$Σ^{+}$ production in pp collisions at $\sqrt{s} = 13$ TeV

This paper presents the first measurement of $\Sigma^{+}$ production in minimum-bias and high-multiplicity pp collisions at $\sqrt{s} = 13$ TeV using a novel reconstruction method that combines converted and calorimeter photons, providing transverse-momentum spectra and ratios that agree with theoretical models and enabling future femtoscopic studies relevant to neutron star physics.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful "particle blender." Scientists smash protons together at nearly the speed of light to see what tiny ingredients come out of the mix. Usually, they look for the common ingredients: protons, electrons, and pions. But sometimes, they are hunting for the "rare spices" of the subatomic world.

This paper is about ALICE, one of the detectors at the LHC, successfully finding a very rare and elusive spice called the Sigma-plus ($\Sigma^+$) baryon.

Here is the story of how they did it, explained simply:

1. The "Ghost" Particle Hunt

In the world of subatomic particles, the Sigma-plus is a bit of a ghost. It's a "strange" particle (it contains a strange quark), but it's notoriously hard to catch.

• The Problem: Most particles ALICE looks for decay into other charged particles that leave clear tracks, like footprints in the snow. The Sigma-plus, however, decays into a proton and a neutral pion ($\pi^0$).
• The Invisible Trail: The neutral pion immediately splits into two photons (light particles). Photons don't leave footprints; they just vanish into the detector walls. It's like trying to find a thief who stole a bag of gold, but the thief immediately turned the gold into invisible light.

2. The "Two-Headed" Detective Method

For a long time, this made the Sigma-plus nearly impossible to study in proton collisions. But the ALICE team invented a clever new trick, a "two-headed" approach to catch the ghost:

• Head One (The Converter): They looked for photons that accidentally hit a piece of metal inside the detector and turned into an electron-positron pair (a process called "conversion"). This gave them a physical track to follow, like finding a shadow cast by the invisible thief.
• Head Two (The Catcher): They used the detector's "calorimeters" (massive energy traps) to catch the other photon directly.

By combining the "shadow" from the first photon and the "energy capture" from the second, they could reconstruct the invisible neutral pion and, consequently, the Sigma-plus. It's like solving a crime by finding one suspect's fingerprint and the other suspect's voice recording.

3. The Experiment: A Busy Party

The team analyzed data from 2016–2018, looking at two types of "parties" (collisions):

• Minimum Bias: A casual gathering where protons just bump into each other occasionally.
• High Multiplicity: A packed, chaotic mosh pit where many protons collide at once.

They found that the Sigma-plus appears in both settings, but it's much more common in the crowded "mosh pit" collisions.

4. The Big Questions Answered

Once they caught the particles, they asked two big questions:

A. Do our computer simulations match reality?
Scientists use complex computer programs (like PYTHIA and EPOS) to predict what happens in these collisions.

• The Result: The old programs (PYTHIA) were like bad weather forecasters; they predicted the shape of the storm correctly but completely underestimated how much rain (particles) would fall. They missed the Sigma-plus yield by about half!
• The Winner: The EPOS model was much closer to the truth, suggesting that our understanding of how these particles form is getting better, but still needs work.

B. Do the particles follow a recipe?
There is a theory called the Statistical Hadronization Model (SHM). Think of it like a baker's recipe: if you have a certain amount of flour, sugar, and eggs (energy and matter), you can predict exactly how many cookies (particles) you will bake.

• The Result: The ratio of Sigma-plus particles to the more common Lambda particles matched the "baker's recipe" perfectly. This suggests that even in these tiny, high-speed collisions, nature follows a very orderly statistical law.

5. Why Does This Matter?

You might ask, "Why do we care about a rare particle that decays in a billionth of a second?"

• Neutron Stars: The inside of a neutron star is like a super-dense cosmic pressure cooker. Scientists think that under that extreme pressure, strange particles like the Sigma-plus might appear and change how the star behaves. By measuring how Sigma-plus interacts with protons here on Earth, we can better understand the "equation of state" (the rulebook) for neutron stars.
• The Standard Model: Every time we measure a rare particle and find it matches (or doesn't match) our theories, we are stress-testing the fundamental laws of physics.

The Bottom Line

The ALICE collaboration didn't just find a needle in a haystack; they built a new, super-sensitive magnet to find the needle. They proved that even the most elusive particles can be caught with the right combination of detective work and technology. This discovery helps us understand the "recipe" of the universe and what happens in the densest objects in the cosmos.

Technical Summary

1. Problem and Motivation

The production of strange baryons is a critical probe for understanding quantum chromodynamics (QCD) and the mechanisms of hadronization in high-energy collisions. However, the Σ baryons (specifically the $S=-1$ isospin triplet members: $\Sigma^+$, $\Sigma^0$, $\Sigma^-$) have historically been difficult to measure with high precision.

• Detection Challenges: Unlike the $\Lambda$ baryon, which decays into charged particles ($p\pi^-$), ground-state $\Sigma$ baryons do not have purely charged decay channels. The $\Sigma^+$ decays primarily via $\Sigma^+ \to p + \pi^0$ (branching ratio $\approx 51.6\%$), where the neutral pion ($\pi^0$) decays into two photons.
• Photon Detection: Photons are difficult to reconstruct in the multi-particle environment of hadronic collisions, especially when they have low energy. Traditional methods relying solely on calorimeters suffer from low efficiency or high background, while methods relying solely on photon conversions suffer from low statistics.
• Theoretical Discrepancies: Previous measurements of strange baryons (like $\Lambda$ and excited $\Sigma$ states) have shown significant tensions between experimental data and Monte Carlo (MC) event generators (e.g., PYTHIA, EPOS), which often underestimate strange hadron yields.
• Astrophysical Relevance: Precise knowledge of $\Sigma^+$ production is essential for constraining the equation of state (EoS) of neutron stars, where the interaction between $\Sigma^+$ and protons is a key factor in determining the star's internal structure.

