$\pi$, K, and p production in high-multiplicity pp collisions at $\sqrt{s} = 13$ TeV

This paper presents new measurements of $\pi$, K, and p production in high-multiplicity proton-proton collisions at 13 TeV that reveal mass-dependent spectral hardening and enhanced baryon-to-meson ratios similar to heavy-ion collisions, suggesting that particle production scales with charged-particle multiplicity rather than system size or collision energy, while highlighting that current Monte Carlo models fail to consistently describe all observed features.

The Gist

Imagine you are a chef trying to understand how a soup changes when you add more and more ingredients. Usually, if you make a tiny pot of soup (a few ingredients), it tastes one way. If you make a massive cauldron (thousands of ingredients), it tastes different because the ingredients are squished together, interacting in complex ways.

For decades, physicists thought that only the "massive cauldrons"—collisions between heavy atomic nuclei like Lead (Pb)—could create a special, super-hot, super-dense state of matter called Quark-Gluon Plasma (QGP). This is a state where the tiny building blocks of matter (quarks and gluons) melt together into a fluid, rather than staying locked inside individual particles.

However, recent experiments have shown that even "tiny pots"—collisions between single protons (pp)—can sometimes behave like the massive cauldrons, if you make the collision "high-multiplicity" (meaning, if you smash the protons together so hard that they produce a huge number of particles).

This paper from the ALICE Collaboration at CERN is like a detailed taste-test of these "tiny pots" when they are packed to the brim. Here is what they found, explained simply:

1. The Experiment: Crashing Protons at "High-Volume"

The scientists took protons (the tiny particles in the center of atoms) and smashed them together at nearly the speed of light. They didn't just look at average crashes; they specifically looked at the top 0.1% of the wildest, most chaotic crashes.

In these extreme crashes, they created a density of particles so high that it rivals the density found in collisions of heavy Lead nuclei. It's like taking a small room and suddenly filling it with as many people as a crowded stadium.

2. The Main Discovery: The "Heavy" Particles Get a Boost

When particles are created in these crashes, they fly out in all directions. The scientists measured how fast they were moving (their momentum).

• The Analogy: Imagine a crowd of people leaving a concert. Usually, the light-footed people (pions, which are very light) run out fast, while the heavy people (protons, which are heavy) move slower.
• The Finding: In these high-multiplicity proton crashes, the heavy people (protons) started running almost as fast as the light-footed people. The "spectrum" of speeds got "harder."
• Why it matters: This "hardening" of the speed distribution is a classic sign of collective flow. It suggests that the particles aren't just flying out independently; they are pushing against each other like a fluid, expanding outward together. This is the same behavior seen in the massive "Lead-lead" collisions where QGP is known to exist.

3. The Ratio Puzzle: More "Burgers" than "Buns"

The scientists also looked at the ratio of different types of particles. Specifically, they compared Protons (heavy) to Pions (light).

• The Analogy: Think of a bakery. In a normal, low-energy crash, you get a lot of buns (pions) and very few burgers (protons).
• The Finding: In these high-multiplicity proton crashes, the ratio of burgers to buns increased significantly at intermediate speeds.
• Why it matters: This "baryon enhancement" (more heavy particles) is another signature of the fluid-like behavior found in heavy-ion collisions. It suggests that the "soup" is so dense that it's easier to form heavy combinations of particles than in a sparse environment.

4. The Big Question: Is it the "Size" or the "Crowd"?

For a long time, physicists thought these strange fluid-like effects only happened because the size of the collision system was big (like Lead vs. Lead).

• The New Insight: This paper shows that if you take a tiny system (proton-proton) and just make the crowd density high enough, it behaves exactly like a big system.
• The Metaphor: It doesn't matter if you are in a small room or a giant hall; if you pack enough people into the space, they will start bumping into each other and moving as a fluid. The "size" of the room matters less than the number of people in it.

5. The Computer Models: "Close, but Not Quite"

The scientists ran these results through super-computer simulations (models like PYTHIA and EPOS) to see if their theories could predict what they saw.

