Measurement of angular correlations inside jets induced by gluon polarization in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV

Using 13.6 TeV proton-proton collision data collected by the CMS detector, this study measures angular correlations within jets induced by gluon polarization and finds that the results strongly favor theoretical models incorporating gluon spin effects over those that neglect them.

The Gist

Here is an explanation of the paper, translated into everyday language with some creative analogies.

The Big Picture: Catching the "Spin" of a Ghost

Imagine you are standing in a crowded room where people are throwing giant, invisible snowballs at each other. When two snowballs collide, they shatter into a million tiny, glowing snowflakes that fly out in a chaotic spray. In the world of physics, these snowballs are protons, and the snowflakes are jets of particles.

Inside these jets, there are tiny messengers called gluons. Gluons are the "glue" that holds the universe's building blocks together. But here's the tricky part: gluons aren't just static glue; they are spinning tops. They have a property called spin (or polarization).

For decades, physicists knew gluons had spin, but they had never been able to see how that spin affected the way the "snowflakes" (particles) arranged themselves inside the jet. It was like knowing a dancer was spinning, but never seeing the specific pattern their arms made while they twirled.

This paper is the first time the CMS Collaboration (a massive team of scientists using the Large Hadron Collider at CERN) successfully took a "slow-motion photo" of that spin pattern inside a jet.

The Experiment: The Ultimate High-Speed Camera

The Setup:
The scientists smashed protons together at record-breaking speeds (13.6 TeV). This created a massive amount of energy, resulting in thousands of jets. They collected data equivalent to 34.7 "inverse femtobarns" (a fancy unit meaning they watched a lot of collisions).

The Challenge:
Inside a jet, the particles are moving so fast and are so close together that it looks like a blurry mess. It's like trying to see the individual threads of a tornado while standing inside it. Furthermore, the "spin" effect they are looking for is very subtle. It's like trying to hear a whisper in a rock concert.

The Solution (The "De-clustering" Trick):
To see the details, the scientists used a clever computer algorithm (the Cambridge–Aachen algorithm). Imagine you have a giant, tangled ball of yarn (the jet). Instead of looking at the whole ball, they used a digital pair of scissors to carefully cut the yarn apart, layer by layer, starting from the outside and working inward.

By "unzipping" the jet, they could reconstruct the history of the collision:

1. First, a big chunk split into two.
2. Then, one of those chunks split again.

They focused specifically on the second split, looking for a moment where a gluon split into a quark and an anti-quark (a pair of particles). Theory says this specific split should show a distinct "twist" or pattern because of the gluon's spin.

The Detective Work: Finding the Needle in the Haystack

The problem is that most of the time, gluons split into other gluons, or quarks split into quarks and gluons. These other splits don't show the spin pattern clearly. It's like trying to find a specific type of red car in a parking lot full of red, blue, and green cars.

To solve this, the scientists trained an Artificial Intelligence (AI)—specifically a Deep Neural Network—to act as a super-sleuth.

• The Training: They taught the AI to look at the shape, energy, and spread of the particles inside the jet.
• The Goal: The AI learned to say, "This jet looks like it came from a gluon splitting into a quark pair," or "This one looks like a mess of other stuff."

Once the AI filtered out the noise and selected only the "quark-pair" jets, the signal became clear.

The Result: The Spin is Real!

When they looked at the angle between the particles in these selected jets, they saw a distinct wave-like pattern.

• If gluons had NO spin: The particles would be scattered randomly, like popcorn popping in a pot.
• If gluons HAVE spin: The particles arrange themselves in a specific, rhythmic pattern, like a synchronized dance.

What they found:
The data matched the "dance" perfectly. The pattern confirmed that gluons are indeed spinning and that this spin dictates how the particles inside the jet are arranged.

They compared their results to two major computer simulations (PYTHIA and HERWIG):

1. The "Spin-On" models: These models included the physics of gluon spin. The data matched these perfectly.
2. The "Spin-Off" models: These models ignored the spin. The data completely disagreed with these.

Why Does This Matter?

