sPHENIX measurement of Open-Charm Baryon-to-Meson Ratios in $p$+$p$ collisions at RHIC

This paper presents the first measurement of open-charm baryon-to-meson ratios, specifically the $\Lambda_c^+ / D^0$ baseline, in $p$+$p$ collisions at RHIC energies using the high-statistics, unbiased dataset collected by the sPHENIX experiment to investigate heavy-flavor hadronization mechanisms.

The Gist

Imagine the subatomic world as a high-speed, chaotic dance floor. When two protons smash into each other at nearly the speed of light, it's like two freight trains colliding head-on. In that split second of impact, a burst of energy creates a shower of new particles, some of which are "heavy" and exotic, like the Charm Quark.

This paper is a progress report from the sPHENIX experiment, a massive, high-tech camera system at the Relativistic Heavy Ion Collider (RHIC) in New York. Here is what they are doing, explained simply:

1. The Mission: Catching the "Heavy" Dancers

Most particles created in these collisions are light and fleeting, like sparks flying off a firework. But Charm Quarks are heavy. Because they are heavy, they are born in the very first fraction of a second of the collision and then have to survive the entire chaotic aftermath.

Scientists want to know: How do these heavy quarks turn into stable particles? Do they just fly off alone, or do they grab a partner to form a "family"?

• Mesons are like a heavy quark holding hands with a light partner (a "couple").
• Baryons are like a heavy quark holding hands with two other partners (a "trio").

For a long time, physicists thought the rules for forming these families were the same everywhere (like a universal recipe). But recent data from Europe (the LHC) suggested that in proton collisions, nature might be making more "trios" (Baryons) than the old recipe predicted. sPHENIX is here to check if this is true in American collisions.

2. The Camera: sPHENIX's Superpower

The sPHENIX detector is like a high-speed, 4D security camera.

• The Problem: In the past, these cameras were like old security systems that only recorded when a loud alarm went off (a "trigger"). This meant they missed the quiet, subtle events where heavy particles are made.
• The Solution: sPHENIX has a "Streaming Readout." Imagine a security guard who doesn't just watch the door; instead, they record everything that happens for hours, 24/7, without stopping.
• The Result: In 2024, they recorded 100 billion proton collisions. That is a massive library of data, giving them a statistical power they've never had before. It's like going from looking at a single grain of sand to analyzing a whole beach.

3. The Detective Work: Finding the Needle in the Haystack

Finding a specific heavy particle (like a $\Lambda_c$ Baryon or a $D^0$ Meson) is incredibly hard.

• The Haystack: The collision creates billions of ordinary particles (the "hay").
• The Needles: The heavy charm particles are rare (the "needles").
• The Trick: These heavy particles don't live long. They travel a tiny distance and then decay (break apart) into other particles. sPHENIX uses its ultra-precise sensors to spot this tiny "jump" or "displacement" from the center of the crash. It's like spotting a specific dancer who steps slightly off the beat before leaving the floor.

The paper shows the team has successfully "caught" these particles for the first time at RHIC. They have identified:

• $D^0$ and $D^+$: The "Meson" couples.
• $\Lambda_c$: The "Baryon" trio.
• $\phi$ and $K^0_S$: Lighter, well-known particles used to calibrate the camera.

4. Why This Matters

The team is now calculating the ratio of Baryons (trios) to Mesons (couples).

• If the ratio is high: It means the heavy quarks are grabbing extra partners, suggesting a new way nature builds matter that we didn't fully understand before.
• If the ratio is low: It confirms the old "universal recipe."

This measurement is crucial because it sets the baseline. Before we can understand the "soup" of matter created in heavy ion collisions (where we study the early universe), we need to know exactly how things behave in simple proton collisions first.

The Bottom Line

Think of sPHENIX as a new, ultra-powerful microscope that has just been turned on. In its first year of full operation, it has taken 100 billion snapshots of particle collisions. The scientists have successfully found the rare, heavy particles they were looking for. Now, they are ready to count them up and answer a big question: Is the universe making more heavy "families" than we thought?

This work paves the way for even bigger experiments in 2025, where they will smash gold and oxygen nuclei together to study the "Quark-Gluon Plasma"—the hot, dense soup that existed microseconds after the Big Bang.

Technical Summary

1. Problem Statement

The paper addresses a critical gap in understanding heavy-flavor hadronization mechanisms in quantum chromodynamics (QCD).

• The Universality Challenge: In elementary collisions ($e^+e^-$ and $e^-p$), charm-hadron production is well-described by universal fragmentation functions. However, LHC measurements in $p+p$ collisions revealed that the $\Lambda_c^+ / D^0$ ratio (baryon-to-meson) is significantly higher than fragmentation function predictions, suggesting universality is violated in hadronic collisions.
• Missing Baseline at RHIC: While the STAR experiment has measured this ratio in heavy-ion ($Au+Au$) collisions, there has been no prior measurement of the $\Lambda_c^+ / D^0$ baseline in $p+p$ collisions at RHIC energies. Without this baseline, interpreting heavy-ion results (where the Quark-Gluon Plasma, or QGP, modifies yields) is impossible.
• Statistical Limitations: Previous RHIC datasets lacked the statistical power to perform precision measurements of open-charm baryons and strange-to-light meson ratios ($D_s^+ / D^+$) due to low trigger efficiencies for low-$p_T$ hadrons.

