Multiplicity dependence of f$_0$(980) production in pp collisions at $\sqrt{s} = 13$ TeV

This paper reports on the multiplicity dependence of f$_0$(980) production in pp collisions at $\sqrt{s}=13$ TeV using the ALICE detector, finding that yield ratios decrease with increasing multiplicity and that thermal model comparisons suggest the f$_0$(980) does not contain significant hidden strangeness.

The Gist

The Big Picture: A Cosmic Smashing Party

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle accelerator. It's like a giant, high-speed racetrack where we smash protons (tiny building blocks of matter) together at nearly the speed of light.

In this specific study, the ALICE collaboration (a team of scientists) is looking at what happens when these protons crash. Specifically, they are hunting for a very specific, short-lived particle called the $f_0(980)$.

Think of the $f_0(980)$ as a "ghost" in the machine. It appears for a split second after a collision and then immediately vanishes, breaking apart into two pions (another type of particle). Because it disappears so fast, it's hard to catch. The scientists have to look at the "debris" (the pions) and reconstruct the ghost to see if it was there.

The Mystery: What is this Ghost Made Of?

For decades, physicists have been arguing about what the $f_0(980)$ actually is. It's like trying to figure out if a mysterious object in a dark room is a simple wooden box, a complex robot, or a balloon filled with helium.

There are three main theories:

1. The Simple Box: It's a standard particle made of a quark and an anti-quark (like a normal atom).
2. The Robot: It's an "exotic" particle made of four quarks (a tetraquark).
3. The Balloon: It's a "molecule" made of two other particles stuck together.

The big question is: Does this particle contain "strange" ingredients? In particle physics, "strange" refers to a specific type of quark (the strange quark).

• If it's a simple box, it has no strange quarks.
• If it's the exotic robot or balloon, it likely does have strange quarks hidden inside.

The Experiment: Counting the Crowd

To solve this mystery, the scientists didn't just look at one crash. They looked at thousands of crashes and sorted them by how "crowded" the aftermath was.

• Low Multiplicity: A crash that produces a few particles. Imagine a quiet party with just a few guests.
• High Multiplicity: A crash that produces a massive shower of particles. Imagine a packed stadium concert.

The scientists asked: "As the crowd gets bigger, does the number of $f_0(980)$ ghosts change in a way that suggests they are made of strange ingredients?"

The Results: The "Strange" Truth

Here is what they found, using a simple analogy:

The Analogy of the Bakery:
Imagine you run a bakery. You have two types of cookies:

1. Plain Cookies (No special ingredients).
2. Exotic Cookies (Made with rare, expensive "strange" spices).

You notice that when you bake a small batch (low crowd), you make a lot of Exotic Cookies. But when you bake a massive batch for a huge party (high crowd), the ratio of Exotic Cookies to Plain Cookies drops.

Why? Because in a massive kitchen, the rare spices get used up faster, or the conditions change so that making Exotic Cookies becomes harder.

What the ALICE data showed:
The scientists found that as the particle collisions got "crowder" (higher multiplicity), the ratio of $f_0(980)$ particles to other common particles (like pions) decreased.

They ran computer simulations (models) to predict what would happen:

• Model A (No Strange Quarks): Predicted that the ratio would go down as the crowd got bigger.
• Model B (With Strange Quarks): Predicted that the ratio would actually go up or stay high because the "strange" ingredients would become more abundant in a crowded environment.

The Verdict: The real data matched Model A. The ratio went down, just like the Plain Cookies.

What Does This Mean?

This is a big deal because it suggests that the $f_0(980)$ is not an exotic particle made of hidden strange quarks. It is likely a standard, "normal" particle made of up and down quarks (the common ingredients of the universe).

It's like finding out that the mysterious "ghost" you were chasing was just a regular person wearing a mask, not a supernatural creature.

The "Traffic Jam" Effect

The paper also discusses something called "hadronic rescattering." Imagine the particles flying out of the crash are like cars leaving a concert.

• In a small parking lot (low multiplicity), cars can leave easily.
• In a massive traffic jam (high multiplicity), cars bump into each other, get stuck, or change lanes.

