in the data, scientists can separate the rare Higgs events from the overwhelming background noise much better than before.

Summary

The paper is essentially a new instruction manual for reading the "fingerprint" of a speeding Higgs boson. It proves that by measuring the angles between energy flows in the debris, we can:

1. Spot the Higgs by finding a specific peak angle that only a two-part decay creates.
2. Measure the speed of the Higgs based on where that peak sits.
3. See the fundamental rules of particle physics (like mass effects and confinement) written directly into the shape of the spray.

This doesn't just help us understand the Higgs; it opens a door to finding new heavy particles. If a new, unknown particle exists and decays into two parts, it will leave a similar "peak" signature, allowing scientists to discover it even if they don't know exactly what it is yet.

Technical Summary

Technical Summary: Precision Jet Substructure of Boosted Boson Decays with Energy Correlators

Problem Statement
At high-energy colliders, electroweak bosons ($W, Z, H$) and potential new heavy resonances are frequently produced with extreme Lorentz boosts. In this regime, their decay products become highly collimated, manifesting in detectors as jet-like radiation patterns that are difficult to distinguish from standard Quantum Chromodynamics (QCD) background jets. While jet substructure techniques have been developed to disentangle these origins, there is a need for precision analytic frameworks that can systematically characterize the radiation patterns of boosted objects, particularly to resolve infrared (IR) scales and heavy-quark mass effects within the boosted distribution.

Methodology
The authors apply the framework of Energy Correlators, specifically the two-point Energy-Energy Correlator (EEC), to the study of boosted Higgs boson decays. The EEC measures correlations between energy-flow operators in different directions, defined as $\langle \Psi | E(\vec{n}_1) E(\vec{n}_2) | \Psi \rangle$.

The core methodological innovation is the factorization of the problem into two steps:

1. Rest-Frame Characterization: The authors first perform precision analytic calculations of the EEC distribution for Higgs decays ($H \to gg$ and $H \to b\bar{b}$) in the rest frame. This involves mapping the distribution across distinct physical regimes:

   • Wide-angle region ($\theta \sim 1$): Calculated at Next-to-Leading Order (NLO) using fixed-order QCD.
   • Collinear regime ($\theta \ll 1$): Factorized into hard and jet functions. Resummation is performed at Next-to-Next-to-Leading Logarithm (NNLL) for $H \to gg$ and Next-to-Leading Logarithm (NLL) for $H \to b\bar{b}$. This regime captures the transition from classical $1/\theta$ scaling to linear scaling driven by IR scales ($m_b$ and $\Lambda_{QCD}$), including the "dead-cone effect" for massive quarks.
   • Back-to-back region ($\theta \to \pi$): Governed by Sudakov double logarithms. The authors perform resummation up to Next-to-Next-to-Next-to-Next-to-Leading Logarithm (N4LL) accuracy.
   • Exclusive measurements: For the $H \to b\bar{b}$ channel, they utilize the track function formalism to isolate correlations exclusively between $B$-hadrons, treating $b$-flavor as a quantum number.

2. Boost Transformation: To obtain the boosted distribution, the authors derive a boost kernel $K_\gamma$ that maps the rest-frame EEC distribution to the boosted frame via a Lorentz transformation. This allows the precision rest-frame calculations to be transformed into the boosted frame without re-calculating the full dynamics in the boosted kinematics.

Key Contributions and Results

• Distinct Angular Peak: The primary result is the demonstration that the two-body decay of a boosted Higgs boson manifests as a distinct angular peak in the EEC distribution at $\theta_{peak} \approx \arccos(1 - 2/\gamma^2)$, where $\gamma$ is the Lorentz boost factor. This peak corresponds to the transformation of the rest-frame back-to-back configuration into a collimated jet-like topology.
• Resolution of IR Scales: The study shows that fundamental QCD scales are resolved within the boosted distribution:
  • The dead-cone effect (suppression of radiation around massive emitters) is visible in the $H \to b\bar{b}$ channel, modifying the scaling behavior near the mass threshold.
  • The confinement scale ($\Lambda_{QCD}$) is resolved in the $H \to gg$ channel, where the distribution saturates to a constant value at very small angles.
• Exclusive vs. Inclusive: The paper analyzes exclusive $B$-hadron correlations, finding a crossover with inclusive predictions. This suggests that mass effects in the jet function are critical near the scale $m_H(\pi - \theta) \sim m_b$.
• Scalar Mass Reconstruction: The authors demonstrate that the angular position of the peak depends systematically on the scalar mass $m_H$ for a fixed energy. This implies that the substructure of the decay jet can be used to reconstruct the mass of the parent resonance.

Significance and Claims
The paper claims that this framework provides a robust observable for characterizing boosted resonances. By leveraging the simple transformation properties of energy flow operators under Lorentz boosts, the authors enable the transfer of precision calculations from the rest frame to the boosted distribution.

The significance of this work lies in its potential to:

• Facilitate precision electroweak studies by providing a clear, analytic understanding of radiation patterns in Higgs jets.
• Assist in the development of high-precision parton showers and improve the performance of machine learning taggers trained on such simulations.
• Open new avenues for new physics searches, specifically by allowing the reconstruction of masses for new heavy scalars directly from the substructure of their decay jets.
• Provide a pathway for precision measurements at future lepton colliders, complementing ongoing programs at the Large Hadron Collider (LHC).

The authors note that the theoretical techniques—combining fixed-order inputs, resummation, and boost kernels—can be extended to other boosted systems, such as top quarks, hadronically decaying $W/Z$ bosons, and novel resonances, including the study of higher-prong decay modes and polarization effects.