Polarization measurement of $Λ^+_c$ and $\overlineΛ{}^-_c$ baryons in $p$Ne collisions at $\sqrt{s_{NN}} = 68.6$ GeV

The LHCb experiment reports the world's first measurement of separate polarizations for $\Lambda^+_c$ and $\overline{\Lambda}^-_c$ baryons produced in $p$Ne collisions at $\sqrt{s_{NN}} = 68.6$ GeV, finding a significant positive polarization for $\Lambda^+_c$ and a consistent-with-zero value for $\overline{\Lambda}^-_c$.

The Gist

The Big Picture: A Cosmic "Spin" Test

Imagine you are watching a high-speed car race. Usually, we just care about how fast the cars go (their speed) or where they end up (their position). But in the world of subatomic particles, there is another property called polarization.

Think of polarization like a spinning top. When a particle is created, it doesn't just fly away; it spins. The question physicists are asking is: Does it spin in a specific direction, or is it just spinning randomly like a coin tossed in the air?

For a long time, we knew that lighter particles (like the "Lambda" baryon made of light quarks) often spin in a specific direction. But for charm baryons (heavier particles containing a "charm" quark), we had never really measured this spin in this specific type of collision before. This paper is the first time the LHCb experiment at CERN has successfully measured the spin of these heavy particles.

The Setup: The "Fixed-Target" Trick

Usually, the Large Hadron Collider (LHC) is like a head-on collision course. Two beams of protons zoom toward each other from opposite directions and smash together.

But for this experiment, the LHCb team did something different. They used a clever trick called fixed-target mode:

• Imagine a high-speed train (the proton beam) zooming through a tunnel.
• Instead of hitting another train, they injected a cloud of neon gas (like a fog) right into the path of the train.
• The protons smashed into the stationary neon atoms.

This created a unique environment where the particles flew off in a specific direction, allowing scientists to study their "spin" in a way they couldn't in a head-on crash. It's like shooting a bullet into a block of wood and studying the splinters, rather than shooting two bullets at each other.

The Discovery: The "Heavy" vs. The "Light"

The team looked at two types of particles:

1. $\Lambda_c^+$ (Lambda-c-plus): The "matter" version (like a regular person).
2. $\Lambda_c^-$ (Lambda-c-minus): The "antimatter" version (like a ghostly mirror image).

The Results:

• The Matter ($\Lambda_c^+$): It was spinning! The team found that about 24% of these particles were spinning in a specific, preferred direction. It's as if 24 out of every 100 tops were all leaning to the left.
• The Antimatter ($\Lambda_c^-$): It was a bit of a mystery. The data showed it might be spinning the opposite way, but the signal was weak and fuzzy (statistically, it looked like zero). It's like trying to hear a whisper in a noisy room; they suspect a pattern, but they need more data to be sure.

Why Does This Matter? (The "Why Should I Care?" Factor)

You might ask, "So what? Who cares if a tiny particle spins left or right?"

Here is the analogy:
Imagine you are trying to understand how a car engine works. If you only look at the wheels, you see them spinning. But if you look at the engine block (the heavy charm quark inside), you see the source of the power.

• Testing the Rules of the Universe: The laws of physics (Quantum Chromodynamics, or QCD) are like a rulebook for how particles interact. We have a great rulebook for light particles, but the "heavy" particles are a bit of a mystery. This measurement is like finding a new page in the rulebook that we didn't have before.
• The "Spin" Connection: The fact that the heavy charm quark drives the spin of the whole particle is a big clue. It tells us that the heavy quark is the "boss" of the particle, dictating how it behaves, unlike lighter particles where the rules are messier.
• Future Tech: Understanding these spins helps scientists eventually measure things like the magnetic moments of these particles. This could one day help us build better particle detectors or understand the fundamental forces that hold the universe together.

The Method: How Did They Do It?

Measuring the spin of a particle that exists for a fraction of a nanosecond is incredibly hard. It's like trying to determine the spin of a bullet while it's still in the air, before it hits the target.