The $f_0(980)$ is a "short-lived" car. It breaks down (decays) very quickly. If it breaks down in a traffic jam, its parts might get hit by other cars before they can escape. This makes it look like there are fewer of them than there actually were. The scientists had to account for this "traffic jam" effect to get the true count.

Summary in One Sentence

By smashing protons together and counting how many "ghost" particles appear in small versus huge crowds, the ALICE team found that the $f_0(980)$ behaves like a normal, non-exotic particle, suggesting it doesn't contain the hidden "strange" ingredients that some theories predicted.

Technical Summary

1. Problem and Motivation

The internal structure of the light scalar meson $f_0(980)$ remains a subject of intense theoretical debate. While it could be a conventional quark-antiquark ($q\bar{q}$) meson, alternative hypotheses suggest it may be a compact tetraquark, a $K\bar{K}$ molecule, or a mixture of these states. A critical distinction lies in its strangeness content:

• $|S|=0$ hypothesis: The particle consists of light quarks only (e.g., mixtures of $u\bar{u}$ and $d\bar{d}$).
• $|S|=2$ hypothesis: The particle contains a hidden strange quark pair ($s\bar{s}$), consistent with tetraquark or molecular models.

Understanding the production mechanisms of $f_0(980)$ in high-multiplicity proton-proton (pp) collisions is essential to distinguish between these scenarios. Furthermore, $f_0(980)$ is a short-lived resonance ($\tau \approx 5\text{--}10$ fm/c), making it a sensitive probe of the hadronic phase that occurs after chemical freeze-out. In this phase, resonances can decay and their daughters rescatter, or they can be regenerated via interactions, altering the observable yields compared to the chemical freeze-out prediction.

The paper aims to:

1. Measure the production of $f_0(980)$ in pp collisions at $\sqrt{s} = 13$ TeV as a function of charged-particle multiplicity.
2. Investigate the strangeness content of $f_0(980)$ by comparing data with the Canonical Statistical Model (CSM).
3. Study the effects of hadronic rescattering by analyzing yield ratios relative to other resonances.

2. Methodology

Experimental Setup:

• Data Sample: Minimum bias (MB) pp collisions collected by the ALICE detector at the LHC during Run 2 (2015–2018) at $\sqrt{s} = 13$ TeV.
• Integrated Luminosity: $19 \text{ nb}^{-1}$.
• Multiplicity Selection: Events are classified based on the amplitude of the V0 detector (V0M), which covers forward and backward pseudorapidity. Classes range from low multiplicity to high multiplicity (INEL > 0).
• Kinematic Region: Midrapidity ($|y| < 0.5$) and transverse momentum ($0 < p_T < 13$ GeV/c).

Reconstruction and Analysis:

• Decay Channel: $f_0(980) \to \pi^+ \pi^-$ (Branching Ratio assumed: $46 \pm 6\%$).
• Track Selection: Charged tracks reconstructed in the Inner Tracking System (ITS) and Time Projection Chamber (TPC) with $p_T > 0.15$ GeV/c and $|\eta| < 0.8$. Strict cuts on the Distance of Closest Approach (DCA) to the primary vertex are applied to reject secondary particles.
• Particle Identification (PID): Pions are identified using specific energy loss ($dE/dx$) in the TPC and Time-of-Flight (TOF) measurements.
• Signal Extraction:
  • Invariant mass ($M_{\pi\pi}$) distributions are constructed for unlike-sign pairs.
  • Combinatorial background is subtracted using the like-sign method ($\sqrt{N_{\pi^+\pi^+} \times N_{\pi^-\pi^-}}$).
  • The signal is extracted via a fit to the background-subtracted mass spectrum using a superposition of:
    • Relativistic Breit-Wigner (rBW) functions for $f_0(980)$, $\rho(770)^0$, and $f_2(1270)$.
    • A Maxwell-Boltzmann-like function for the residual background.
  • The fit range is $0.8 < M_{\pi\pi} < 1.76$ GeV/$c^2$.

Corrections and Systematics:

• Yields are corrected for acceptance, tracking efficiency, PID efficiency, trigger efficiency, and vertex reconstruction efficiency.
• A signal loss correction ($f_{SL}$) is applied to account for event selection biases, derived using $\phi$ meson scaling.
• Systematic uncertainties are evaluated by varying selection criteria, fit ranges, and fit parameters (masses/widths of background resonances).

