Deuteron coalescence probability in jets in p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV

This paper presents the first measurement of deuteron coalescence parameters in p-Pb collisions at 5.02 TeV, revealing a significant enhancement of the coalescence parameter within jets compared to the underlying event, a finding that exceeds similar observations in pp collisions and is qualitatively reproduced by PYTHIA 8.314 simulations.

The Gist

The Big Picture: Building Blocks in a Cosmic Storm

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful "smash-up" machine. Scientists fire protons and lead nuclei at each other at nearly the speed of light. When they collide, they create a tiny, super-hot fireball of energy that instantly turns into a shower of new particles.

For decades, physicists have been trying to understand how these particles stick together to form heavier things, like deuterons (a nucleus made of one proton and one neutron). Think of a deuteron as a tiny "magnetic couple" that forms when a proton and a neutron happen to be close enough and moving at the same speed to grab onto each other.

This paper asks a very specific question: Does the environment where these particles are born change how likely they are to stick together?

Specifically, the team looked at two different "neighborhoods" inside the collision:

1. The Underlying Event: The chaotic, messy background noise of the collision, where particles are flying everywhere randomly.
2. The Jet: A focused, high-speed "stream" of particles shooting out in a specific direction, like a firehose of debris.

The Analogy: The Crowd vs. The Parade

To understand the difference between these two neighborhoods, imagine a massive concert:

• The Underlying Event (The Crowd): Imagine the general audience. People are scattered all over the stadium, moving in different directions, chatting, and bumping into each other randomly. If you wanted two specific people (a proton and a neutron) to find each other and hold hands (form a deuteron), it would be pretty hard. They are too far apart and moving too chaotically.
• The Jet (The Parade): Now, imagine a marching band (the jet) moving through the crowd. Everyone in the band is walking in the same direction, at the same speed, and standing very close to one another. If you wanted two band members to hold hands, it would be incredibly easy because they are already right next to each other and moving in sync.

What They Found

The ALICE team measured how often deuterons formed in these two different "neighborhoods" during proton-lead collisions.

1. The "Jet" Effect: They found that deuterons form much more often inside the "Jet" (the parade) than in the "Underlying Event" (the crowd).

   • In fact, the probability of them sticking together in the jet was more than 20 times higher than in the background chaos.
   • Why? Because in the jet, the particles are "bunched up" in space and time. They are closer together and moving more similarly, making it much easier for them to coalesce (stick together).

2. The Comparison: The team compared these results to similar experiments done with just proton-proton collisions (smaller smash-ups). They found that the "bunching up" effect was even stronger in the proton-lead collisions than in the smaller ones. This suggests that the size of the collision "room" matters. In the larger proton-lead collision, the background crowd is more spread out, making the "parade" (the jet) look even more special by comparison.

Why Does This Matter?

You might be wondering, "Why do we care about tiny proton-neutron couples?"

1. Solving the Mystery of Matter: We still don't fully understand the exact recipe for how light nuclei form in the universe. This experiment helps test our theories. It confirms that the "Coalescence Model" (the idea that particles stick together if they are close and moving together) is a good description of reality.
2. Searching for Dark Matter: This is a big one. Scientists use space telescopes (like AMS-02) to look for anti-deuterons (the antimatter version of deuterons) in cosmic rays. If they find them, it could be a sign of Dark Matter annihilating in space.
   • The Problem: We don't know how many anti-deuterons are created naturally by cosmic rays hitting space dust (the "background noise").
   • The Solution: By understanding exactly how these particles form in particle collisions (like the ones at CERN), scientists can better predict the natural background. This helps them filter out the noise and spot the real signal of Dark Matter.

The Verdict

The paper concludes that context is everything. Just like it's easier to find a friend in a crowded room if you are both standing in a tight huddle (the jet) rather than scattered across the stadium (the background), particles are much more likely to stick together if they are born in a focused, high-energy stream.

The team also tested a computer simulation (PYTHIA) to see if it could predict this. The simulation got the general idea right (it saw the "huddle" effect), but it slightly underestimated just how strong that effect was. This tells physicists that their computer models need a little tuning to perfectly match the messy reality of the quantum world.

