The effect of recoils on soft-drop-groomed observables in $\gamma$-tagged jets in a multistage approach

This study utilizes multistage Monte Carlo simulations to demonstrate that recoil-induced medium responses cause nonmonotonic flavor-dependent modifications in soft-drop-groomed observables of $\gamma$-tagged jets, establishing these hard substructures as powerful tools for probing jet-medium interactions in heavy-ion collisions.

The Gist

Imagine you are trying to understand how a car behaves when driving through a thick, sticky mud pit versus driving on a smooth, dry highway. In the world of particle physics, the "car" is a jet (a spray of particles created when two protons smash together), and the "mud pit" is the Quark-Gluon Plasma (QGP)—a super-hot, super-dense soup of matter created in heavy-ion collisions (like smashing two lead atoms together).

For a long time, scientists have been studying these jets to see how the "mud" slows them down or changes their shape. But there was a problem: it was hard to tell if the changes they saw were actually caused by the mud, or just because they were looking at the wrong cars to begin with.

Here is a simple breakdown of what this new paper does, using some everyday analogies.

1. The Problem: The "Selection Bias" Trap

Imagine you are a detective trying to see how a muddy road affects cars. You decide to only look at cars that are still moving fast enough to pass a specific speed checkpoint at the end of the road.

• The Issue: If a car hits a big patch of mud and slows down, it might never reach the checkpoint. So, your list of "fast cars" only includes the ones that either didn't hit much mud or were already super powerful. You miss all the cars that got stuck or slowed down significantly.
• In Physics: When scientists looked at "inclusive jets" (all jets they could find), they saw that jets with wide, messy structures were disappearing. They thought the mud was tearing them apart. But the paper argues: "No, the mud didn't destroy them; we just stopped counting them because they slowed down too much!" This is called selection bias.

2. The Solution: The "Golden Ticket" (Photon-Tagged Jets)

To fix this, the scientists needed a way to pick out specific cars before they hit the mud, so they could track exactly what happened to them, regardless of how fast they were going at the end.

They used Photon-Tagged Jets.

• The Analogy: Imagine a race where a car is paired with a laser beam (a photon) right at the starting line. The laser beam is special: it doesn't get stuck in the mud. It flies straight through the mud pit at the exact same speed it started with.
• How it helps: By measuring the laser beam, the scientists know exactly how fast the car started. Even if the car slows down to a crawl in the mud, the scientists know, "Ah, this car started at 100 mph, so it lost a lot of speed." This removes the bias. They can now study every car, not just the ones that stayed fast.

3. The Discovery: Quarks vs. Gluons

The paper also found that not all "cars" are built the same.

• Gluon Jets: Think of these as heavy trucks. They are big, bulky, and have a lot of internal parts (radiation). When they hit the mud, they are so big and complex that the mud doesn't change their core shape very much. They just get a little slower.
• Quark Jets: Think of these as sleek sports cars. They are lighter and more streamlined. When they hit the mud, the mud interacts with them differently. The paper found that the mud actually makes these sports cars wider and messier in a specific way.

4. The "Recoil" Effect: The Mud Pushes Back

This is the most exciting part of the discovery.

• The Analogy: When a sports car drives through mud, the mud doesn't just slow the car down; the car also kicks the mud out of the way. The mud splashes back, hitting the car and pushing it sideways.
• In Physics: When a jet particle hits the QGP, it knocks some of the mud particles (medium constituents) out of the way. These "recoil" particles bounce back and hit the jet, adding energy to it in strange places.
• The Result: For the sleek "quark jets," this "mud splash" (recoil) creates a bump in the data. It makes the jet look like it has a wider, more spread-out structure than it did before. The "heavy trucks" (gluon jets) are so big that this splash doesn't change their shape as noticeably.

5. Why This Matters

Before this study, scientists were mostly seeing a "monotonic" trend (a simple, steady decline) in how jets changed, which they blamed on the mud destroying the jets.

This paper says: "Wait a minute! If we look at the right jets (the ones tagged with a photon) and remove the bias, we see something new."