2. Methodology

The ALICE Collaboration analyzed proton-proton ($pp$) collision data recorded at a center-of-mass energy of $\sqrt{s} = 13$ TeV during the LHC runs from 2016 to 2018. The analysis focused on two event classes: Minimum-Bias (MB) and High-Multiplicity (HM) collisions.

A. Novel Reconstruction Technique

The core innovation of this paper is a hybrid reconstruction method for the $\pi^0$ in the decay chain $\Sigma^+ \to p + \pi^0 \to p + \gamma + \gamma$:

1. Photon 1 (Conversion Method - PCM): One photon is reconstructed via its conversion into an electron-positron pair ($\gamma \to e^+e^-$) within the detector material. This utilizes the Inner Tracking System (ITS) and Time Projection Chamber (TPC) to identify the distinct "V0" topology. This method provides excellent topological purity and vertex resolution.
2. Photon 2 (Calorimetry): The second photon is detected directly in the electromagnetic calorimeters (PHOS and EMCal). This leverages the high detection efficiency of calorimeters for photons that do not convert.
3. Combination: By combining a PCM photon with a calorimeter photon, the method achieves both high purity (from the PCM vertex) and high efficiency (from the calorimeter).

B. Particle Identification and Selection

• Proton: Identified via specific energy loss ($dE/dx$) in the TPC (within $3\sigma$) and Time-of-Flight (TOF) measurements for $p_T > 0.9$ GeV/c.
• Secondary Vertex: The $\Sigma^+$ decay vertex is reconstructed using a Kalman Filter. Cuts are applied on the distance of closest approach (DCA) and the pointing angle (PA) to suppress background from primary particles and material interactions.
• Background Subtraction: The combinatorial background is estimated using the event-mixing technique, where protons and conversion photons from one event are paired with calorimeter clusters from different events with similar vertex positions and multiplicities.

C. Corrections and Systematics

• Efficiency Correction: The raw spectra are corrected for acceptance and reconstruction efficiency using MC simulations (PYTHIA 8 Monash 2013 with injected $\Sigma^+$ samples).
• Systematic Uncertainties: Evaluated by varying selection criteria (track, PID, kinematic, topological) in groups. Additional uncertainties arise from material budget, matching efficiency, and cluster finding.

3. Key Contributions

• First Measurement: This is the first measurement of $\Sigma^+$ (and $\Sigma^-$) production in $pp$ collisions at $\sqrt{s} = 13$ TeV.
• Methodological Breakthrough: The paper demonstrates a novel, high-efficiency reconstruction technique for $\Sigma^+$ that overcomes the limitations of previous methods, enabling future studies of $\Sigma^+$-proton interactions via femtoscopy.
• Comprehensive Dataset: Results are provided for both minimum-bias and high-multiplicity events, allowing for the study of strangeness enhancement as a function of event activity.

4. Results

• Transverse Momentum ($p_T$) Spectra: The differential yields ($d^2N/dp_T dy$) were measured for $p_T$ up to $\approx 7$ GeV/c. The spectra are well-described by Lévy-Tsallis functions.
• Rapidity Density ($dN/dy$):
  • High-Multiplicity: $0.313 \pm 0.007 (\text{stat}) \pm 0.027 (\text{syst})$
  • Minimum-Bias: $0.071 \pm 0.003 (\text{stat}) \pm 0.008 (\text{syst})$
• Comparison with Event Generators:
  • PYTHIA 8 (Monash 2013): Reproduces the spectral shape well but underestimates the yield by a factor of ~2, confirming the known underestimation of strangeness production in standard string fragmentation models.
  • PYTHIA 6 (Perugia 2011): Closer in yield at low $p_T$ but fails to describe the spectral shape.
  • EPOS LHC: Provides the best overall description, matching both the spectral shape and the yield closely. This suggests the importance of the "core-corona" model and coalescence mechanisms in EPOS.
  • EPOS4: Shows similar performance to EPOS LHC at low $p_T$ but converges toward PYTHIA 8 at intermediate $p_T$.
• Yield Ratios: The ratio of $(\Sigma^+ + \Sigma^-)$ to $(\Lambda + \bar{\Lambda})$ is measured to be approximately 0.27–0.28 in both MB and HM events.
  • This ratio is in excellent agreement with Statistical Hadronization Model (SHM) calculations (both canonical and grand-canonical ensembles), suggesting that $\Sigma$ production scales with multiplicity similarly to $\Lambda$ production.

5. Significance

• Constraining QCD Models: The data provides a stringent constraint on MC generators, highlighting the need to improve strangeness production mechanisms in models like PYTHIA. The success of EPOS LHC supports the relevance of collective effects (coalescence) even in small $pp$ systems.
• Equation of State of Neutron Stars: The high purity and efficiency of the new reconstruction method pave the way for femtoscopic measurements of the $\Sigma^+$-proton interaction. These interactions are crucial for understanding the stiffness of the neutron star equation of state and the potential existence of hyperons in neutron star cores.
• Strangeness Enhancement: The results confirm that the enhancement of strange baryon yields with increasing multiplicity (observed previously for $\Lambda$) also applies to $\Sigma$ baryons, reinforcing the idea that high-multiplicity $pp$ collisions exhibit collective behavior similar to heavy-ion collisions.
• Inclusive Spectra Correction: The measured $\Sigma^+$ spectra provide necessary inputs for correcting inclusive charged-particle spectra, as $\Sigma$ contributions were previously inferred from $\Lambda$ data due to a lack of direct measurements.