1. The Decay: The charm baryons are unstable. They immediately break apart into three other particles: a proton, a kaon, and a pion.
2. The Dance: The way these three particles fly apart depends on how the original particle was spinning. It's like a dance routine; if the leader spins one way, the partners move in a specific pattern.
3. The Math: The LHCb team used a massive computer model (an "amplitude model") to analyze the angles of these three particles. They compared the real data against millions of simulated scenarios to figure out the spin.
4. The "Sidekick" Data: To make their math model accurate, they used a huge amount of other data (from different collisions) to calibrate their "dance steps" before applying it to this specific neon gas experiment.

The Conclusion

This paper is a first step. It's the first time we've successfully measured the spin of these heavy charm baryons in this specific type of collision.

• Good News: We found a clear spin signal for the matter particles ($\Lambda_c^+$).
• Work to Do: The antimatter signal ($\Lambda_c^-$) is still fuzzy, and we need more data to confirm if it spins the opposite way.
• The Future: This opens the door to a whole new field of study. Just as we learned about the spin of lighter particles decades ago, this gives us the tools to understand the heavyweights of the particle world.

In short: The LHCb team caught a glimpse of the "spinning dance" of heavy particles for the first time, proving that even the heaviest particles in the universe have a preferred direction when they are born.

Technical Summary

1. Problem and Motivation

• Scientific Context: Charm baryon polarization is a unique probe for heavy-quark spin-dependent physics. Unlike light baryons, where polarization is not directly tied to constituent spins, the heavy charm quark drives baryon properties due to its mass being significantly larger than the QCD scale.
• Knowledge Gap: While polarization trends for light hyperons (like $\Lambda$) and averaged charm baryons have been studied in fixed-target experiments (e.g., NA32, E791), there has been no separate measurement of the polarization for $\Lambda_c^+$ and $\Lambda_c^-$ baryons. Furthermore, no measurement of charm baryon polarization as a function of the Feynman-$x$ variable ($x_F$) had been performed.
• Theoretical Need: Existing data is sparse, and theoretical models (such as QCD-based hybrid models) require new inputs to test non-perturbative QCD dynamics, spin-orbit correlations, and the distinct roles of valence vs. sea quarks in baryon vs. antibaryon production.
• Goal: To perform the first measurement of charm baryon polarization by the LHCb experiment in fixed-target mode, specifically separating $\Lambda_c^+$ and $\Lambda_c^-$, and investigating kinematic dependencies ($p_T$ and $x_F$).

2. Methodology

Experimental Setup

• Facility: LHCb experiment at CERN operating in fixed-target mode using the SMOG (System for Measuring the Overlap with Gas) system.
• Collision System: Proton beam (2.51 TeV) incident on a gaseous Neon (Ne) target.
• Energy: Nucleon-nucleon center-of-mass energy $\sqrt{s_{NN}} = 68.6$ GeV.
• Dataset: Recorded in 2017 with an integrated luminosity of 21.7 nb$^{-1}$.
• Event Selection: Events were selected where a beam bunch crossed the interaction region without a corresponding bunch in the opposite direction (to suppress $pp$ collisions). The primary vertex (PV) was required to be outside the standard $pp$ interaction region ($|z_{PV}| > 100$ mm).

Reconstruction and Selection

• Decay Channel: $\Lambda_c^+ \to p K^- \pi^+$ (and charge conjugate $\Lambda_c^- \to \bar{p} K^+ \pi^-$).
• Track Requirements: Charged tracks identified as hadrons with $p_T > 200$ MeV, $p > 3$ GeV, and significant displacement from the PV.
• Background Suppression:
  • A Boosted Decision Tree (BDT) classifier was trained on simulation (signal) and mass sidebands (background) to optimize the signal-to-background ratio.
  • Selection criteria included decay vertex displacement, impact parameter, and flight direction angles.
• Yields: After selection, the signal yields were determined to be 997 $\pm$ 39 for $\Lambda_c^+$ and 710 $\pm$ 32 for $\Lambda_c^-$, with background fractions of ~27% and ~25%, respectively.