2. Methodology

The study leverages the unique capabilities of the sPHENIX detector at the Relativistic Heavy Ion Collider (RHIC) during Run 24 (2024).

• Data Acquisition Strategy:
  • Streaming Readout: Unlike traditional minimum-bias triggers, sPHENIX utilized a "streaming readout" mode, recording approximately 20–30% of all $p+p$ collisions delivered by RHIC. This bypassed hardware trigger biases, particularly for low-$p_T$ particles.
  • Dataset: The analysis is based on 100 billion unbiased $p+p$ collision events at $\sqrt{s} = 200$ GeV, corresponding to an integrated luminosity of 2.9 pb$^{-1}$. This represents an order-of-magnitude increase in statistics compared to previous RHIC heavy-flavor measurements.
• Detector Systems:
  • Vertexing: A Monolithic Active Pixel Sensor (MAPS) based vertex detector (MVTX) provides primary vertex resolution $<10$ microns.
  • Tracking: An Intermediate Silicon Tracker (INTT) and a Time Projection Chamber (TPC) with GEM-based continuous readout provide 4D track reconstruction (space + time).
  • Pile-up Mitigation: The INTT's timing resolution (sufficient to resolve 106.5 ns bunch crossings) allows for proper track-to-crossing association, mitigating pile-up effects in the high-rate streaming environment.
• Reconstruction & Analysis:
  • Calibration: Initial analysis focused on calibrating silicon alignment and correcting TPC space-charge distortions using field-off data and lamination fitting.
  • Validation: Light-flavor resonances ($K_S^0, \Lambda, \phi, \Xi^-, \Sigma(1385)^-$) were reconstructed to validate tracking and vertexing performance (using the KFParticle package).
  • Signal Extraction: Open-charm signals were extracted via invariant mass reconstruction of decay channels:
    • $\Lambda_c^+ \to pK^-\pi^+$
    • $D^0 \to K^-\pi^+$
    • $D^+ \to K^-\pi^+\pi^+$
  • Background Suppression: The analysis utilized displaced secondary vertex reconstruction and low-momentum $dE/dx$ information from the TPC to suppress the large combinatorial background inherent in open-charm measurements.

3. Key Contributions

• First RHIC Observation: This work presents the first observation of the $\Lambda_c^+$ baryon and the $D^+$ meson in $p+p$ collisions at RHIC energies.
• First sPHENIX Open-Charm Signals: It reports the first $D^0$ signal observed by the sPHENIX experiment.
• Baseline Establishment: It establishes the essential $p+p$ baseline required to interpret future heavy-ion ($Au+Au$) and small-system ($O+O$) results regarding charm hadronization.
• Demonstration of Streaming Readout: The paper validates the feasibility of using high-rate streaming readout for heavy-flavor physics, achieving unbiased data collection rates $\sim$20–50 times higher than traditional triggers.

4. Results

• Tracking Performance: The analysis demonstrated stable tracking performance across beam crossings, with uniform reconstruction efficiency confirmed by the $K_S^0$ band in the $\pi^+\pi^-$ invariant mass vs. beam crossing distribution.
• Resonance Reconstruction: Clear signals were reconstructed for light-flavor resonances ($K_S^0, \Lambda, \phi, \Xi^-, \Sigma(1385)^-$), validating the detector alignment and distortion corrections.
• Open-Charm Signals:
  • $\Lambda_c^+$: A clear signal was observed in the $pK^-\pi^+$ channel with a fitted yield of $101 \pm 33$ events and a mass peak at $2285 \pm 4$ MeV.
  • $D^0$: A signal was observed in the $K^-\pi^+$ channel with a yield of $248 \pm 44$ events and a mass peak at $1862.6 \pm 2.1$ MeV.
  • $D^+$: A signal was observed in the $K^-\pi^+\pi^+$ channel with a yield of $140 \pm 44$ events and a mass peak at $1873.0 \pm 6.5$ MeV.
• Ratio Projection: A statistical projection for the $\Lambda_c^+ / D^0$ ratio as a function of transverse momentum ($p_T$) was presented, indicating the feasibility of measuring this ratio with high precision once full calibration is complete.

5. Significance

• Theoretical Constraints: The ability to measure the $\Lambda_c^+ / D^0$ ratio at RHIC energies allows for the discrimination between competing hadronization models (e.g., color reconnection, statistical hadronization, and coalescence) that attempt to explain the baryon enhancement seen at the LHC.
• QGP Studies: Establishing a precise $p+p$ baseline is indispensable for quantifying the modification of charm quark yields in the Quark-Gluon Plasma created in $Au+Au$ collisions.
• Future Physics Program: The successful demonstration of these capabilities paves the way for a comprehensive heavy-flavor program in 2025, including high-statistics measurements in $O+O$ and $Au+Au$ collisions, enabling new investigations into strange-quark abundance ($D_s^+ / D^+$) and the space-time evolution of the collision system.

In summary, this paper marks a pivotal transition for sPHENIX from commissioning to physics output, proving that the experiment can deliver world-leading precision measurements of open-charm baryon-to-meson ratios, filling a critical knowledge gap in QCD heavy-flavor physics at RHIC.