Characterization of nuclear breakup as a function of hard-scattering kinematics using dijets measured by ATLAS in $p$+Pb collisions

Using 8.16 TeV $p$+Pb collision data from the ATLAS detector, this study demonstrates that event geometry estimators based on forward energy deposition are sensitive to the initial-state hard-scattering kinematics, specifically showing a strong dependence on the proton-side parton's Bjorken-$x$ that is significantly more pronounced in the Forward Calorimeter than in the Zero-Degree Calorimeter.

The Gist

The Big Picture: A High-Speed Crash Test

Imagine the Large Hadron Collider (LHC) as a massive, high-speed racetrack. Usually, scientists crash two heavy trucks (lead nuclei) into each other to see what happens inside. But sometimes, they crash a tiny, fast sports car (a proton) into one of those heavy trucks (a lead nucleus).

This paper is about a specific type of crash: Proton + Lead. The scientists want to understand the "geometry" of the crash. Did the sports car hit the truck head-on (a "central" collision), or did it just graze the bumper (a "peripheral" collision)?

The Problem: The "Traffic Light" is Broken

In these crashes, scientists need a way to tell how hard the crash was. They usually look at the "debris" flying out the front.

• The Old Way: They used a detector called the Forward Calorimeter (FCal) to measure the total energy of the debris. Think of this like a traffic light that turns red if there is a lot of debris (a big crash) and green if there is little debris (a small crash).
• The Glitch: The paper found that this traffic light is unreliable when the sports car (proton) is carrying a very specific type of "cargo" inside it.

Inside the proton, there are smaller particles called partons. Sometimes, a parton carries a huge amount of the proton's energy (high "Bjorken-$x$"). When this happens, the proton acts like a compact, aerodynamic sports car that slips through the traffic without hitting many other cars.

• Because it hits fewer cars, there is less debris.
• The traffic light (FCal) sees the low debris and says, "Oh, this must be a weak, glancing crash!"
• But it's a lie! The crash was actually a hard, high-energy event; the proton just happened to be "small" and slippery at that moment. This is called an event activity bias.

The New Experiment: Two Different Detectors

To fix this, the ATLAS team decided to look at the crash from two different angles using two different tools:

1. The Forward Calorimeter (FCal): The "Traffic Light" that measures the total energy of the debris.
2. The Zero-Degree Calorimeter (ZDC): A special detector far down the track that only catches spectator neutrons.
   • Analogy: Imagine the lead truck is made of Lego bricks. When the proton hits it, some bricks (neutrons) get knocked loose and fly straight forward. The ZDC counts how many bricks fell off. If the proton hit the truck hard, many bricks fall off. If it was a glancing blow, few bricks fall off.

What They Did

They looked at dijets (pairs of particle jets) produced in the crash. These jets act like a "receipt" that tells them exactly how much energy was involved in the initial hit. They sorted these crashes based on how "slippery" the proton was (the $x_p$ value).

Then, they asked: Does the amount of debris (FCal) and the number of fallen bricks (ZDC) change when the proton is "slippery"?

The Results

1. The Traffic Light (FCal) is Very Sensitive: When the proton was "slippery" (high energy parton), the FCal saw a massive drop in debris. The signal changed by about 40%. It was very easy to tell the difference.
2. The Brick Counter (ZDC) is Stubborn: When the proton was "slippery," the ZDC also saw a drop in fallen bricks, but it was much smaller—only about 5%.
3. The Ratio: The paper concludes that the ZDC is about six times less sensitive to these "slippery proton" tricks than the FCal is.

The Takeaway

If you want to study these proton-lead crashes without getting fooled by the "slippery proton" effect, counting the fallen bricks (ZDC) is a much better way to judge the crash size than measuring the total debris energy (FCal).

The ZDC gives a more honest picture of the collision geometry because it is less easily confused by the internal structure of the proton. This helps scientists understand the true nature of nuclear matter without being misled by the "aerodynamics" of the incoming proton.

Technical Summary

Technical Summary: Characterization of Nuclear Breakup as a Function of Hard-Scattering Kinematics in $p$+Pb Collisions

Problem Statement
In proton–lead ($p$+Pb) collisions at the Large Hadron Collider (LHC), the definition of collision centrality is critical for studying hard processes like jet production. Traditionally, centrality is estimated using "global" event-level variables, such as the forward transverse energy ($E_T$) measured in the Forward Calorimeter (FCal) or the number of forward neutrons. However, previous ATLAS measurements revealed a significant "event activity bias": the production rate of jets, when normalized to the number of binary collisions ($N_{coll}$), was suppressed in events selected as "central" based on high forward activity. This suppression was found to be a function of jet kinematics, specifically the Bjorken-$x$ ($x_p$) of the parton originating from the proton.

This bias is attributed to color fluctuation (CF) effects in Quantum Chromodynamics (QCD). In configurations where a single parton carries a large fraction of the proton's momentum (large $x_p$), the proton's transverse color field becomes spatially compact. This "small" proton configuration interacts with fewer nucleons in the lead nucleus, resulting in lower event activity (fewer spectator neutrons and lower forward $E_T$) despite the hard scattering occurring. Consequently, selecting events based on high forward activity inadvertently biases the sample against large-$x_p$ configurations, complicating the interpretation of jet quenching signals in small systems. While Zero-Degree Calorimeters (ZDCs), which measure spectator neutrons, have been proposed as a less biased centrality estimator, the specific sensitivity of nuclear breakup observables to the initial-state kinematics of hard scattering had not been quantitatively characterized.