In short: The universe is a chaotic place, but when particles get organized into a high-speed stream, they are much more likely to team up and build something new.

Technical Summary

1. Problem Statement and Motivation

The production mechanism of light (anti)nuclei (such as deuterons, tritons, and helium-3) remains an open question in high-energy nuclear physics. Two primary theoretical frameworks exist:

• Statistical Hadronization Model (SHM): Assumes hadrons are emitted from a source in thermal equilibrium.
• Coalescence Model: Posits that nuclei form when protons and neutrons are close in phase space (momentum and position).

While these models describe bulk production well, they struggle to predict yields in specific kinematic environments. A critical test for the coalescence model is the production of light nuclei inside jets versus the underlying event (UE).

• Hypothesis: In jets, hadrons are produced via the fragmentation of high-energy partons, resulting in particles that are closer in phase space compared to the uncorrelated particles in the underlying event. The coalescence model predicts a significant enhancement of the coalescence probability ($B_2$) inside jets.
• Context: Previous measurements in $pp$ collisions at 13 TeV showed this enhancement. This paper aims to extend the study to $p$–Pb collisions at 5.02 TeV to investigate:
  1. Whether the enhancement persists in a system with a larger source size (due to the lead nucleus).
  2. Whether the "jet hadrochemistry" (particle species composition) depends on the collision system ($pp$ vs. $p$–Pb).
  3. To provide constraints for indirect dark matter searches, where antinuclei fluxes from cosmic ray interactions must be precisely modeled.

2. Methodology

Data Sample and Event Selection

• Collision System: Proton-Lead ($p$–Pb) collisions at a center-of-mass energy per nucleon pair $\sqrt{s_{NN}} = 5.02$ TeV.
• Dataset: Run 2 data (2016), approximately 310 million minimum-bias events.
• Jet Definition: Events were selected containing at least one charged primary particle with transverse momentum $p_T^{lead} > 5$ GeV/c. This leading particle serves as a proxy for the jet axis.
• Azimuthal Regions: The analysis divides the event into three regions relative to the leading particle ($\Delta\phi = |\phi - \phi_{lead}|$):
  1. Toward: $|\Delta\phi| < 60^\circ$ (Contains the leading jet + underlying event).
  2. Away: $|\Delta\phi| > 120^\circ$ (Contains the recoil jet + underlying event).
  3. Transverse: $60^\circ < |\Delta\phi| < 120^\circ$ (Dominated by the underlying event).
• In-Jet Extraction: The "in-jet" yield is obtained by subtracting the Transverse region distribution (background) from the Toward region distribution.

Particle Identification (PID) and Reconstruction

• Detectors: Inner Tracking System (ITS), Time Projection Chamber (TPC), and Time-Of-Flight (TOF).
• Species: (Anti)deuterons ($d/\bar{d}$) and antiprotons ($\bar{p}$).
  • Note: Both matter and antimatter deuterons are used to maximize statistics, while antiprotons are used as a proxy for primary protons (as secondary contamination is negligible for antimatter).
• PID Strategy:
  • Low $p_T$ ($0.3 < p_T < 0.7$ GeV/c for $\bar{p}$; $0.6 < p_T < 1.2$ GeV/c for $d/\bar{d}$): Identified via specific energy loss ($dE/dx$) in the TPC within $3\sigma$ of the Bethe-Bloch expectation.
  • High $p_T$: Combined TPC ($dE/dx$) and TOF (time-of-flight) information. Signal extraction involves fitting $n\sigma$ distributions with modified Gaussian functions (signal) and exponential/polynomials (background).
• Corrections: Raw yields are corrected for reconstruction efficiency and acceptance using Monte Carlo (MC) simulations (HIJING for underlying event, Geant4 for detector response). Secondary particle contamination (spallation for deuterons, weak decays for antiprotons) is subtracted using template fits based on the Distance of Closest Approach (DCA).

