Jet quenching and its substructure dependence due to color decoherence

Motivated by color coherence and decoherence effects, this paper proposes a theoretical framework combining vacuum-like evolution and medium-induced radiation to successfully describe the inclusive jet modification factor and its substructure dependence in 0–10% PbPb collisions at $\sqrt{s_{NN}} = 5.02~\rm{TeV}$ as measured by ATLAS.

The Gist

The Big Picture: The "Jet" and the "Soup"

Imagine you are at a massive, chaotic party (the Quark-Gluon Plasma or QGP). This party is made of extremely hot, dense "soup" created when two heavy atomic nuclei smash together at nearly the speed of light.

Now, imagine a very fast, high-energy particle (a parton) gets shot out of the collision. As it zooms through the party, it doesn't travel alone. It sprays out a shower of smaller particles, like a firework exploding into sparks. This whole bundle of particles is called a Jet.

In a normal vacuum (like empty space), this firework would fly straight and keep its shape. But in our "party soup," the jet crashes into the crowd. It loses energy, slows down, and gets scattered. This phenomenon is called Jet Quenching.

Scientists want to know: How much energy does the jet lose? And does it matter how the jet is built inside?

The Core Idea: The "Soloist" vs. The "Choir"

The main discovery in this paper is about Color Decoherence. This is a fancy physics term that we can understand with a simple analogy: The Soloist vs. The Choir.

1. The Soloist (Coherent Jet):
   Imagine a single singer (the main parton) walking through the crowd. If the crowd sees them as one single person, they might bump into the singer once or twice. The singer loses a little energy, but they stay together. In physics, this is called a color-coherent state. The jet acts like one big, solid object.

2. The Choir (Decoherent Jet):
   Now, imagine that same singer starts splitting up into a choir of many different voices (subjets) as they walk. If the crowd can see that there are actually many people walking together, they will bump into each of them.

   • The crowd hits the tenor.
   • The crowd hits the soprano.
   • The crowd hits the bass.
     Because the crowd interacts with every single person in the choir, the group loses much more energy than the soloist would have.

The Paper's Insight:
The authors realized that high-energy jets don't just stay as one "Soloist." As they travel, they split into a "Choir" of smaller sub-particles. The denser the medium (the party), the sooner the crowd can see the individual members of the choir. Once the crowd sees them individually, the energy loss explodes. This is Color Decoherence.

How They Studied It: The "Two-Step Dance"

The authors built a new mathematical model to track this process. They broke the jet's journey into two distinct steps:

Step 1: The Vacuum Dance (Before the Soup)
Before the jet even hits the dense soup, it starts splitting up in the "vacuum" (empty space). It's like a firework starting to explode. The authors used a method called Double Logarithmic Approximation (think of it as a very precise calculator) to count how many sparks (sub-particles) are created and how far apart they are.

• Key Variable: They set a "cutoff" point ($Q_0$). Think of this as the size of the smallest spark the crowd can see. If the spark is smaller than this, the crowd ignores it. If it's bigger, the crowd hits it.

Step 2: The Soup Interaction (The Energy Loss)
Once the jet has split into these sparks, they enter the "soup." The authors used a famous formula (BDMPS-Z) to calculate how much energy each spark loses when it hits the crowd.

• The Twist: If the jet is still a "Soloist" (all sparks are stuck together), it loses less energy. If it has split into a "Choir" (many independent sparks), it loses way more energy.

The Results: What Did They Find?

The team compared their calculations with real data from the ATLAS experiment at the Large Hadron Collider (LHC), where they smashed Lead (Pb) nuclei together.

1. Bigger Jets Lose More:
   They looked at "Large Radius" jets (big, wide firework cones) vs. "Small Radius" jets (tight, narrow cones).

   • Analogy: A wide cone captures more of the "choir" members. A narrow cone might only catch the "soloist."
   • Result: The wide jets lost significantly more energy. This confirmed that the more sub-particles (choir members) the medium can see, the more energy is stolen.

2. The "Choir" Effect is Real:
   They found that for high-energy jets, the "Choir" (multiple sub-particles) becomes the dominant factor. The jet isn't just one thing; it's a collection of independent particles that the medium attacks one by one.