They found that the mud doesn't just destroy jets; it actually reshapes them. The "recoil" effect (the mud pushing back) creates a distinct "bump" in the structure of quark jets. This proves that the jet and the mud are having a two-way conversation, not just the mud beating up the jet.

Summary

• Old Way: Looking at all jets and getting confused because the slow ones disappeared from the data (Selection Bias).
• New Way: Using a "photon tag" (like a GPS tracker on the starting line) to track specific jets, ensuring no data is lost.
• Big Finding: The "mud" (QGP) pushes back against the jets. This "recoil" makes the lighter jets (quarks) look wider and messier, creating a unique signature that proves the jet and the medium are interacting dynamically.

This study gives scientists a much sharper tool to understand the fundamental rules of how energy moves through the densest matter in the universe.

Technical Summary

1. Problem Statement

High-energy heavy-ion collisions create a Quark-Gluon Plasma (QGP), through which energetic partons traverse, losing energy and modifying their internal structure (jet quenching). While global observables like the nuclear modification factor ($R_{AA}$) quantify energy loss, they do not reveal the detailed mechanisms of jet-medium interactions.

Recent studies of jet substructure using grooming techniques (like Soft Drop) have aimed to isolate "hard branchings" within jets to probe these interactions. However, a significant challenge remains: selection bias. Inclusive jet measurements are heavily biased by the requirement that the reconstructed jet retain a high transverse momentum ($p_T^{jet}$). Jets with large-angle hard branchings tend to lose more energy outside the jet cone and are less likely to pass the $p_T$ trigger, leading to a suppression of large-angle structures that mimics medium effects but is actually an artifact of the selection criteria.

Furthermore, it is unclear whether observed modifications in substructure observables (splitting radius $r_g$, momentum fraction $z_g$, etc.) arise from intrinsic medium-induced changes to the hard parton shower or from the medium response (recoils and "hole" partons) generated when the jet scatters off the medium constituents.

2. Methodology

The authors utilize the JETSCAPE framework with the multistage matter+lbt model (specifically the JETSCAPEv3.5 AA22 tune) to simulate jet evolution in central Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV.

• Simulation Setup:

  • Background: (2+1)-D viscous hydrodynamics (VISHNU) with fluctuating initial conditions (Trento) and pre-equilibrium evolution.
  • Jet Evolution: A multistage approach where high-virtuality partons evolve via the matter module (vacuum-like splittings with medium coherence effects) until virtuality drops below a switching scale ($Q_{sw} = 2$ GeV). Low-virtuality partons then evolve via the lbt (Linear Boltzmann Transport) module, which handles elastic and inelastic scatterings with medium constituents.
  • Medium Response: The model explicitly tracks recoil partons (scattered medium constituents) and hole partons (energy-momentum deficits in the medium). Recoils are hadronized and included in jet reconstruction; holes are subtracted.
  • Control Cases: Simulations are run with and without medium response (recoils/holes) and with medium effects turned off in the low-virtuality phase to isolate specific mechanisms.

• Jet Selection Strategies:

  • Inclusive Jets: Triggered on the jet's $p_T$.
  • $\gamma$-Tagged Jets: Triggered on a hard photon ($p_T^\gamma$) produced in association with a jet. Since photons do not interact strongly with the QGP, $p_T^\gamma$ approximates the initial parton $p_T$, effectively removing the $p_T$-loss selection bias. These jets are predominantly quark-initiated.
  • Isolation Cuts: Photons are required to be isolated ($E_T^{iso} < 5$ GeV) and back-to-back with the jet ($|\phi_{jet} - \phi_\gamma| > 7\pi/8$) to ensure leading-order $\gamma$-jet production.

• Observables:

  • Soft-drop groomed observables: Momentum fraction ($z_g$), splitting radius ($r_g$), relative transverse momentum ($k_{T,g}$), and groomed mass ($m_g$).
  • Parameters: $z_{cut} = 0.2$, $\beta = 0$.

