Measurement of the transverse-momentum fraction of strange hadrons from jet-like correlation structures in pp collisions at $\sqrt{s} = 13$ TeV

The ALICE Collaboration reports the first measurements of the average transverse-momentum fraction for strange hadrons in 13 TeV pp collisions, revealing distinct production trends for mesons and baryons that current Monte Carlo models fail to describe.

The Gist

Imagine you are at a massive, chaotic concert where thousands of people (particles) are crashing into each other. Usually, when we think of high-energy physics, we imagine these crashes happening in giant stadiums (heavy-ion collisions) where the crowd is so dense it turns into a super-hot, liquid-like soup called the Quark-Gluon Plasma (QGP).

But here's the twist: Scientists at CERN's ALICE experiment noticed that even in tiny, "small system" crashes—like two single protons smashing together (which is like two people bumping into each other in a hallway)—strange things are happening. The particles are behaving as if they are part of that giant liquid soup, even though the crowd is tiny.

This paper is a detective story trying to figure out how these particles are born and how they carry energy in these tiny crashes.

The Mystery: The "Strange" Family

In this experiment, the scientists are focusing on a specific family of particles called strange hadrons. Think of them as the "exotic" guests at the party. There are two main types they are watching:

1. Strange Mesons ($K^0_S$): Like the "messengers" of the group.
2. Strange Baryons ($\Lambda$): Like the "heavyweights" or the "leaders" of the group.

In the past, scientists noticed that in these tiny crashes, the "heavyweights" (baryons) seem to get a bigger boost of energy than the "messengers" (mesons). It's as if the baryons are getting VIP treatment while the mesons are stuck in the general admission section. The big question is: Why?

The New Tool: The "Momentum Share"

To solve this, the scientists didn't just look at how fast the particles were going. Instead, they asked a different question: "What fraction of the original energy did this particle steal?"

Imagine a parent (the original high-energy particle, or "parton") gives a child a bag of candy (transverse momentum).

• If the child takes 60% of the candy, that's a high "share."
• If they take 30%, that's a lower "share."

The scientists measured this "share" ($\langle z \rangle$) for both the mesons and the baryons.

The Discovery: Two Different Stories

The results were surprising and told two very different stories:

1. The Mesons ($K^0_S$): They were consistent. No matter how fast they were going, they always took about the same 60% share of the energy. It's like a reliable employee who always takes the same percentage of the paycheck, regardless of the company's size. This suggests they are being produced in a standard, predictable way (like breaking a stick into pieces).

2. The Baryons ($\Lambda$): They were acting weird. When they were moving slower (lower energy), they started taking a much bigger share of the energy—up to 78%. It's as if the baryons are grabbing the whole bag of candy when the parent is distracted, but only taking a normal amount when the parent is paying close attention.

What does this mean?
This suggests that the "heavyweight" baryons and the "messenger" mesons are being created by two different mechanisms.

• The mesons are likely just breaking apart from a high-energy crash (fragmentation).
• The baryons might be forming in a different way, perhaps by "recombining" or sticking together from a pool of energy, which gives them a bigger boost. This supports the idea that even in tiny proton crashes, there is a collective "fluid-like" behavior happening, similar to the giant soup in heavy-ion collisions.

The "Model" Check: Did the Computers Get it Right?

The scientists then ran their data through super-computer simulations (like PYTHIA and AMPT). These models are like video game physics engines that try to predict how particles should behave.

• The Result: The computers failed.
• The models predicted that both types of particles should behave similarly, or that the baryons should drop off in energy share much faster than they actually did.
• The models couldn't explain why the baryons were grabbing so much extra energy at lower speeds.

The Big Picture Analogy

Think of the proton collision as a fireworks display.

• The Mesons are the standard sparks flying out in a predictable pattern.
• The Baryons are the giant, heavy shells that seem to be propelled by a hidden, extra force, especially when the explosion isn't at its peak intensity.