   • Surprise: At very high energies, the jet splits so much that the "Choir" effect causes massive energy loss, far more than if the jet had stayed together as a single unit.

3. Matching the Data:
   By tweaking their "cutoff" parameter ($Q_0$) and the "stickiness" of the soup ($\hat{q}$), their model matched the experimental data almost perfectly. This proves that their picture of "Vacuum splitting first, then Medium hitting the pieces" is correct.

Why Does This Matter?

Think of the Quark-Gluon Plasma as a mysterious, invisible fluid. We can't see it directly. But by watching how the "fireworks" (jets) get smashed up, we can figure out the properties of the fluid.

This paper tells us that how the jet is built inside matters.

• If we ignore the internal structure (the "Choir"), we underestimate how much energy the jet loses.
• If we account for Color Decoherence (the crowd seeing the individual choir members), we get a perfect picture of the soup.

In a nutshell: The authors showed that high-speed particles don't just get hit by a medium; they break apart first, and then the medium hits every single piece. This "breaking apart" is the key to understanding the secrets of the hottest matter in the universe.

Technical Summary

1. Problem Statement

The primary objective of heavy-ion collision physics is to characterize the transport properties of the Quark-Gluon Plasma (QGP). A key observable for this is jet quenching, the suppression of high-transverse momentum ($p_T$) jets due to energy loss as partons traverse the medium.

While various theoretical frameworks exist (e.g., SCET$_G$, Higher-Twist, JETSCAPE), a complete first-principles description of jet evolution in a QCD medium remains challenging. Specifically, there is a need to better understand the interplay between:

• Vacuum-like emissions: The parton shower evolution driven by virtuality.
• Medium-induced radiation: Energy loss due to interactions with the medium (Landau–Pomeranchuk–Migdal effect).
• Color Decoherence: The transition where the medium resolves individual partons within a jet, causing them to lose energy as independent color charges rather than a single coherent object.

Current models often struggle to consistently describe the dependence of jet suppression on jet cone size and substructure (e.g., why large-radius jets are more suppressed than small-radius ones) across the full $p_T$ range.

2. Methodology

The authors propose a hybrid theoretical framework that combines vacuum-like evolution with medium-induced energy loss, explicitly incorporating color decoherence effects.

A. Theoretical Framework

1. Vacuum-like Evolution (DLA):

   • The initial hard parton (scale $Q \approx p_T R$) undergoes a parton shower described by the Double Logarithmic Approximation (DLA) using generating functions.
   • This evolution proceeds from the hard scale $Q$ down to an infrared scale $Q_0$.
   • The number of partons (multiplicity) at scale $Q_0$ is calculated using recursive relations derived from the generating functions. This multiplicity determines the number of independent subjets.

2. Color Decoherence Scale ($Q_0$):

   • $Q_0$ is treated as a phenomenological parameter representing the scale where the medium resolves the parton shower.
   • Above $Q_0$: Partons evolve via vacuum-like emissions; the medium does not resolve individual splittings (color coherence).
   • Below $Q_0$: The medium resolves the partons. The resulting subjets (multiplicity $n$) lose energy independently as individual color charges (color decoherence).

3. Medium-Induced Energy Loss (BDMPS-Z):

   • Once the virtuality drops to $Q_0$, the subjets undergo energy loss described by the BDMPS-Z formalism.
   • Energy loss is calculated using quenching weights ($D_i(\epsilon)$), which give the probability distribution for a parton losing energy fraction $\epsilon$ due to multiple soft scatterings.
   • The total energy loss for a jet is the sum of losses from all resolved subjets, weighted by their production probability $P_i(n, Q)$.

4. Medium Modeling:

   • The QGP bulk evolution is modeled using the OSU (2+1)-dimensional viscous hydrodynamic model.
   • The jet transport coefficient $\hat{q}$ is temperature-dependent: $\hat{q}(\tau) = \hat{q}_0 (T(\tau)/T_0)^3$.
   • The characteristic gluon frequency $\omega_c$ is integrated along the jet path through the hydrodynamic medium.