• The Result: The models were like students who studied hard but still missed the exam.
  • Some models got the general shape right but missed the details.
  • Some models predicted the "heavy" particles moving too slowly.
  • None of the models could perfectly explain all the features at once.
• The Takeaway: Our current understanding of how these tiny particles interact is incomplete. We know that they act like a fluid, but our mathematical recipes for how they do it need to be updated.

Summary

This paper tells us that proton-proton collisions, when they are violent enough to create a massive crowd of particles, can mimic the behavior of heavy atomic nuclei. They show signs of a fluid-like state (Quark-Gluon Plasma) even in the smallest collision systems.

This bridges the gap between "small" and "large" physics, suggesting that the key to creating this exotic state of matter isn't the size of the colliding objects, but simply how crowded the collision gets. It's a reminder that sometimes, the smallest things, when packed tight enough, can behave like the biggest things in the universe.

Technical Summary

1. Problem and Motivation

The primary physics goal of this study is to investigate the origin of collective-like phenomena observed in small collision systems (proton-proton, $pp$) and determine if they share the same underlying mechanisms as those in large systems (nucleus-nucleus, $AA$), where a Quark-Gluon Plasma (QGP) is established.

• The Puzzle: In heavy-ion collisions, signatures of QGP formation include mass-dependent hardening of transverse momentum ($p_T$) spectra, strangeness enhancement, and an enhanced baryon-to-meson ratio at intermediate $p_T$. Surprisingly, similar features have been observed in high-multiplicity (HM) $pp$ and $p$–Pb collisions, despite the small system size.
• The Gap: Previous measurements in $pp$ collisions at $\sqrt{s}=13$ TeV reached an average charged-particle multiplicity density ($\langle dN_{ch}/d\eta \rangle$) of approximately 26.0. This paper aims to extend these measurements to significantly higher multiplicities (up to 35.8) to bridge the gap between small ($pp$) and large ($Pb$–$Pb$) collision systems.
• The Question: Does particle production scale with collision energy/system size, or is it driven primarily by the final-state charged-particle multiplicity?

2. Methodology

Data Sample and Event Selection:

• Experiment: ALICE detector at the LHC.
• Collision System: Proton-proton ($pp$) collisions at a center-of-mass energy of $\sqrt{s} = 13$ TeV.
• Dataset: Run 2 data (2016) with an integrated luminosity of 13 pb$^{-1}$ for the high-multiplicity triggered sample.
• Trigger: Events were selected using a High-Multiplicity (HM) trigger based on the V0 detector amplitude, selecting the top 0.1% of minimum bias events.
• Multiplicity Classes: The data was divided into three distinct classes based on the V0M signal percentile:
  • HM I: Top 0–0.01% ($\langle dN_{ch}/d\eta \rangle \approx 35.8$)
  • HM II: Top 0.01–0.05% ($\langle dN_{ch}/d\eta \rangle \approx 32.2$)
  • HM III: Top 0.05–0.1% ($\langle dN_{ch}/d\eta \rangle \approx 30.1$)
  • Note: These densities are comparable to peripheral (70–80%) $Pb$–$Pb$ collisions at $\sqrt{s_{NN}} = 2.76$ TeV.

Particle Identification (PID) and Reconstruction:

• Detectors: Used the Inner Tracking System (ITS), Time Projection Chamber (TPC), and Time-Of-Flight (TOF) detectors.
• Techniques:
  • ITS Stand-alone (ITSsa): Used for low-$p_T$ particles ($0.1–0.75$ GeV/c) utilizing specific energy loss ($dE/dx$) in the silicon layers.
  • TPC–TOF: Used for higher $p_T$ ($0.6–4.0$ GeV/c) utilizing a 2D fit of $dE/dx$ (TPC) and time-of-flight (TOF) to separate pions ($\pi$), kaons ($K$), and protons ($p$).
• Corrections: Applied corrections for tracking efficiency, acceptance, matching efficiency, and contamination from secondary particles (weak decays and material interactions).

Theoretical Comparisons:
The experimental results were compared against several Monte Carlo (MC) event generators:

• PYTHIA 8: Various tunes including Monash 2013 (standard), Ropes (color rope fragmentation), Shoving (string repulsion), and CLR-BLC 3 (color reconnection with string junctions).
• EPOS4: A model utilizing a core-corona approach where high-density regions undergo collective expansion.