The fact that our current "fireworks manuals" (the computer models) can't explain why the heavy shells are behaving this way tells us that we are missing a piece of the puzzle. There is a new, collective force at play in these tiny collisions that we don't fully understand yet.

Conclusion

This paper is a crucial step in understanding the universe. It shows that even in the smallest, simplest collisions, nature is doing something complex and collective. The strange baryons are breaking the rules, hinting that the "soup" of the early universe might be forming in places we never expected. The ALICE team is now going to look at even more complex particles to see if this "VIP treatment" for baryons continues.

Technical Summary

1. Problem Statement and Motivation

The paper addresses a fundamental question in high-energy nuclear physics: What are the hadronization mechanisms of strange particles in "small systems" (proton-proton collisions) where collective effects, typically associated with Quark-Gluon Plasma (QGP) in heavy-ion collisions, are observed?

• Context: Phenomena such as strangeness enhancement and baryon-to-meson yield ratios ($\Lambda/K^0_S$) increasing with multiplicity have been observed in $pp$ collisions. These are traditionally attributed to radial flow and parton recombination in QGP. However, the origin of these effects in small systems remains debated.
• Limitation of Previous Methods: Previous studies relied on reconstructing high-energy jets ($p_T > 10$ GeV/c) or measuring inclusive particle ratios. A key limitation is that particles produced outside a reconstructed jet cone may still originate from hard scattering processes, making it difficult to isolate the fragmentation dynamics of low-energy partons.
• Goal: To measure the average transverse-momentum fraction ($\langle z \rangle$) carried by strange hadrons ($\Lambda, \bar{\Lambda}, K^0_S$) relative to the originating parton. Unlike standard jet analyses, this study focuses on mini-jets defined by angular correlations, allowing the investigation of fragmentation in lower energy regimes where jet reconstruction is impossible.

2. Methodology

The analysis utilizes a novel $p_T$-weighted two-particle correlation method to estimate the momentum fraction without reconstructing full jet cones.

Data and Experimental Setup

• Dataset: $pp$ collisions at $\sqrt{s} = 13$ TeV collected by the ALICE detector during LHC Run 2 (2016–2018).
• Selection: Minimum bias (MB) events with a primary vertex within $\pm 10$ cm. Approximately $1.7 \times 10^9$ events were analyzed.
• Particles:
  • Trigger: Strange hadrons ($K^0_S, \Lambda, \bar{\Lambda}$) reconstructed via their V0 decay topology ($K^0_S \to \pi^+\pi^-$, $\Lambda \to p\pi^-$) in the kinematic range $0.6 < p_T < 20.0$ GeV/c.
  • Associated: Primary charged particles ($0.2 < p_T < 20$ GeV/c) reconstructed using the ITS and TPC.

The Novel Observable: $\langle z \rangle$

Instead of defining a jet cone, the analysis uses angular correlations ($\Delta\phi - \Delta\eta$) between the strange trigger and associated charged particles.

1. Correlation Function: A $p_T$-weighted correlation function is constructed:
   $$C_{p_T\text{-weighted}}(\Delta\eta, \Delta\phi) = \frac{1}{N_{trig}} \frac{d^2 \sum p_T}{d\Delta\phi d\Delta\eta}$$
   where $\sum p_T$ is the sum of transverse momenta of associated particles in a given angular bin.
2. Integration: The integral under the "near-side" peak (centered at $\Delta\phi = \Delta\eta = 0$) yields the total correlated transverse momentum ($\sum_{NS} p_T$) associated with the trigger.
3. Calculation of $\langle z \rangle$: The average momentum fraction is calculated as:
   $$\langle z(p_T^s) \rangle = \frac{p_T^s}{\langle \sum_{NS} p_T \rangle + p_T^s}$$
   Here, the denominator approximates the transverse momentum of the originating parton ($p_T^{parton}$).

