Dijet invariant mass of charged-particle jets in pp and p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV

The ALICE collaboration reports the first measurement of charged-particle dijet invariant mass spectra in pp and p-Pb collisions at 5.02 TeV, finding a nuclear modification factor consistent with unity that suggests the low-mass region is sensitive to subtle anti-shadowing effects currently below experimental sensitivity.

The Gist

The Big Picture: Smashing Protons to See the Invisible

Imagine you have two high-speed trains (protons) barreling toward each other on a collision course. When they smash together at nearly the speed of light, they don't just break; they explode into a shower of new particles.

The ALICE experiment at CERN is like a giant, ultra-high-speed camera that takes pictures of these explosions. The goal of this specific paper is to study a very specific type of explosion: Dijets.

What is a "Dijet"? (The Two-Headed Firework)

In the world of subatomic physics, when two particles collide hard, they often shoot out two streams of debris in opposite directions. Think of these streams as jets.

• The Analogy: Imagine two firework rockets launching from a single point. They shoot off in exactly opposite directions. As they fly, they leave behind a trail of sparks and smoke. In physics, we call these trails "jets."
• The "Dijet": When we look at a pair of these rockets (one going left, one going right) together, we call it a dijet.

The scientists in this paper measured the mass (or "heaviness") of these two-jet systems. They wanted to see if the "weight" of the explosion changes depending on what the trains were made of.

The Experiment: Two Different Scenarios

The researchers ran two different types of races to compare the results:

1. The Solo Race (pp collisions): They smashed a single proton against another single proton. This is the "control group." It's like two identical cars crashing in a clean, empty parking lot.
2. The Heavy Truck Race (p–Pb collisions): They smashed a single proton against a Lead nucleus (which is a heavy atom with 208 protons and neutrons stuck together). This is like crashing a small sports car into a massive, dense semi-truck.

The Question: Does the "traffic" inside the massive semi-truck (the lead nucleus) change how the fireworks (the jets) behave compared to the empty parking lot?

The Mystery: Cold Nuclear Matter vs. Hot Soup

In heavy-ion collisions (like smashing two lead trucks together), scientists know that the debris creates a super-hot, super-dense soup called the Quark-Gluon Plasma (QGP). This soup acts like thick molasses, slowing down the jets and stealing their energy.

However, in this paper, they are looking at proton-lead collisions. They don't expect to create that hot soup. Instead, they are looking for "Cold Nuclear Matter" effects.

• The Analogy: Imagine the lead nucleus isn't a hot soup, but a dense fog. The question is: Does this fog change the way the fireworks look before they even explode? Does the fog make the fireworks seem brighter, dimmer, or heavier?

The Key Finding: The "Ghost" Effect

The scientists measured the Nuclear Modification Factor ($R_{pPb}$). In plain English, this is a ratio:

• How much did we see in the Lead crash?
• Divided by: How much did we expect to see based on the Solo crash?

The Result: The ratio was 1.

• What this means: The fireworks in the Lead crash looked exactly the same as the fireworks in the Solo crash. The "fog" of the lead nucleus didn't seem to change the weight of the dijets at all.
• The Verdict: Within the limits of their current tools, the "cold" lead nucleus didn't mess with the jets.

The "Maybe" Hint: The Anti-Shadowing Whisper

Even though the main result was "no change," the scientists looked very closely at the data and compared it to computer simulations. They found a tiny, subtle hint.

• The Analogy: Imagine you are looking at a crowd of people through a slightly warped window. Most of the time, the people look normal. But if you squint really hard, you might see that the people on the left side of the window look just a tiny bit larger than they should.
• The Science: The computer models suggested that the "fog" inside the lead nucleus might have a property called anti-shadowing. This is a fancy way of saying that at certain energy levels, the particles inside the lead nucleus might actually be more visible or active than expected, rather than less.
• The Catch: The effect was so small that the scientists couldn't say for sure if it was real or just a statistical fluke. Their "camera" (the detector) wasn't quite sensitive enough to prove it yet.