Methodology
This analysis utilizes $p$+Pb collision data recorded by the ATLAS detector at a nucleon–nucleon center-of-mass energy of $\sqrt{s_{NN}} = 8.16$ TeV, corresponding to an integrated luminosity of 56 nb$^{-1}$. The study focuses on dijet events to reconstruct the initial-state kinematics of the hard scattering.

• Event Selection: Events are selected requiring two reconstructed jets with transverse momenta $p_{T,1} > 40$ GeV and $p_{T,2} > 30$ GeV within the pseudorapidity range $-2.8 < \eta < 4.5$. The positive $\eta$ direction corresponds to the proton beam.
• Kinematic Variable ($x_p$): The Bjorken-$x$ of the parton from the proton ($x_p$) is estimated using the kinematics of the two highest-$p_T$ jets:
  $$x_p = \frac{p_{T,1}e^{y_{CM,1}} + p_{T,2}e^{y_{CM,2}}}{\sqrt{s_{NN}}}$$
  This variable is unfolded to the particle level to correct for detector resolution and acceptance effects.
• Geometry Estimators: Two observables measured on the Pb-going side are analyzed as a function of $x_p$:
  1. $E^{Pb}_{ZDC}$: The energy deposited in the Zero-Degree Calorimeter, primarily from spectator neutrons resulting from nuclear breakup.
  2. $\Sigma E^{Pb}_{T}$: The total transverse energy recorded in the Forward Calorimeter (FCal).
• Analysis Strategy: The distributions of $E^{Pb}_{ZDC}$ and $\Sigma E^{Pb}_{T}$ are measured in intervals of $x_p$. The mean values of these distributions ($\langle E^{Pb}_{ZDC} \rangle$ and $\langle \Sigma E^{Pb}_{T} \rangle$) are extracted to characterize the evolution of forward energy production. The correlation between the two estimators is also investigated. Monte Carlo simulations (Pythia8 overlaid with $p$+Pb minimum bias data) are used to evaluate detector performance and apply necessary corrections, though $E^{Pb}_{ZDC}$ and $\Sigma E^{Pb}_{T}$ are reported at the reconstructed level without unfolding.

Key Contributions and Results
The paper presents the first quantitative characterization of very forward energy in dijet events as a function of the hard-scattering kinematics ($x_p$).

1. Confirmation of Event Activity Bias: The analysis confirms that both $\Sigma E^{Pb}_{T}$ and $E^{Pb}_{ZDC}$ distributions shift as a function of $x_p$. Specifically, events with higher $x_p$ (large partonic momentum fraction) exhibit significantly lower forward transverse energy and fewer spectator neutrons compared to low-$x_p$ events. This directly validates the event activity bias observed in previous inclusive jet measurements.
2. Quantitative Sensitivity Comparison:
   • The mean forward transverse energy, $\langle \Sigma E^{Pb}_{T} \rangle$, decreases by up to 40% as $x_p$ increases from low values to $x_p \gtrsim 0.02$.
   • The mean ZDC energy, $\langle E^{Pb}_{ZDC} \rangle$, shows a much smaller variation, decreasing by approximately 5% over the same $x_p$ range. This 5% reduction corresponds, on average, to a loss of two beam-energy neutrons.
   • The ratio of the relative change in $\langle \Sigma E^{Pb}_{T} \rangle$ to the relative change in $\langle E^{Pb}_{ZDC} \rangle$ is found to be approximately constant at 5.5 to 6. This indicates that the ZDC energy is about six times less sensitive to the initial-state kinematics of the hard scattering than the FCal transverse energy.
3. Correlation Analysis: A linear relationship is observed between $\langle \Sigma E^{Pb}_{T} \rangle$ and $E^{Pb}_{ZDC}$ across the measured $x_p$ range. However, the slope of this correlation decreases progressively as $x_p$ increases. Additionally, the Pearson correlation coefficient between the two observables decreases by 3% from high-$x_p$ to low-$x_p$ selections, suggesting that in smaller proton configurations, the forward transverse energy produced by participant interactions is slightly less correlated with the number of spectator neutrons.

Significance and Claims
The authors claim that these results provide the first direct, quantitative investigation of global observables in the presence of color fluctuation effects. By demonstrating that the ZDC energy is significantly more robust against variations in event kinematics compared to the FCal transverse energy, the paper supports the use of ZDC-based centrality selections for reducing biases in measurements of hard process rates in $p$+Pb collisions.

The findings qualitatively support theoretical models connecting color fluctuations to the dynamics of nuclear breakup and neutron evaporation. The authors state that these results can inform the simultaneous modeling of event activity and nuclear breakup in $p$+Pb collisions involving hard scattering. Furthermore, the paper suggests that understanding the link between hard scatterings and nuclear breakup dynamics is relevant for future studies, such as dijet production in ultra-peripheral collisions (UPCs) and $e$+A collisions at the future Electron-Ion Collider, where forward neutrons are proposed as centrality tags. The paper does not propose new experimental setups but rather provides essential empirical constraints for interpreting existing and future centrality-dependent measurements in small collision systems.