Azimuthal decorrelation in diffractive dijet production

This paper calculates the azimuthal angular decorrelation of diffractive dijets in ultra-peripheral heavy-ion, $ep$, and $eA$ collisions using all-order resummation of soft gluon emissions to demonstrate that this observable serves as a promising probe for non-perturbative diffractive transverse momentum-dependent distributions, with numerical predictions provided for LHC, HERA, and the future EIC.

The Gist

Imagine the inside of a proton or an atomic nucleus not as a solid ball, but as a bustling, chaotic city filled with tiny, invisible messengers called gluons. These gluons hold the nucleus together, but they are also constantly moving, colliding, and radiating energy. Physicists want to take a "snapshot" of this city to see exactly how these messengers are arranged and moving.

This paper is about a new, clever way to take that snapshot using high-energy particle collisions. Here is the breakdown of their idea, using simple analogies:

1. The Goal: Seeing the Invisible City

The researchers want to map out the transverse momentum-dependent distributions (TMDs) of gluons. Think of this as trying to figure out not just where the gluons are, but also how fast they are moving sideways.

• The Problem: Usually, when scientists try to look at these gluons, the tools they use are a bit blurry. It's like trying to take a photo of a speeding car at night with a shaky camera; you get a smear instead of a clear picture.
• The Solution: They propose looking at diffractive dijet production. Imagine shooting a photon (a particle of light) at a nucleus. Sometimes, the photon splits into two jets of particles (like two streams of water) that fly out in almost opposite directions. If the nucleus stays intact (it doesn't break apart), it's called "diffractive."

2. The Twist: The "Tri-Jet" Surprise

In the past, scientists focused on the "exclusive" case where only two jets come out. But this paper argues that the most common event is actually a "semi-inclusive" tri-jet event.

• The Analogy: Imagine you throw a ball at a wall, and it bounces back as two balls. In the "exclusive" version, you only see those two. But in reality, a third, smaller pebble (a semi-hard gluon) often flies off the wall too, but it's hard to see because it's small and flies near the wall.
• Why it matters: This third "pebble" changes the physics. Because the two main jets are now in a different "color state" (a quantum property) due to this extra pebble, they interact with the nucleus differently. This makes the event much more common and easier to study than the rare "exclusive" version.

3. The New Tool: The "Acoplanarity" Compass

To measure the gluons' sideways movement, the researchers focus on acoplanarity.

• The Old Way: They used to measure the "momentum imbalance" (how much the two jets didn't perfectly cancel each other out). This is like trying to measure the speed of a car by weighing how much fuel it burned. It's messy and prone to errors because your scale (the detector) isn't perfect.
• The New Way: They measure the angle between the two jets. If the jets were perfectly back-to-back, the angle would be exactly 180 degrees. If they are slightly off, the angle is a tiny bit less.
• The Metaphor: Measuring the angle is like using a laser pointer. Even if the laser is a bit dim, you can tell exactly where it's pointing. Angles are much easier to measure precisely than energy levels. This "acoplanarity" gives a much sharper picture of the gluons' internal motion.

4. The "Noise" Problem: Initial vs. Final State Radiation

One of the paper's biggest discoveries is about "noise" in the signal.

• The Noise: When the jets fly out, they emit more tiny particles (soft gluons). This is like a car exhaust fanning out. This emission can make the jets look like they are wobbling or spreading out, even if the nucleus itself is calm.
• The Insight: The authors found that in this specific "tri-jet" scenario, there is a lot of "Initial State Radiation" (noise coming from the start of the collision) that pushes the jets apart.
• The Analogy: Imagine two people walking away from each other holding hands. If a third person (the initial radiation) pushes them from behind, they will drift apart. If you don't account for that push, you might wrongly think the ground (the nucleus) is shaking. The paper provides a mathematical "noise-canceling" formula to separate the push from the ground shaking.

5. Heavy vs. Light: The "Dead Cone" Effect

They also looked at what happens when the jets are made of heavy quarks (like charm or bottom quarks) instead of light ones.