Think of the computer models (PYTHIA and HERWIG) as the "GPS" physicists use to navigate the subatomic world. If your GPS is wrong, you get lost.

1. Better Maps: This discovery proves that the current GPS (the models) needs to keep the "spin" feature turned on. If we turn it off, the map is wrong.
2. New Physics: Understanding how gluons spin helps us understand the fundamental forces of nature. It's like finally understanding the rules of how a dancer moves, which helps us predict where they will step next.
3. Future Discoveries: This technique could help scientists find even rarer things in the future, like how the Higgs boson (the "God particle") decays. If the Higgs decays into two gluons, knowing how those gluons spin will help scientists spot it more easily.

The Bottom Line

The CMS team successfully took a high-speed, high-definition video of the "spin" of a gluon inside a jet for the first time. They proved that the universe's "glue" has a specific dance move, and our computer simulations must learn to copy that dance to be accurate. It's a small step for a jet, but a giant leap for understanding the quantum world.

Technical Summary

Here is a detailed technical summary of the paper "Measurement of angular correlations inside jets induced by gluon polarization in proton-proton collisions at $\sqrt{s} = 13.6$ TeV" by the CMS Collaboration.

1. Problem Statement and Motivation

• Physics Context: Gluons are spin-1 gauge bosons mediating the strong interaction (QCD). While their spin nature was established decades ago in $e^+e^-$ annihilation via jet spin correlations, these effects have never been directly observed within the collinear and soft parton radiation inside jets produced in high-energy hadron collisions.
• Theoretical Challenge: In proton-proton ($pp$) collisions, the parton shower (PS) involves successive branchings (e.g., $g \to gg$, $g \to q\bar{q}$, $q \to qg$). The interference of helicity states in intermediate partons creates angular correlations. However, in a standard parton shower, the spin effects from $g \to gg$ and $g \to q\bar{q}$ processes largely cancel each other out due to opposite signs and different rates.
• Goal: The primary objective is to isolate the specific contribution of gluon polarization in the $g \to q\bar{q}$ splitting process within a jet shower. This requires measuring a specific angular observable, $\Delta\phi$, and comparing data against Monte Carlo (MC) models that either include or neglect these spin correlations. Accurate modeling is crucial for jet substructure studies and flavor tagging (e.g., distinguishing Higgs decays to gluons).

2. Methodology

Data and Simulation

• Data Source: Proton-proton collisions at $\sqrt{s} = 13.6$ TeV collected by the CMS detector in 2022 (Run 3).
• Integrated Luminosity: $34.7 \text{ fb}^{-1}$.
• Event Selection:
  • Jets reconstructed using the anti-$k_T$ algorithm (radius parameter $R=0.8$, denoted AK8) with $p_T > 700$ GeV and $|\eta| < 1.7$.
  • Events required to have at least two such jets separated by $\Delta\phi > 2$ radians.
• Monte Carlo Generators:
  • PYTHIA 8.306: Uses $p_T$-ordered showers and the CP5 tune.
  • HERWIG 7.3.0: Uses angular-ordered showers and the CH3 tune.
  • Both generators were run in two modes: "Correlation-on" (incorporating gluon spin effects) and "Correlation-off" (neglecting spin correlations).

Jet Substructure and Declustering

• Algorithm: Jets were declustered using the Cambridge–Aachen (CA) algorithm to reconstruct the branching history.
• Branching Selection: The analysis focuses on two successive branchings: $X \to 1+2$ followed by $2 \to 3+4$.
  • Subjets 1 and 2 are selected from the primary splitting (highest $k_T$ in the primary Lund plane).
  • Subjets 3 and 4 are selected from the secondary splitting (highest $k_T$ in the secondary Lund plane).
• Observable: The angle $\Delta\phi$ is defined as the angle between the production plane (formed by partons 1 and 2) and the decay plane (formed by partons 3 and 4):
  $$\cos \Delta\phi = \hat{n}_{1,2} \cdot \hat{n}_{3,4} \cdot \text{sign}[(\hat{n}_{1,2} \times \hat{n}_{3,4}) \cdot \vec{p}]$$
  where $\vec{p}$ is the momentum of the harder parton in the first splitting.