Corrections and Systematics

• Background Subtraction: Sideband subtraction is used to remove combinatorial background from the invariant mass distributions of V0 candidates.
• Efficiency & Acceptance: Corrections are applied for tracking efficiency (derived from MC) and detector acceptance using the event-mixing technique to normalize the correlation function.
• Systematic Uncertainties: Evaluated by varying selection criteria (vertex position, signal window, background subtraction regions, pileup rejection). Total uncertainties range from 1.5% to 7.9% depending on the particle and $p_T$.

3. Key Contributions

• First Measurement of $\langle z \rangle$ in Mini-jets: This is the first measurement of the transverse-momentum fraction for strange hadrons in $pp$ collisions using a correlation-based approach that does not require high-$p_T$ jet reconstruction.
• Differentiation of Hadronization Mechanisms: The study provides direct evidence of distinct fragmentation behaviors between strange mesons ($K^0_S$) and strange baryons ($\Lambda$) in the intermediate $p_T$ region.
• Model Benchmarking: It provides a stringent test for Monte Carlo models (PYTHIA 8 and AMPT) regarding their ability to describe strangeness production and baryon enhancement in small systems.

4. Results

The results are presented as $\langle z \rangle$ as a function of the strange particle's transverse momentum ($p_T^s$):

• High $p_T$ ($> 6$ GeV/c): Both $K^0_S$ and $\Lambda$ exhibit $\langle z \rangle \approx 0.6$. This high value is attributed to trigger bias, where the steeply falling parton spectrum favors events where the trigger particle carries a large fraction of the parton's momentum.
• Strange Mesons ($K^0_S$): $\langle z \rangle$ remains flat (constant at $\approx 0.6$) across the entire measured $p_T$ range (0.6–6 GeV/c). This suggests a consistent production mechanism dominated by hard fragmentation processes even at intermediate $p_T$.
• Strange Baryons ($\Lambda$): $\langle z \rangle$ shows a decreasing trend as $p_T$ increases (or conversely, an increase as $p_T$ decreases).
  • At the lowest $p_T$ interval, $\langle z \rangle \approx 0.78$, roughly 30% higher than the high-$p_T$ limit.
  • This deviation from the $K^0_S$ trend below $\approx 4$ GeV/c indicates a different hadronization mechanism, possibly involving harder fragmentation or a significant contribution from isolated $\Lambda$ production in soft processes (recombination/coalescence).
• Comparison with Models:
  • PYTHIA 8 (Monash & Color Rope): Both tunes fail to describe the data. They predict a minimum near 2 GeV/c and a steep rise at low $p_T$, which is not observed. They significantly underestimate $\langle z \rangle$ for $K^0_S$ in the intermediate region.
  • AMPT (String Melting): Reproduces the general decreasing trend for $\Lambda$ better than PYTHIA but still fails to describe the magnitude and the flat behavior of $K^0_S$.
  • Conclusion: None of the standard models satisfactorily describe the $\langle z \rangle$ distributions at low and intermediate $p_T$, highlighting a gap in understanding the interplay between fragmentation and recombination in small systems.

5. Significance

• Insight into QGP-like Effects: The distinct behavior of baryons vs. mesons supports the hypothesis that baryon enhancement in small systems is driven by mechanisms different from standard jet fragmentation, potentially linked to parton recombination or collective flow effects even in $pp$ collisions.
• Refining Hadronization Models: The failure of current tunes (Monash, Color Rope) and the AMPT model to reproduce the $\langle z \rangle$ distributions suggests that current implementations of color reconnection, string tension, and coalescence need revision to accurately model strangeness production in small systems.
• New Observable: The $p_T$-weighted correlation method offers a robust alternative to jet reconstruction for studying parton fragmentation in low-energy regimes, opening new avenues for investigating the transition from soft to hard physics.

In summary, this paper demonstrates that strange baryons and mesons follow different momentum-fraction distributions in $pp$ collisions, challenging existing theoretical models and providing crucial constraints for understanding the onset of collective behavior in small collision systems.