Why Does This Matter?

1. Setting the Baseline: Before we can study the "hot soup" (QGP) created in heavy lead-lead crashes, we need to know exactly how things behave when there is no soup. This paper says, "Okay, in proton-lead crashes, the jets act normally." This gives scientists a solid ruler to measure against when they study the messy, hot crashes later.
2. Future Sensitivity: The paper suggests that if we collect more data in the future (with the LHC running longer and brighter), we might finally be able to see that tiny "anti-shadowing" whisper. It's like upgrading from a standard camera to a super-microscope.

Summary in One Sentence

The ALICE team smashed protons against lead atoms to see if the heavy lead "fog" changed the behavior of particle jets; they found that the jets behaved normally, but their data hints that with better tools in the future, we might finally see a tiny, mysterious effect where the lead nucleus actually boosts the activity of the particles inside it.

Technical Summary

1. Problem Statement and Motivation

The primary objective of this study is to investigate Cold Nuclear Matter (CNM) effects in proton-lead (p–Pb) collisions, specifically focusing on the modification of parton distribution functions (nPDFs) within the nucleus.

• Context: While heavy-ion (Pb–Pb) collisions are used to study the Quark-Gluon Plasma (QGP) and jet quenching, p–Pb collisions serve as a crucial baseline where QGP formation is not expected. However, CNM effects such as nuclear shadowing, anti-shadowing, and energy loss can still modify jet production.
• Specific Gap: Previous studies have largely focused on inclusive jet suppression or dijet momentum imbalance ($A_J$). This paper addresses the dijet invariant mass ($M_{jj}$) spectrum in the low-mass region (75–150 GeV/c²). This kinematic region corresponds to lower transverse momentum partons, where medium-induced modifications and nPDF effects (specifically anti-shadowing around momentum fraction $x \approx 0.1$) are theoretically expected to be more pronounced than at very high masses.
• Goal: To provide the first measurement of the charged-particle dijet invariant mass spectrum in pp and p–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV and determine the nuclear modification factor ($R_{pPb}$) to constrain nPDF models.

2. Methodology and Experimental Setup

Data Samples and Detector

• Collisions: Data collected during LHC Run 2 at a center-of-mass energy of $\sqrt{s_{NN}} = 5.02$ TeV.
  • p–Pb: Integrated luminosity $L_{p-Pb} = (349 \pm 13) \, \mu\text{b}^{-1}$ ($730 \times 10^6$ minimum bias events).
  • pp: Integrated luminosity $L_{pp} = (20.3 \pm 0.5) \, \text{nb}^{-1}$ ($1042 \times 10^6$ minimum bias events).
• Detector: The ALICE detector, utilizing the Inner Tracking System (ITS) and Time Projection Chamber (TPC) for track reconstruction in the central barrel ($|\eta| < 0.9$).
• Trigger: Minimum Bias (MB) trigger based on coincident signals from the V0A and V0C forward detectors.

Jet Reconstruction and Selection

• Algorithm: Charged particle tracks ($p_T > 150$ MeV/c) are clustered into jets using the anti-$k_T$ algorithm with a resolution parameter $R = 0.4$.
• Kinematic Cuts:
  • Leading and subleading jets must have $p_T > 20$ GeV/c.
  • Jets must be contained within $|\eta_{jet}| < 0.5$.
  • Dijets must be back-to-back in the transverse plane with an azimuthal difference $|\Delta\phi| > \pi/2$ to ensure they originate from the same hard scattering.
• Background Subtraction: The underlying event (soft interactions) is subtracted using the four-momentum background subtraction method. The background density ($\rho$) is estimated using the sparse event method with $k_T$ jets, excluding the leading and subleading jets.

