Space-time evolution of particle emission in p$-$Pb collisions at $\mathbf{\sqrt{s_{\rm NN}}=~5.02}$ TeV with 3D kaon femtoscopy

This paper presents the first measurement of three-dimensional femtoscopic correlations between identical charged kaons in p$-$Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV, revealing that source sizes increase with multiplicity and decrease with transverse momentum, align with trends in other collision systems, and indicate a kaon emission evolution comparable to peripheral Pb$-$Pb collisions.

The Gist

The Cosmic "Snap" and the Ghostly Footprints

Imagine the Large Hadron Collider (LHC) as a giant, high-speed racetrack where scientists smash particles together at nearly the speed of light. Usually, they smash heavy lead balls into other lead balls (Pb–Pb) to create a massive, super-hot soup called the Quark-Gluon Plasma (QGP). But sometimes, they smash a single proton (p) into a lead ball (Pb).

For a long time, scientists weren't sure what happened in these proton-lead collisions. Was it just a tiny, messy bump? Or was it a mini-explosion that created a tiny drop of that same super-hot soup?

This paper is like a high-speed camera taking a "snapshot" of that proton-lead crash, but instead of taking a picture of the crash itself, it looks at the ghostly footprints left behind by the particles flying out.

The Detective Work: Femtoscopy

The technique used here is called femtoscopy. Think of it like this: If you throw two identical snowballs into a blizzard, they might land close together or far apart. If they land very close together, it tells you something about the size of the cloud they came from and how long the cloud lasted before the snowballs flew off.

In this experiment, the "snowballs" are kaons (a type of particle made of strange quarks). The scientists looked at pairs of identical kaons (two positive or two negative) flying out of the crash. By measuring how often they fly out together versus apart, they can reconstruct the size and shape of the explosion at the moment the particles stopped interacting and started flying freely.

What They Found: The Expanding Balloon

The researchers found three main things about this "mini-explosion":

1. Bigger Crash, Bigger Footprint: When the collision was more violent (creating more particles), the "footprint" of the source was larger. It's like blowing up a balloon: the more air you put in, the bigger the balloon gets.
2. Fast Particles, Smaller Footprint: When the kaons were flying out very fast (high momentum), the source looked smaller. Imagine a crowd of people running out of a stadium. If you only look at the fastest runners, they seem to have come from a smaller, more focused exit point than the slow walkers.
3. The "Proton vs. Lead" Mystery: When they compared these proton-lead crashes to lead-lead crashes (the big explosions), they found something interesting. At the same number of particles produced, the proton-lead explosion was roughly the same size as a proton-proton crash, but smaller than a lead-lead crash.

The Analogy: Imagine dropping a pebble (proton) into a pond versus dropping a boulder (lead nucleus).

• The pebble creates a small splash.
• The boulder creates a massive, expanding wave.
• The proton-lead collision is like dropping a heavy rock into a small puddle. The splash is bigger than the pebble, but it doesn't behave exactly like the massive wave from the boulder. It seems to act more like a slightly larger version of the pebble splash than a tiny version of the boulder wave.

The Computer Model vs. Reality

The scientists compared their "footprints" to a computer simulation called EPOS 3.

• The Good News: The computer model predicted the size of the explosion very well for "medium" and "small" crashes.
• The Bad News: For the most violent, central crashes, the computer model underestimated the size. It thought the explosion was smaller than the actual "footprints" showed. This suggests our computer models need a little tuning to understand the most extreme conditions.

The Timing: When Did the Particles Leave?

One of the coolest things they measured was the time of maximal emission. This is essentially asking: "How long did the explosion last before the particles flew away?"

They found that in these proton-lead collisions, the particles flew out at the same time as they do in the very edge-cases of lead-lead collisions (where the lead balls just barely graze each other). This suggests that even in these smaller, asymmetric crashes, the particles are behaving in a very organized, fluid-like way, similar to the massive lead-lead explosions, just on a smaller scale.

The Bottom Line

This paper tells us that when a proton hits a lead nucleus, it creates a tiny, short-lived "drop" of matter that expands and cools down.

• It behaves like a fluid (a "soup").
• Its size depends on how hard the crash was.
• It looks more like a scaled-up proton-proton crash than a scaled-down lead-lead crash.
• The particles fly out at a speed and time that matches what we see in the very edges of massive nuclear collisions.

In short, even a small crash between a proton and a lead nucleus creates a tiny, organized universe that expands and evolves in a way that helps us understand how the very first moments of our own universe might have behaved.

Technical Summary

Technical Summary: Space-time evolution of particle emission in p–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV with 3D kaon femtoscopy

Problem and Motivation
The ALICE Collaboration presents the first measurement of three-dimensional (3D) femtoscopic correlations between identical charged kaons ($K^\pm K^\pm$) in proton–lead (p–Pb) collisions at a center-of-mass energy per nucleon pair of $\sqrt{s_{NN}} = 5.02$ TeV. While signatures of quark–gluon plasma (QGP) formation, such as jet quenching and collective flow, are well-established in lead–lead (Pb–Pb) collisions, the mechanisms driving particle production in smaller systems like p–Pb remain a subject of debate. Specifically, there is no general consensus on whether p–Pb collisions exhibit collective expansion similar to heavy-ion collisions or if they are dominated by incoherent nucleon–nucleon interactions.