3. Key Contributions

• Extended Multiplicity Range: This work presents the first measurements of identified particle production in $pp$ collisions at $\sqrt{s}=13$ TeV reaching $\langle dN_{ch}/d\eta \rangle \approx 35.8$, roughly a factor of five higher than the average inelastic $pp$ collisions.
• Systematic Multiplicity Study: It provides a continuous view of particle production trends from low multiplicity to the highest multiplicities achievable in $pp$, effectively reducing the "multiplicity gap" between small and large systems.
• Model Constraints: By providing high-precision data on spectra and ratios at extreme multiplicities, the paper offers stringent constraints on phenomenological models attempting to describe collective effects without a QGP.

4. Key Results

A. Transverse Momentum ($p_T$) Spectra:

• Hardening: The $p_T$ spectra for $\pi$, $K$, and $p$ show a distinct "hardening" (shift toward higher $p_T$) as multiplicity increases.
• Mass Dependence: This hardening is more pronounced for heavier particles (protons > kaons > pions), a feature characteristic of radial flow in hydrodynamic systems.

B. Particle Ratios ($K/\pi$ and $p/\pi$):

• $p/\pi$ Ratio: An enhancement of the proton-to-pion ratio is observed at intermediate $p_T$ ($\sim 3$ GeV/c). This enhancement increases with multiplicity, mirroring the behavior seen in $Pb$–$Pb$ collisions.
• $K/\pi$ Ratio: The ratio increases at low $p_T$ and saturates at higher $p_T$. The measurements align with trends observed in $Pb$–$Pb$ collisions, suggesting strangeness enhancement scales with multiplicity.
• Scaling: When comparing $K/\pi$ and $p/\pi$ ratios across different systems ($pp$, $p$–Pb, $Pb$–$Pb$) and energies, the data collapses onto a single curve when plotted against $\langle dN_{ch}/d\eta \rangle$. This strongly suggests that particle production scales with charged-particle multiplicity, rather than collision energy or system size.

C. Mean Transverse Momentum ($\langle p_T \rangle$):

• $\langle p_T \rangle$ increases continuously with multiplicity for all species.
• The slope of this increase is steeper for heavier particles, consistent with radial flow effects.
• At similar multiplicities, $\langle p_T \rangle$ in $pp$ is slightly higher than in $Pb$–$Pb$.

D. Comparison with Models:

• PYTHIA 8:
  • The Monash and Ropes tunes qualitatively reproduce the pion spectra but fail to capture the full mass-dependent hardening.
  • CLR-BLC 3 improves the description of the $p/\pi$ ratio at low $p_T$ but underestimates the integrated ratios at high multiplicity.
  • Shoving provides a good description of pion $\langle p_T \rangle$ but underestimates kaon and proton $\langle p_T \rangle$.
  • None of the PYTHIA 8 tunes consistently describe all features (spectra, ratios, and $\langle p_T \rangle$) across all multiplicities.
• EPOS4:
  • Describes the increasing trend of pion $\langle p_T \rangle$ well across the full multiplicity range.
  • Provides a more consistent qualitative description of the $p_T$-dependent $K/\pi$ and $p/\pi$ ratios compared to PYTHIA 8.
  • However, it underestimates the proton $\langle p_T \rangle$ in the highest multiplicity classes.

5. Significance

This paper provides compelling evidence that the "collective-like" signatures (mass ordering, baryon enhancement, strangeness enhancement) observed in high-multiplicity $pp$ collisions are not unique to the formation of a QGP in large systems. Instead, these features appear to be driven by the final-state charged-particle multiplicity density.

• Implication for QGP: The results challenge the strict dichotomy between "small" and "large" systems, suggesting that hydrodynamic-like behavior or strong final-state interactions can emerge in small systems if the particle density is sufficiently high.
• Theoretical Impact: The failure of current standard tunes (like Monash) to consistently describe the data highlights the need for improved theoretical frameworks. While EPOS4 and specific PYTHIA 8 tunes capture certain aspects, no single model currently provides a complete quantitative description of the data, indicating that the mechanisms governing hadronization and collective expansion in high-density small systems are not yet fully understood.
• Future Directions: These results serve as a critical benchmark for future theoretical developments aimed at unifying the description of particle production across all collision systems.