Jet cone size dependence of single inclusive jet suppression due to jet quenching in Pb+Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV

This paper presents a comprehensive perturbative QCD framework incorporating both elastic and inelastic energy loss mechanisms to calculate jet nuclear modification factors ($R_{AA}$) in Pb+Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV, demonstrating that jet suppression decreases with increasing cone size due to reduced in-cone energy loss and successfully reproducing experimental data from ALICE, ATLAS, and CMS.

The Gist

Imagine you are at a massive, chaotic concert where thousands of people are packed together. Suddenly, a group of VIPs (high-energy particles) tries to sprint through the crowd to get to the other side.

In a normal, empty hallway (like a collision between two single protons), these VIPs run straight through without slowing down. But in a heavy-ion collision (like smashing two lead nuclei together), the "hallway" is filled with a super-hot, super-dense fog called the Quark-Gluon Plasma (QGP). As the VIPs sprint through this fog, they bump into people, get jostled, and lose energy. This phenomenon is called Jet Quenching.

This paper is a detailed investigation into how much energy these VIPs lose and, crucially, how the size of the "net" we use to catch them changes the result.

Here is the breakdown of the study using everyday analogies:

1. The "Net" Size (Jet Cone Radius)

When physicists detect these high-speed particles, they don't just look at the VIP themselves; they look at a cluster of particles around them. They draw an invisible circle (a "cone") around the VIP to see everything that belongs to that group.

• Small Cone (R=0.2): A small net. You only catch the VIP and the people immediately hugging them.
• Large Cone (R=1.0): A giant net. You catch the VIP, their friends, and anyone who bumped into them a few steps away.

The big question the paper asks: Does the size of this net change how much energy we think the VIP lost?

2. The Two Ways Energy is Lost

The paper looks at two ways the VIPs lose energy while running through the crowd:

• The "Bump" (Elastic Scattering): The VIP bumps into a crowd member.

  • The Twist: If the crowd member gets knocked backward but stays inside your net, their energy is still counted as part of the VIP's group. It's like if you bumped someone, they stumbled back into your arms, and you caught them. You didn't actually lose that energy; you just shared it.
  • The Paper's Finding: As you make your net bigger, you are more likely to catch these "stumbling" crowd members. So, a bigger net makes it look like the VIP lost less energy because you recovered the energy that was knocked around.

• The "Shout" (Radiative Energy Loss): As the VIP runs, they might shout or throw things (gluons) out of their hand.

  • The Twist: If the VIP throws a ball and it lands outside your net, that energy is gone forever. But if the VIP is running through a windy crowd (transverse momentum broadening), the ball might get blown back inside your net.
  • The Paper's Finding: A bigger net catches more of these "thrown" items, even if they were blown sideways. This also reduces the apparent energy loss.

3. The Main Discovery: Bigger Nets = Less Apparent Loss

The researchers built a complex computer simulation (a "digital twin" of the collision) to test this. They found that:

• Small Nets: The VIP looks like they lost a lot of energy because the "bumps" and "shouts" happened just outside the net.
• Big Nets: The VIP looks like they lost less energy. Why? Because the big net scooped up the scattered crowd members and the sideways-thrown items that would have otherwise been lost.

The Analogy: Imagine trying to measure how much water a sponge lost by squeezing it.

• If you use a tiny cup to catch the drips, you think the sponge lost a lot of water.
• If you use a giant bucket, you catch the splashes and the drips that flew sideways. Suddenly, it looks like the sponge didn't lose much water at all.

4. Comparing Theory to Reality

The team compared their simulation with real data from three giant particle detectors: ALICE, ATLAS, and CMS at the Large Hadron Collider.

• The Result: Their model worked very well, especially for small nets and very fast VIPs (high energy).
• The Discrepancy: For medium-sized nets and medium speeds, the real data showed the VIPs lost slightly less energy than the model predicted. This suggests that the "crowd" (the plasma) might be doing something slightly more complex than the model currently accounts for—perhaps the crowd members are helping the VIPs recover energy in ways we don't fully understand yet.