Femtoscopic analysis offers a unique probe into the space-time geometry of the particle-emitting source at freeze-out. While one-dimensional (1D) analyses have been performed for p–Pb collisions, they provide only a generalized source size without information on the source shape. 3D analyses, which resolve radii along the "out," "side," and "long" directions, are more data-intensive and have previously been limited to pion correlations or heavy-ion systems. Kaon femtoscopy is particularly valuable as it probes the hotter, strangeness-rich regions of the source and is less affected by resonance decays compared to pions. This study aims to constrain the dynamics of high-energy collision evolution by comparing kaon source sizes across different multiplicities and collision systems (pp, p–Pb, Pb–Pb) and against theoretical models.

Methodology
The analysis utilizes data collected by the ALICE detector during LHC Run 2, comprising approximately $250 \times 10^6$ minimum-bias p–Pb collision events.

• Event and Track Selection: Events were selected based on V0 detector signals. Charged kaons were identified using the Time Projection Chamber (TPC) and Time-Of-Flight (TOF) detectors within the pseudorapidity range $|\eta| < 0.8$ and transverse momentum $0.14 < p_T < 1.5$ GeV/c. Strict selection criteria on the distance of closest approach (DCA) to the primary vertex were applied to suppress secondary particles from weak decays.
• Correlation Function Construction: The correlation function (CF) was constructed as the ratio of the pair distribution in the same event to a reference distribution generated via event mixing. The analysis was performed in two variants: a 1D analysis in the pair rest frame (PRF) using the invariant relative momentum $q_{inv}$, and a 3D analysis in the longitudinally comoving system (LCMS) using projections $q_{out}$, $q_{side}$, and $q_{long}$.
• Parametrization and Fitting: The CFs were corrected for purity and momentum resolution. The 1D and 3D correlations were fitted using the Bowler–Sinyukov formula, which incorporates quantum statistics (QS) and Coulomb final-state interactions (modeled via the Lednický model). The fits extracted the source radii ($R_{inv}$ for 1D; $R_{out}$, $R_{side}$, $R_{long}$ for 3D) and the correlation strength ($\lambda$).
• Systematic Uncertainties: Uncertainties were evaluated by varying selection criteria (DCA, TPC points, $\eta$ range), fit ranges, baseline descriptions (using EPOS 3 and DPMJET models), and the Coulomb interaction radius.
• Model Comparison: Experimental results were compared with predictions from the EPOS 3 hadronic interaction model.
• Emission Time Extraction: The time of maximal emission ($\tau_K$) was estimated by performing a combined fit of the $R^2_{long}$ dependence on transverse mass ($m_T$) and the transverse momentum spectra of pions and kaons.

Key Results

1. Source Size Trends: The measured source radii ($R_{inv}$ and 3D radii) exhibit clear dependencies: they increase with charged-particle multiplicity and decrease with increasing pair transverse momentum ($k_T$). These trends are consistent with hydrodynamic expansion scenarios observed in Pb–Pb and high-multiplicity pp collisions.
2. Comparison with Other Systems: At comparable multiplicities, the source sizes measured in p–Pb collisions agree within uncertainties with those in pp collisions. However, they are generally smaller than those observed in Pb–Pb collisions. The data supports a "scaling hypothesis" where the interferometry volume is proportional to the total multiplicity, with a linear trend for pp and p–Pb that is vertically offset from the Pb–Pb trend. This offset increases with $k_T$, suggesting differences in transverse flow velocities or initial source geometry between small and large collision systems.
3. Model Performance: The EPOS 3 model successfully describes the source sizes for semicentral and peripheral p–Pb collisions. However, the model tends to underestimate the source size for the most central (0–5%) collisions. Furthermore, EPOS 3 consistently overestimates the correlation strength $\lambda$ (predicting $\approx 0.65$ vs. experimental $\approx 0.35$), likely due to an insufficient accounting of kaons from long-lived resonance decays (e.g., $K^*$).
4. 3D Radii and Scaling: The 3D radii ($R_{out}$, $R_{side}$, $R_{long}$) for kaons agree with those for pions within uncertainties at the same multiplicity and $k_T$. The data does not currently allow a definitive conclusion on whether the radii scale better with transverse mass ($m_T$) or transverse momentum ($k_T$), though $k_T$ scaling was observed in previous Pb–Pb kaon analyses.
5. Emission Duration: The extracted time of maximal emission for kaons in p–Pb collisions is $\tau_K = 2.7 \pm 0.25 \text{ (stat.)} \pm 0.15 \text{ (syst.)}$ fm/c. This value is comparable to that found in highly peripheral Pb–Pb collisions at the same energy, indicating that the kaon emission evolution in p–Pb is similar to that in peripheral heavy-ion collisions.

Significance and Claims
The paper claims that these measurements provide the first 3D femtoscopic constraints on kaon emission in p–Pb collisions, offering a bridge between small (pp) and large (A–A) collision systems. The results reinforce the conclusion that the dynamics of the source in p–Pb collisions at low multiplicities are similar to those in pp collisions, rather than exhibiting the stronger collective expansion seen in central Pb–Pb collisions. The discrepancy between the data and the EPOS 3 model for central events suggests that current hadronic interaction models may need refinement to fully describe the space-time evolution in high-multiplicity small systems. Additionally, the extraction of $\tau_K$ provides a direct temporal constraint on the emission process, showing that the duration of kaon emission in p–Pb is comparable to peripheral Pb–Pb, supporting the view that the emission mechanism evolves similarly in these regimes.