• The Analogy: Imagine a heavy bowling ball rolling down a lane versus a light ping-pong ball. The heavy ball is harder to knock off course.
• The Result: Heavy quarks have a "dead cone" effect. They are so heavy that they don't emit the "exhaust fumes" (gluons) at sharp angles. This means the jets stay straighter and the "wobble" (decorrelation) is much smaller.
• Why it helps: Because the heavy jets are less "noisy," they act like a clean reference point. By comparing the heavy jets to the light jets, scientists can isolate the true signal of the nucleus's internal structure.

6. Where This Happens

The paper predicts what we should see in three specific places:

1. LHC (Large Hadron Collider): Smashing heavy ions together at very high speeds.
2. EIC (Electron-Ion Collider): A future machine that will be a "clean laboratory" for these studies.
3. HERA: A past machine that provides a baseline for comparison.

The Bottom Line

This paper says: "We have found a better way to take a photo of the inside of an atomic nucleus. By measuring the angle between two jets instead of their energy, and by carefully accounting for the 'noise' caused by extra particles flying off, we can see the gluon traffic inside the nucleus much more clearly. We also found that using heavy quarks gives us a cleaner picture because they are less affected by the noise."

This method promises to help physicists finally map out the full "Wigner distribution" of gluons—a complete 3D map of where they are and how they are moving inside matter.

Technical Summary

Technical Summary: Azimuthal Decorrelation in Diffractive Dijet Production

Problem Statement
Diffractive dijet production in lepton-nucleon and lepton-nucleus scattering serves as a critical probe for the internal structure of hadrons, specifically targeting gluon Generalized Parton Distributions (GPDs), gluon saturation, and the gluon Wigner distribution. While exclusive dijet production has traditionally been the focus, recent theoretical developments indicate that in the large dijet invariant mass region, the cross-section is dominated by coherent semi-inclusive processes (often termed diffractive tri-jet production). In this channel, a semi-hard gluon is emitted alongside the primary quark-antiquark ($q\bar{q}$) pair. Unlike the exclusive channel, where the $q\bar{q}$ pair is in a color-singlet state and suffers from color transparency suppression, the semi-inclusive channel leaves the pair in a color-octet state at short distances. This allows the system to scatter as a gluon-gluon dipole, significantly enhancing the cross-section.

A major challenge in probing the non-perturbative diffractive transverse momentum-dependent distributions (DTMDs) via these processes is the experimental difficulty in measuring the transverse momentum imbalance ($q_\perp$). Determining $q_\perp$ relies on jet energy measurements, which are subject to poor resolution and instrumental smearing. Furthermore, the azimuthal correlations in these events are complicated by the interplay between Initial State Radiation (ISR) and Final State Radiation (FSR). Previous analyses suggested that while FSR can mimic certain asymmetries, ISR—kinematically allowed in the dominant semi-inclusive channel—tends to wash out these signals. There is a need for a theoretically clean observable that minimizes clustering ambiguities and allows for a precise separation of saturation signals from radiative broadening.

Methodology
The authors propose utilizing the Transverse Energy-Energy Correlator (TEEC) and the dijet acoplanarity ($\phi_\perp$) as robust observables. Unlike standard jet observables, TEEC is defined via energy-weighted correlation functions of final-state particles, making it infrared and collinear safe and reducing dependence on jet clustering algorithms and axis definitions.