5. Cross Section Calculation:

   • Initial State: Uses LO pQCD with CT18NLO PDFs and EPPS21 nuclear PDFs (incorporating cold nuclear matter effects).
   • Final State: The nuclear modification factor ($R_{AA}$) is calculated by convoluting the vacuum jet spectrum with the energy loss probability distributions, accounting for the multiplicity of subjets.

3. Key Contributions

• Unified Framework: The paper establishes a consistent link between virtuality evolution, parton multiplicity, and color decoherence. It treats the jet not as a single object but as a collection of subjets whose number depends on the evolution scale $Q_0$.
• Substructure Decomposition: The authors explicitly decompose the total jet energy loss and $R_{AA}$ into contributions from single-subjet (coherent) and multiple-subjet (decoherent) configurations.
• Phenomenological Fit: They determine the optimal values for the decoherence scale ($Q_0$) and the initial jet transport coefficient ($\hat{q}_0$) by fitting to ATLAS data for inclusive jets in 0-10% PbPb collisions at $\sqrt{s_{NN}} = 5.02$ TeV.

4. Key Results

A. Parameter Determination

• A $\chi^2$ analysis of ATLAS data for $R=0.2$ and $R=1.0$ jets yields optimal parameters:
  • Decoherence scale: $Q_0 = 35$ GeV.
  • Initial transport coefficient: $\hat{q}_0 = 6.4$ GeV$^2$/fm (at $\tau_0 = 0.6$ fm/c).
• The model successfully describes the $R_{AA}$ for inclusive jets across the entire $p_T$ range (up to 1 TeV).

B. Cone-Size Dependence

• Larger Jets, Stronger Suppression: The model predicts that jets with larger cone radii ($R$) are more strongly suppressed than narrow jets.
  • Reason: Larger cones capture more vacuum-like emissions, leading to a higher multiplicity of subjets at scale $Q_0$. More subjets mean more independent color charges losing energy.
• $p_T$ Dependence: The difference in suppression between large and small radii increases with $p_T$. At high $p_T$, the multiplicity is higher, enhancing the decoherence effect.

C. Substructure Analysis (Single vs. Multiple Subjets)

• Probability Shift: As $p_T$ increases, the probability of a jet containing multiple resolved subjets increases significantly, especially for gluon jets.
  • For quark jets at $p_T \approx 1000$ GeV, multiple subjets contribute ~77% of the total energy loss.
  • For gluon jets, this transition to multiple-subjet dominance occurs at lower $p_T$ (~200 GeV) due to the larger color factor ($C_A$).
• $R_{AA}$ Separation:
  • Single-subjet jets (coherent) exhibit the weakest suppression (highest $R_{AA}$).
  • Multiple-subjet jets (decoherent) exhibit significantly stronger suppression (lowest $R_{AA}$).
  • This separation serves as a clear signature of color decoherence in the QGP.

D. Comparison with Data

• The theoretical predictions for $R_{AA}$ (both inclusive and cone-size dependent) show excellent agreement with ATLAS measurements.
• The model naturally explains why large-radius jets ($R=1.0$) reconstructed from small-radius subjets ($R=0.2$) are more suppressed: the reconstruction captures the energy loss of the subjets but excludes the soft medium-induced radiation that falls outside the small subjets but inside the large cone.

5. Significance

• Mechanism Validation: The work provides strong evidence that color decoherence is a critical mechanism governing jet quenching, particularly for large-radius jets and high-$p_T$ observables.
• Substructure as a Probe: It demonstrates that jet substructure (specifically the number of resolved subjets) is a sensitive probe of the QGP's resolving power and the decoherence scale.
• Theoretical Improvement: By separating vacuum evolution from medium interaction via the scale $Q_0$, the framework offers a more physically motivated approach to calculating jet energy loss than models that treat the jet as a single color charge or ignore the multiplicity dependence.
• Future Directions: The authors suggest that this framework can be extended to study other jet observables and that a fully unified first-principles calculation combining vacuum and medium radiation remains a goal for future research.

In summary, this paper successfully bridges the gap between parton shower dynamics and medium-induced energy loss, demonstrating that the multiplicity of subjets generated by vacuum evolution is the key driver for the enhanced suppression of large-radius jets via color decoherence.