5. Why This Matters

This isn't just about counting particles; it's about understanding the nature of the Quark-Gluon Plasma.

• If we know exactly how the "net size" changes the energy loss, we can reverse-engineer the properties of the QGP.
• It tells us how "sticky" the plasma is, how it flows, and how it reacts when hit by a high-speed particle.

Summary

Think of this paper as a study on how to best measure a leak in a boat.
The physicists realized that if you use a small bucket to catch the water, you think the boat is sinking fast. If you use a huge tarp, you catch the splashes and realize the boat isn't sinking as fast as you thought. By understanding exactly how the bucket size changes the measurement, they can figure out the true speed of the leak and the strength of the boat's hull (the Quark-Gluon Plasma).

Their conclusion? Bigger nets recover more energy, making the particles look "healthier" than they do in small nets. This helps scientists refine their models of the universe's most extreme state of matter.

Technical Summary

1. Problem Statement

The suppression of high-transverse-momentum ($p_T$) jets in heavy-ion collisions (jet quenching) is a primary probe of the Quark-Gluon Plasma (QGP). While the suppression of single hadrons is well understood, the dependence of inclusive jet suppression on the jet cone size ($R$) remains a subject of debate.

• Experimental Discrepancy: Experimental data from ALICE, ATLAS, and CMS at $\sqrt{s_{NN}} = 5.02$ TeV show conflicting trends regarding the $R$-dependence. Some data suggest suppression is independent of $R$, while others (particularly ATLAS) suggest larger-$R$ jets experience stronger suppression or exhibit complex substructure effects.
• Theoretical Challenge: Existing models often struggle to simultaneously describe the magnitude of suppression and its dependence on $R$. Key physical mechanisms—specifically the interplay between elastic scattering (collisional energy loss), inelastic scattering (radiative energy loss), medium response (recoil partons), and transverse momentum ($p_T$) broadening—need to be quantified to understand how energy is redistributed within the jet cone.

2. Methodology

The authors employ a Next-to-Leading Order (NLO) perturbative QCD (pQCD) parton model integrated with a unified energy-loss framework.

• Baseline Calculation:

  • Single inclusive jet cross-sections in $p+p$ collisions are calculated at NLO using the anti-$k_T$ jet clustering algorithm.
  • Nuclear Parton Distribution Functions (nPDFs) are incorporated using EPPS21 parametrizations with spatial dependence.
  • The factorization scale $\mu$ is tuned for different $R$ values to ensure the $p+p$ baseline matches experimental data, compensating for the lack of non-perturbative hadronization modeling in this parton-level study.

• Energy Loss Mechanisms in A+A Collisions:
  The model calculates the net energy loss ($\Delta E$) for a jet traversing the QGP by combining two distinct mechanisms:

  1. Collisional (Elastic) Energy Loss:
     • Calculated via elastic scattering rates between the leading parton and thermal medium partons.
     • Key Feature: Explicitly accounts for recoil thermal partons. If a recoil parton falls inside the jet cone after scattering, its energy is recovered, reducing the net energy loss.
  2. Radiative (Inelastic) Energy Loss:
     • Based on the Higher-Twist (HT) formalism.
     • Key Features:
       • Angular Distribution: Only gluons radiated outside the jet cone contribute to net energy loss.
       • Soft Gluon Thermalization: Gluons with energy below the Debye mass ($\mu_D$) are assumed to thermalize into the medium, contributing to energy loss regardless of angle.
       • $p_T$ Broadening: The model includes the effect of transverse momentum broadening ($\langle \Delta l_T^2 \rangle$) accumulated along the path. This broadening increases the probability that radiated gluons are deflected outside the jet cone, thereby increasing net energy loss.