Polarization Extraction Technique

• Formalism: The polarization was extracted using a helicity formalism amplitude model.
• Novelty: Unlike previous analyses (e.g., E791), this model ensures that the spin states of final particles have the exact same definition for all intermediate resonant contributions, correctly accounting for interference effects.
• Model Determination: The amplitude model parameters were determined using a high-statistics sample ($4 \times 10^5$ candidates) from semileptonic $b$-hadron decays in $pp$ collisions (LHCb Run 2), rather than the current fixed-target dataset. This "external model" approach reduces bias.
• Fit Variables: The fit utilized five variables describing the decay phase space:
  1. Squared invariant masses: $m^2_{pK^-}$ and $m^2_{K^-\pi^+}$.
  2. Angular variables: $\cos \theta_p$, $\phi_p$, and $\chi$ (defining the decay orientation relative to the production plane).
• Systematics: Uncertainties were evaluated via bootstrapping, alternative amplitude models, background parametrization variations, and detector efficiency calibration.

3. Key Contributions

1. First Separate Measurement: This is the world's first measurement of polarization for $\Lambda_c^+$ and $\Lambda_c^-$ baryons separately, allowing for the probing of different production mechanisms for matter vs. antimatter.
2. First $x_F$ Dependence: It provides the first investigation of charm baryon polarization as a function of the Feynman-$x$ variable ($x_F$).
3. Advanced Amplitude Analysis: The application of a refined helicity-formalism-based amplitude model that correctly handles spin-state matching and interference, validated on a large independent dataset.
4. Fixed-Target Regime: Extends polarization studies to a new energy regime ($\sqrt{s_{NN}} = 68.6$ GeV) not previously tested for charm baryons.

4. Results

Global Polarization

The transverse polarization ($P$) was measured with respect to the production plane:

• $\Lambda_c^+$ Polarization:
  $$P_{\Lambda_c^+} = (24 \pm 9 \text{ (stat)} \pm 2 \text{ (syst)})\%$$
  Significance: The result indicates a sizable positive polarization with a statistical significance of 2.4$\sigma$.
• $\Lambda_c^-$ Polarization:
  $$P_{\Lambda_c^-} = (-8 \pm 12 \text{ (stat)} \pm 3 \text{ (syst)})\%$$
  Significance: Compatible with zero within uncertainties.

Kinematic Dependencies

The data was split into intervals of transverse momentum ($p_T$) and Feynman-$x$ ($x_F$):

• $p_T$ Trend: The $\Lambda_c^+$ polarization shows a trend of increasing magnitude with higher $p_T$ (e.g., rising to $45 \pm 17\%$ in the highest bin, $p_T \ge 4$ GeV), consistent with trends observed in previous light hyperon and charm measurements, though statistical significance is currently inconclusive.
• $x_F$ Trend: The $\Lambda_c^+$ polarization is positive in the measured negative $x_F$ region ($x_F \approx -0.1$ to $-0.3$). Given the symmetry relation $P(-x_F) = -P(x_F)$, this suggests a negative polarization trend at positive $x_F$, consistent with the "increasing negative polarization with $|x_F|$" trend seen in light baryons.
• $\Lambda_c^-$: No clear kinematic dependencies were observed for the antibaryon, consistent with its central value being compatible with zero.

5. Significance and Impact

• QCD Dynamics: These results provide critical constraints for non-perturbative QCD models, particularly those describing heavy-baryon spin physics and the interplay between valence and sea quarks.
• Future Physics: A significant non-zero polarization in fixed-target collisions at LHC energies opens the door for future measurements of charm-baryon electric and magnetic dipole moments via spin precession techniques (using bent crystals), which are sensitive probes of CP violation and new physics.
• Model Validation: The results challenge and refine existing hybrid models of inclusive charm production, which previously relied on limited data from the E791 experiment.
• Asymmetry: The observation of a substantial particle-antiparticle production asymmetry (higher yield and polarization for $\Lambda_c^+$ vs. $\Lambda_c^-$) in proton-induced collisions is consistent with expectations for fixed-target kinematics where the valence quarks of the beam play a dominant role.

In summary, this paper establishes a new benchmark in heavy-flavor physics by delivering the first differential polarization measurements for charm baryons, utilizing a sophisticated amplitude analysis technique to reveal a significant positive polarization for $\Lambda_c^+$ that varies with kinematic variables.