Observable Definition

The Coalescence Parameter ($B_2$) is calculated as:
B_2 = \frac{1}{(2\pi/3)p_T^d} \frac{d^2N_d/dydp_T^d}{\left( \frac{1}{(2\pi/3)p_T^p} \frac{d^2N_p/dydp_T^p} \right)^2}
where $p_T^p = p_T^d / 2$. This parameter quantifies the probability of coalescence. The analysis compares $B_2$ in jets ($B_2^{jet}$) versus the underlying event ($B_2^{UE}$).

3. Key Contributions

• First Measurement in $p$–Pb: This is the first measurement of (anti)deuteron and antiproton distributions and the coalescence parameter specifically in and out of jets in proton-nucleus collisions.
• System Size Dependence: It provides a direct comparison between $pp$ (small system) and $p$–Pb (larger system) to test the dependence of coalescence on source size.
• Model Validation: The results are compared against PYTHIA 8.314 using the Angantyr model (which includes a reaction-based deuteron production model), testing the model's ability to reproduce jet-induced nuclear formation.
• Hadrochemistry Check: The study investigates the deuteron-to-proton yield ratio ($d/p$) to determine if jet composition varies between collision systems.

4. Results

Transverse Momentum Distributions

• The $p_T$ distributions for deuterons and antiprotons in the Toward and Away regions are compatible, while the Transverse region is approximately 90% of the Toward yield.
• The "in-jet" distributions show a hardening (shift to higher $p_T$) compared to the out-of-jet distributions, consistent with jet fragmentation expectations.

Coalescence Parameter ($B_2$) Enhancement

• Significant Enhancement: A large enhancement of $B_2$ is observed in jets compared to the underlying event in $p$–Pb collisions.
  • Magnitude: $B_2^{jet}$ is enhanced by a factor of >20 relative to $B_2^{UE}$.
  • Significance: This corresponds to a statistical significance of 4.6$\sigma$.
• Comparison with $pp$: This enhancement is larger than the factor of ~15 observed in $pp$ collisions at 13 TeV.
• Underlying Event Suppression: The $B_2$ value in the underlying event of $p$–Pb is lower than in $pp$. This is consistent with the coalescence model prediction that a larger source size (measured via femtoscopy as ~1.5 fm in $p$–Pb vs. ~1 fm in $pp$) leads to a lower coalescence probability due to nucleons being more spread out in phase space.
• Model Comparison: PYTHIA 8.314 (Angantyr) qualitatively reproduces the large enhancement of $B_2$ in jets relative to the UE. However, the model tends to underestimate $B_2^{jet}$ at low $p_T/A$, though current statistical uncertainties prevent a definitive conclusion.

Deuteron-to-Proton Ratio ($d/p$)

• The $d/p$ ratio is enhanced in jets compared to the UE in both collision systems.
  • $pp$: Enhancement factor of 1–2.
  • $p$–Pb: Enhancement factor of 2–4.
• Double Ratio: The ratio of the $d/p$ ratios between $p$–Pb and $pp$ (in both jets and UE) is compatible with unity within $1\sigma$ uncertainty. This suggests that the jet hadrochemistry (relative composition of species) is likely independent of the collision system, though limited statistics prevent a firm conclusion.

5. Significance and Conclusion

• Validation of Coalescence: The results strongly support the coalescence picture, demonstrating that the proximity of nucleons in phase space (as found in jets) significantly enhances bound-state formation.
• Source Size Effect: The observation of a lower $B_2$ in the $p$–Pb underlying event compared to $pp$ confirms the inverse relationship between source size and coalescence probability.
• Astrophysical Implications: These measurements provide crucial constraints for modeling antinuclei production in cosmic rays. Understanding the production mechanisms in jets helps refine background estimates for dark matter searches (e.g., by AMS-02 and GAPS), where antideuterons are a potential signature.
• Future Outlook: The authors note that the current results are dominated by statistical uncertainties. Future analyses using the larger LHC Run 3 dataset will extend these studies to heavier nuclei (like $^3$He) and employ full jet reconstruction algorithms to further constrain the formation process of light nuclei.