• Medium Evolution:

  • The QGP medium evolution is modeled using the (3+1)-dimensional CLVisc hydrodynamic model.
  • Initial conditions are provided by the TRENTo model, averaged over 200 events per centrality class.
  • Energy loss ceases when the medium temperature drops below the pseudocritical temperature ($T_c = 0.165$ GeV).

• Parameter Extraction:

  • The strong coupling constant ($\alpha_s$) is the sole free parameter. It is determined via a global $\chi^2/d.o.f.$ fit to experimental $R_{AA}$ data for specific centrality bins (0–10% and 30–50%).

3. Key Contributions

• Unified Framework: The study integrates elastic recoil, radiative angular distribution, soft gluon thermalization, and $p_T$ broadening into a single NLO pQCD framework to systematically study $R$-dependence.
• Quantification of Recoil Effects: It explicitly demonstrates how recoil thermal partons falling inside the cone reduce net energy loss, a mechanism often overlooked or simplified in other models.
• Role of $p_T$ Broadening: The paper quantifies how $p_T$ broadening enhances radiative energy loss by pushing gluons out of the cone, creating a competing effect against the cone-size recovery.
• Systematic Comparison: Provides a comprehensive comparison with ALICE, ATLAS, and CMS data across a wide kinematic range ($p_T \approx 40$–$1000$ GeV) and multiple cone sizes ($R = 0.2$ to $1.0$).

4. Key Results

• Cone Size Dependence ($R$):

  • The nuclear modification factor ($R_{AA}$) increases with increasing jet radius $R$.
  • Mechanism: As $R$ grows, the probability of radiated gluons escaping the cone decreases, and the probability of recoiling thermal partons falling inside the cone increases. Both effects lead to a reduction in net in-cone energy loss.
  • Double Ratios: The double ratio $R_{AA}(R)/R_{AA}(R=0.2)$ is approximately unity for small radii ($R=0.4$) and high $p_T$ ($\gtrsim 200$ GeV), consistent with data. For $R > 0.6$ at intermediate $p_T$, the model predicts ratios $>1$, indicating weaker suppression for larger cones, though the data shows a weaker $R$-dependence than predicted in this specific region.

• Transverse Momentum ($p_T$) Dependence:

  • $R_{AA}$ increases with $p_T$ and approaches unity at very high $p_T$.
  • This is attributed to the increasing fraction of quark jets (which lose less energy than gluons) at high $p_T$ and the diminishing relative impact of energy loss.

• Centrality Dependence:

  • Results for central (0–10%) and semi-central (30–50%) collisions are consistent with data.
  • The extracted $\alpha_s$ values differ slightly between centralities ($0.189\text{--}0.223$ for 0–10% vs. $0.202\text{--}0.232$ for 30–50%), reflecting the temperature dependence of the jet transport coefficient $\hat{q}$.

• Discrepancies:

  • For large radii ($R > 0.6$) at intermediate $p_T$ ($< 200$ GeV), the theoretical suppression is slightly weaker than experimental measurements. The authors suggest this indicates that the microscopic dynamics of in-cone energy recovery and medium response require further refinement.

5. Significance

• Validation of Mechanisms: The study confirms that including medium recoil and $p_T$ broadening is essential for describing the $R$-dependence of jet suppression. Without recoil, the model would overestimate energy loss for large $R$.
• Constraint on QGP Properties: By successfully describing the $R$-dependence across different centralities and $p_T$, the model provides tighter constraints on the jet transport coefficient $\hat{q}$ and the strong coupling $\alpha_s$ in the QGP.
• Future Directions: The paper highlights that while parton-level calculations capture the main trends, future work must incorporate jet fragmentation and hadronization to fully resolve the discrepancies at intermediate $p_T$ and large $R$, as non-perturbative effects become more significant in these regimes.

In summary, this work provides a robust theoretical explanation for why larger jet cones generally exhibit less suppression (higher $R_{AA}$) due to the recovery of energy from recoil partons and the reduced escape probability of radiated gluons, offering a comprehensive framework for interpreting high-precision jet quenching data at the LHC.