The theoretical framework employs Diffractive Transverse Momentum Dependent (DTMD) factorization. The key methodological steps include:

1. Resummation of Soft Gluons: The authors perform an all-order resummation of soft gluon emissions for both ISR and FSR. A central feature is the consistent inclusion of ISR, which arises from the color-octet nature of the $q\bar{q}$ pair in the semi-inclusive process.
2. Factorization Formula: The differential cross-section is formulated using a one-dimensional Fourier transform with respect to the impact parameter $b_x$. This reduction is physically motivated by the acoplanarity observable's exclusive sensitivity to the orthogonal projection of the transverse momentum imbalance.
3. Jet Axis Definitions: The study contrasts two jet axis definitions: the Standard Jet Axis (SJA), which is sensitive to soft recoil within the jet cone, and the Winner-Take-All (WTA) scheme, where the axis aligns with the most energetic constituent, rendering it insensitive to soft radiation inside the cone.
4. Heavy Quark Analysis: The framework is extended to heavy-quark pair production ($c\bar{c}$ and $b\bar{b}$). The authors incorporate the dead-cone effect, which dynamically suppresses collinear gluon emissions at angles $\theta \lesssim m_Q/E$. This suppression truncates the collinear logarithmic evolution in the Sudakov factor at the heavy quark mass scale $m_Q$.
5. Non-Perturbative Modeling: The non-perturbative Sudakov form factor is modeled using parameters fitted to SIDIS and Drell-Yan data, while the diffractive scattering off the saturated nucleus is described using the Golec-Biernat-Wüsthoff (GBW) model for the dipole amplitude.

Key Contributions and Results
The paper provides numerical predictions for azimuthal decorrelations in three distinct kinematic environments: Ultra-Peripheral Collisions (UPCs) of Pb-Pb at the LHC ($\sqrt{s} = 5.02$ TeV), $eA$ collisions at the future Electron-Ion Collider (EIC, $\sqrt{s} = 89$ GeV), and $ep$ collisions at HERA ($\sqrt{s} = 320$ GeV).

• TEEC Distributions: The predicted TEEC distributions show a pronounced peak in the back-to-back limit ($\tau \to 0$). The nuclear modification factor ($R_{pA}$) exhibits a characteristic suppression at small $\tau$ and enhancement in the tail, a hallmark of saturation physics driven by the larger nuclear saturation scale ($Q_{sA}$).
• Impact of ISR: The analysis demonstrates that ISR induces a significant broadening of the azimuthal correlation. This effect acts as a major background that must be disentangled from the saturation signal, underscoring the necessity of a comprehensive perturbative baseline.
• Jet Axis Sensitivity: The comparison between SJA and WTA schemes reveals distinct responses to soft gluon radiation. The SJA is more sensitive to recoil within the jet cone, leading to broader distributions compared to the WTA scheme.
• Heavy Quark Suppression: Heavy-quark pair production shows a much narrower azimuthal decorrelation compared to light dijets. This is attributed to the dead-cone effect, which suppresses collinear radiation. The $b\bar{b}$ pairs exhibit slightly narrower distributions than $c\bar{c}$ pairs due to their larger mass. This mass hierarchy provides a clean probe to isolate genuine saturation signals from perturbative radiative effects.
• EIC Prospects: The EIC is identified as a critical facility for these studies. Unlike hadronic collisions where factorization breaking complicates interpretation, the EIC offers a clean environment to rigorously test the formalism. The TEEC at the EIC is shown to be sensitive to the nuclear saturation scale.

Significance and Claims
The paper claims that the acoplanarity of diffractive dijet production, particularly when measured via TEEC, serves as a promising and experimentally practical probe for diffractive DTMDs. By utilizing the high angular resolution of modern detectors rather than relying on jet energy measurements, the acoplanarity observable mitigates systematic limitations associated with energy resolution.

The authors emphasize that their work establishes a necessary perturbative baseline that accounts for the significant broadening caused by ISR, FSR, and jet axis definitions. This baseline is crucial for unambiguously isolating saturation signals in future experimental data. The study highlights that heavy-quark pair production offers a complementary, highly perturbative channel to probe the nuclear saturation scale due to the suppression of soft radiation. Ultimately, the paper posits that these observables can facilitate the extraction of the gluon Wigner distribution and advance the study of saturation physics at the high-energy frontier, provided that higher-order corrections to hard and soft functions are incorporated in future work to further reduce theoretical uncertainties.