Unfolding and Corrections

• Fluctuations: Background fluctuations are estimated using rotated cones perpendicular to the jet axes. The difference between the default background subtraction and the rotated cone method ($\delta M_{jj}$) is modeled using an asymmetric generalized Gaussian distribution.
• Unfolding: A Bayesian iterative unfolding procedure (using the RooUnfold package) is employed to correct for detector effects (resolution, efficiency) and background fluctuations.
  • Response Matrix: Constructed using Monte Carlo (MC) simulations (PYTHIA6/8 and POWHEG+PYTHIA) matched to "truth" level particles.
  • Iterations: 3 iterations for p–Pb and 5 for pp.
• Systematic Uncertainties: Dominated by tracking efficiency (3% for pp, 1–2.5% for p–Pb) and unfolding procedure variations (binning, priors, iteration counts).

Theoretical Models

• Simulations: Comparisons are made against:
  • PYTHIA8 (Monash 2013 tune) with CT14NLO/CT18ANLO proton PDFs.
  • POWHEG+PYTHIA8 (NLO pQCD) with CT14NLO/CT18ANLO.
• nPDF Effects: Simulations include nuclear modifications using EPPS16 (for PYTHIA) and EPPS21 (for POWHEG) to model the lead nucleus. The rapidity shift of the center-of-mass system ($\Delta y_{cm} = -0.465$) is accounted for.

3. Key Contributions

1. First Measurement: This is the first measurement of the charged-particle dijet invariant mass spectrum in the low-mass region (75–150 GeV/c²) for both pp and p–Pb collisions at this energy.
2. Methodological Rigor: The analysis introduces a robust treatment of background fluctuations via rotated cones and incorporates them into the unfolding matrix, ensuring a precise extraction of the physical cross-section.
3. Baseline Establishment: It establishes a high-precision baseline for future Pb–Pb measurements, isolating CNM effects from hot medium effects (QGP).

4. Results

• Dijet Mass Spectrum: The differential cross-section $d\sigma/dM_{jj}$ was measured for both collision systems. The p–Pb spectrum, scaled by the mass number of lead ($A=208$), is compared directly to the pp spectrum.
• Nuclear Modification Factor ($R_{pPb}$):
  • The $R_{pPb}$ is calculated as the ratio of the p–Pb cross-section to the scaled pp cross-section.
  • Finding: The measured $R_{pPb}$ is consistent with unity ($1.0$) within the experimental uncertainties across the entire measured mass range (75–150 GeV/c²).
  • Implication: No significant suppression or enhancement due to CNM effects was observed at the current level of precision.
• Comparison with MC:
  • Both PYTHIA and POWHEG+PYTHIA simulations (including nPDFs) predict a slight enhancement (1–7%) in the p–Pb yield, attributed to anti-shadowing effects in the nPDFs at $x \sim 0.01$.
  • The experimental data is consistent with these simulations within the large systematic and statistical uncertainties. The expected anti-shadowing signal is subtle and currently below the experimental sensitivity to be definitively distinguished from unity.

5. Significance and Conclusion

• Validation of Small-System Physics: The result $R_{pPb} \approx 1$ aligns with previous small-system jet studies, confirming that significant jet quenching or strong CNM modifications are not dominant in this kinematic regime for charged-particle dijets.
• Sensitivity to nPDFs: While the current data does not show a statistically significant deviation from unity, the analysis demonstrates that the low-mass dijet region is theoretically sensitive to the anti-shadowing region of nuclear parton distribution functions.
• Future Prospects: The paper highlights that the current uncertainties limit the ability to discriminate between different nPDF models. Future measurements with Run 4 data (projected integrated luminosity of $\sim 300 \, \text{nb}^{-1}$ for p–Pb) are expected to significantly improve sensitivity, potentially allowing for the first definitive observation of anti-shadowing effects in dijet production.
• Reference for Heavy Ions: These results provide a critical reference for interpreting dijet measurements in Pb–Pb collisions, where any deviation from this baseline can be more confidently attributed to QGP-induced energy loss rather than initial-state nuclear effects.