Theoretical Comparison:

• Results are compared with the Canonical Statistical Model with strangeness undersaturation ($\gamma_S$CSM).
• Two scenarios are tested: $|S|=0$ (no strange quarks) and $|S|=2$ (hidden strangeness).

3. Key Contributions

1. First Measurement at 13 TeV: This work provides the first detailed measurement of $f_0(980)$ production in pp collisions at $\sqrt{s} = 13$ TeV, extending previous results from 5.02 TeV.
2. Multiplicity Dependence: It establishes the evolution of $f_0(980)$ yields and mean transverse momentum ($\langle p_T \rangle$) across a wide range of charged-particle multiplicities.
3. Strangeness Content Constraint: By comparing particle yield ratios ($f_0/\pi$ and $f_0/K^*$) with $\gamma_S$CSM predictions, the study provides strong evidence against the $|S|=2$ hypothesis.
4. Hadronic Phase Insights: The analysis of yield ratios offers new constraints on hadronic rescattering effects in small collision systems (pp), complementing observations in heavy-ion collisions.

4. Results

Spectral Shapes and Yields:

• $p_T$ Spectra: The spectra show a "hardening" (shift to higher $p_T$) as multiplicity increases for $p_T < 4$ GeV/c. For $p_T > 4$ GeV/c, the spectral shapes become consistent across multiplicity classes.
• Integrated Yield ($dN/dy$): Increases linearly with charged-particle multiplicity.
• Mean $p_T$ ($\langle p_T \rangle$): Increases with multiplicity and appears to saturate at high multiplicities, a trend consistent with other hadron species.

Particle Yield Ratios:

• $f_0(980)/\pi^\pm$: The ratio decreases with increasing charged-particle multiplicity.
  • The $\gamma_S$CSM calculation assuming $|S|=0$ qualitatively describes this decreasing trend.
  • The calculation assuming $|S|=2$ predicts an increase with multiplicity, which contradicts the data.
  • Note: The model underestimates the ratio in low-multiplicity events and overestimates it in high-multiplicity events, likely due to unmodeled hadronic rescattering effects.
• $f_0(980)/K^*(892)^0$: This ratio also decreases with increasing multiplicity.
  • Similar to the pion ratio, the $|S|=0$ scenario matches the decreasing trend, while the $|S|=2$ scenario does not.
  • The model underestimates the ratio by $\sim 35\%$ across the range, suggesting that rescattering effects (specifically $\pi\pi$ vs $K\pi$ cross-sections) modify the yields differently.

Double Ratios:

• The double ratio (multiplicity class ratio divided by the INEL > 0 ratio) for $f_0/\pi$ shows suppression at low $p_T$ in high-multiplicity events, approaching unity at high $p_T$. This suggests that the suppression mechanism is most effective for low-momentum resonances, consistent with hadronic rescattering.

5. Significance and Conclusion

• Exclusion of Hidden Strangeness: The data strongly disfavors the hypothesis that $f_0(980)$ contains hidden strangeness ($|S|=2$). The observed decrease in $f_0/\pi$ and $f_0/K^*$ ratios with multiplicity is only consistent with the $|S|=0$ scenario in the statistical model. This suggests $f_0(980)$ is likely a conventional meson or a state dominated by light quarks, rather than a tetraquark or $K\bar{K}$ molecule with significant $s\bar{s}$ content.
• Hadronic Rescattering: The discrepancy between the model (which assumes chemical freeze-out) and the data (showing suppression in high-multiplicity events) confirms the presence of significant hadronic rescattering effects in high-multiplicity pp collisions. The short lifetime of $f_0(980)$ makes it particularly susceptible to these effects.
• Future Directions: The authors note that precise knowledge of the $f_0(980) \to \pi^+\pi^-$ branching ratio and $p_T$-differential model calculations for hadronic interactions are needed to refine these conclusions.

In summary, this study utilizes the ALICE detector to constrain the internal structure of the $f_0(980)$ meson, providing experimental evidence that favors a non-strange quark composition and highlighting the importance of hadronic phase interactions in small collision systems.