Machine Learning and Event Categorization

• Challenge: The $g \to q\bar{q}$ topology (where the intermediate gluon splits into a quark-antiquark pair) is a small fraction of events and is mixed with other topologies ($g \to gg$, $q \to qg$) that dilute the spin signal.
• Solution: A Deep Neural Network (DNN) was trained to categorize events based on the type of the second splitting ($g \to q\bar{q}$, $g \to gg$, $q \to qg$, or unmatched).
  • Inputs: 12 variables describing subjet kinematics, particle multiplicity, and splitting features (e.g., $z$ fractions, $k_T$, subjet width).
  • Selection: Events with a DNN score for the $g \to q\bar{q}$ class ($\text{score}_{g\to q\bar{q}}$) greater than 0.6 were selected. This enhanced the purity of the $g \to q\bar{q}$ sample to 38% while maximizing the statistical significance against the "correlation-off" hypothesis.

Unfolding

• To correct for detector effects (resolution, efficiency), the measured $\Delta\phi$ distribution was unfolded to the particle level.
• The unfolding utilized a symmetrized distribution ($\pi/2 - |\Delta\phi - \pi/2|$) to reduce statistical uncertainties.
• Systematic uncertainties (jet energy scale, pileup, modeling) were propagated through the unfolding matrix.

3. Key Contributions

1. First Observation in Jets: This is the first direct measurement of angular correlations induced by gluon polarization inside jets in $pp$ collisions. Previous observations were limited to $e^+e^-$ environments.
2. Novel Tagging Technique: Development of a machine-learning-based method to isolate specific parton splitting topologies ($g \to q\bar{q}$) within the complex environment of a hadronic jet, utilizing infrared- and collinear-safe flavor definitions.
3. High-Energy Validation: The measurement covers a center-of-mass energy of 13.6 TeV, probing a dynamic range of intrajet radiation significantly higher than previous $e^+e^-$ studies.

4. Results

• Inclusive Sample: In the inclusive sample (all events), the difference between "correlation-on" and "correlation-off" models is small (~0.5%) due to the cancellation of spin effects across different splitting types.
• Selected $g \to q\bar{q}$ Sample:
  • In the category enriched with $g \to q\bar{q}$ splittings ($\text{score}_{g\to q\bar{q}} > 0.6$), a clear modulation in the $\Delta\phi$ distribution is observed.
  • Significance: The data deviate from the "correlation-off" hypothesis by 6.8 standard deviations ($6.8\sigma$). The deviation from the "correlation-on" hypothesis is only **1.9$\sigma$**.
  • Model Comparison:
    • The data strongly favor models that include gluon polarization.
    • Models neglecting spin correlations are strongly disfavored.
    • PYTHIA 8 (with correlation-on) describes the data shape well.
    • HERWIG 7 (with correlation-on) predicts a stronger modulation than observed, indicating a discrepancy in the modeling of the spin effects or non-perturbative corrections in that specific generator.

5. Significance

• Validation of QCD: The results confirm that gluon spin correlations persist even in the presence of non-perturbative final-state effects and dense hadronic environments, validating the theoretical framework of QCD parton showers beyond leading-logarithmic accuracy.
• Impact on Event Generators: The measurement provides critical constraints for tuning Monte Carlo event generators. The observed discrepancies with HERWIG 7 suggest a need for refinement in how spin-density matrices are handled in angular-ordered showers.
• Future Applications: The ability to tag intermediate gluon splittings into quark pairs is vital for precision physics, particularly for identifying Higgs boson decays to gluons ($H \to gg$), where spin correlations are expected to be significant. This technique opens the door to studying flavor-dependent parton dynamics in the Lund plane.

In conclusion, the CMS Collaboration has successfully isolated and measured the subtle imprint of gluon spin on jet substructure, providing a stringent test of QCD dynamics and a new tool for future high-energy physics analyses.