3. Key Contributions

1. Disentangling Selection Bias from Physical Modification: The paper demonstrates that the suppression of large-angle structures in inclusive jets is primarily driven by selection bias, whereas $\gamma$-tagged jets reveal intrinsic medium modifications.
2. Flavor Dependence: It establishes a clear distinction between quark and gluon jet modifications. Quark jets, having narrower vacuum structures, are more susceptible to medium-induced broadening of hard branchings than gluon jets.
3. Role of Medium Response (Recoils): The study identifies that recoil partons are the dominant driver of structural modifications in quark jets. These recoils, generated during low-virtuality scatterings, can satisfy the soft-drop condition and be identified as "hard" prongs, leading to observable broadening.
4. Validation of $\gamma$-Tagged Jets: It confirms that $\gamma$-tagged jets serve as a "golden channel" for probing jet-QGP interactions, offering a cleaner signal of medium response compared to inclusive jets.

4. Key Results

A. Momentum Fraction ($z_g$)

• Inclusive vs. $\gamma$-tagged: The $z_g$ distribution shows negligible medium modification in both inclusive and $\gamma$-tagged jets when normalized by the number of jets passing the soft-drop condition.
• Mechanism: Modifications are driven by the loss of soft constituents (recoils) populating the softer prong, but the overall shape remains robust against selection bias.

B. Splitting Radius ($r_g$)

• Inclusive Jets: Exhibit a monotonically decreasing modification (suppression of large $r_g$) as $r_g$ increases. This is almost entirely due to selection bias: jets with large $r_g$ lose more energy and fail the $p_T$ trigger.
• $\gamma$-Tagged Jets: Show a distinct non-monotonic behavior. While large $r_g$ is still suppressed (bias), there is a pronounced broadening (bump structure) in the mid-$r_g$ region ($\approx 0.1$).
• Flavor & Recoil Origin:
  • The bump is absent in gluon jets and disappears when recoil effects are turned off.
  • It arises because quark jets have lower initial virtuality; medium-induced scatterings in the low-virtuality lbt phase generate large-angle recoils that are reconstructed as hard branchings by the soft-drop algorithm.

C. Relative Transverse Momentum ($k_{T,g}$) and Groomed Mass ($m_g$)

• $k_{T,g}$: Similar to $r_g$, inclusive jets show suppression at large $k_{T,g}$ due to $p_T$ loss. $\gamma$-tagged quark jets show a slight flattening/broadening at small $k_{T,g}$, driven by recoils.
• $m_g$: Inclusive jets show a shift toward smaller masses (mass depletion). $\gamma$-tagged quark jets exhibit a bump structure at intermediate masses, indicating mass gain from recoils.
• Low Virtuality Dominance: All structural modifications (broadening, mass gain) are found to originate predominantly from the low-virtuality phase ($Q < 2$ GeV) where the lbt module operates. High-virtuality splittings remain largely vacuum-like.

D. Comparison with Experimental Data

• The simulations successfully reproduce existing experimental data from ALICE and CMS for inclusive jets (monotonic suppression).
• For $\gamma$-tagged jets, the model predicts that lowering the $x_{J\gamma}$ cut (allowing more energy loss) reduces the selection bias, making the intrinsic broadening (bump) more visible. Current experimental binning resolution may obscure this feature, but future high-precision measurements are expected to reveal it.

5. Significance

This work fundamentally shifts the understanding of jet substructure in heavy-ion collisions:

• Beyond Selection Bias: It proves that previous observations of "suppression" in inclusive jets were largely artifacts of the trigger, masking the true physical effect of the medium.
• Recoil Dynamics: It highlights that medium response (recoils) is not just a soft background effect but can significantly alter the "hard" substructure of jets, particularly for quark jets.
• Future Probes: The paper establishes $\gamma$-tagged jets as a critical tool for future Bayesian analyses. By isolating quark jets and removing selection bias, these observables can provide stringent constraints on the transport properties of the QGP and the dynamics of jet-medium parton scatterings.
• Theoretical Insight: It validates the necessity of multistage models that include explicit medium response (recoils) to accurately describe jet substructure, moving beyond models that only consider radiative energy loss.

In summary, the paper argues that $\gamma$-tagged jets are the key to unlocking the "hidden" structural modifications of jets caused by the QGP, specifically the broadening of hard branchings due to recoil interactions at low virtuality.