Measurement of transverse polarization of $Λ$ and $\barΛ$ hyperons inside jets in $pp$ collisions at $\sqrt{s}=200$ GeV

This paper reports the first measurement of transverse polarization for $\Lambda$ and $\bar{\Lambda}$ hyperons inside jets in unpolarized proton-proton collisions at $\sqrt{s}=200$ GeV, providing crucial constraints on polarizing fragmentation functions and testing TMD evolution.

The Gist

The Big Mystery: Why Do Particles Spin?

Imagine you are at a massive, high-speed car crash. Two cars smash into each other, and debris flies everywhere. In the world of particle physics, this is what happens when two protons (the building blocks of atoms) collide at nearly the speed of light.

For 50 years, physicists have been puzzled by a strange phenomenon: when a specific type of debris called a Lambda hyperon (a heavy cousin of the proton) is created in these crashes, it doesn't just fly away randomly. It starts spinning like a top, and it spins in a very specific direction (transverse polarization).

It's as if you threw a handful of marbles at a wall, and every single marble that bounced off started spinning to the left. This is weird because the wall (the collision) wasn't spinning to begin with. For decades, scientists didn't know why these particles decided to spin.

The New Experiment: Catching the Debris in a Net

The STAR Collaboration at the Relativistic Heavy Ion Collider (RHIC) decided to solve this mystery. Instead of just looking at the debris flying everywhere, they decided to catch the debris inside a "net."

In this experiment, the "net" is called a jet.

• The Analogy: Imagine a fire hose spraying water. The water shoots out in a tight, fast stream. In particle physics, when protons collide, they often shoot out a tight stream of particles called a jet.
• The Goal: The scientists wanted to see if the spinning Lambda particles were still spinning when they were caught inside these tight streams (jets).

They smashed protons together at 200 GeV (a very high energy) and looked at the jets produced. They measured how the Lambda particles were spinning relative to the direction of the jet stream.

The Key Discovery: It Depends on the Speed

The most exciting finding is that the spin of the Lambda particles changes depending on how fast the "net" (the jet) is moving.

1. Slow Jets: When the jet is moving slower, the Lambda particles tend to spin in one direction (negative polarization).
2. Fast Jets: When the jet is moving very fast, the Lambda particles start to flip and spin in the opposite direction (positive polarization).

The Metaphor: Think of a spinning coin. If you flick it gently, it might wobble one way. If you flick it with all your might, it might spin the other way. The scientists found that the "flick" (the energy of the collision) changes the direction of the spin.

They also looked at the anti-Lambda particles (the antimatter twins). These behaved differently, mostly spinning in the opposite direction to their matter counterparts, which tells us that matter and antimatter might be following slightly different rules in how they are formed.

Why This Matters: The "Glue" of the Universe

To understand why this happens, we need to know what these particles are made of.

• Quarks: The tiny particles that make up protons and neutrons.
• Gluons: The "glue" that holds quarks together.

Previous experiments (using electron collisions) could only see how quarks spin. They were like looking at a car engine and only seeing the pistons, but not the spark plugs.

This new experiment is special because it happens in proton-proton collisions. In this environment, the gluons (the glue) are very active.

• The Breakthrough: This is the first time scientists have been able to measure how the glue (gluons) contributes to the spinning of these particles.
• The Result: The data shows that the "glue" plays a huge role. Current theories that only looked at quarks were wrong; they couldn't explain the data. This new data forces scientists to rewrite the rules about how the "glue" works.

The "Universal" Rule

There is a big question in physics: Is the rule for how particles spin the same everywhere?

• In electron collisions, particles spin one way.
• In proton collisions, do they spin the same way?

This experiment suggests that the "Polarizing Fragmentation Function" (a fancy name for the rulebook of how particles spin) is universal. It means the same rule applies whether you are smashing protons or electrons, provided you account for the "glue" (gluons). This is a huge step toward a "Theory of Everything" for the strong force.

Summary in a Nutshell

1. The Puzzle: Particles called Lambdas spin strangely after collisions, and no one knew why.
2. The Test: Scientists caught these particles inside high-speed streams (jets) to see if the spin changed.
3. The Discovery: The spin direction flips depending on how fast the stream is moving.
4. The Impact: This proves that the "glue" holding atoms together (gluons) is the secret ingredient causing the spin. It's the first time we've seen this clearly, and it helps us understand the fundamental laws of the universe better.

This paper is like finding the missing piece of a 50-year-old jigsaw puzzle, finally showing us how the "glue" of the universe makes things spin.

Technical Summary

1. Problem Statement and Scientific Context

• The Puzzle: For 50 years, experiments have observed a surprisingly large transverse polarization of $\Lambda$ hyperons produced in unpolarized hadron-nucleon/nucleus collisions. This polarization can reach $\sim 40\%$ in certain kinematic regions.
• Theoretical Gap: Perturbative QCD (pQCD) predicts negligible contributions to this observable. The phenomenon is believed to arise from non-perturbative hadronization dynamics, specifically described by the Polarizing Fragmentation Function (PFF).
• Current Limitations:
  • The PFF is a leading-twist, transverse-momentum-dependent (TMD) fragmentation function.
  • Previous constraints on PFFs came primarily from $e^+e^-$ annihilation (e.g., BELLE, LEP) and $e^-p$ scattering. These processes are sensitive to quark fragmentation but provide little to no constraint on gluon fragmentation.
  • The universality of the PFF (specifically its time-reversal-odd nature) has not been fully tested across different processes, particularly in the presence of significant gluon contributions.
• Objective: To measure the transverse polarization of $\Lambda$ and $\bar{\Lambda}$ hyperons inside jets in unpolarized $pp$ collisions. This environment allows for the simultaneous probing of quark and gluon fragmentation, offering the first direct constraints on the gluon PFF.

2. Methodology and Experimental Setup

• Experiment: The measurement was performed by the STAR experiment at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory.
• Collision Data:
  • System: Unpolarized proton-proton ($pp$) collisions.
  • Energy: $\sqrt{s} = 200$ GeV.
  • Dataset: 2015 run with an integrated luminosity of $133 \text{ pb}^{-1}$.
• Detector Components:
  • Time Projection Chamber (TPC): For charged particle tracking and particle identification (PID) via $dE/dx$.
  • Barrel/Endcap Electromagnetic Calorimeters (BEMC/EEMC): For jet energy measurement and triggering.
• Event Selection & Reconstruction:
  • Triggers: Jet Patch (JP) triggers requiring transverse electromagnetic energy ($E_T$) in calorimeter patches (thresholds: 5.4 GeV and 7.3 GeV).
  • $\Lambda/\bar{\Lambda}$ Reconstruction: Identified via the weak decay channel $\Lambda \to p + \pi^-$ (and charge conjugate). Candidates were selected using topological cuts to suppress combinatorial background. Purity in the signal mass region ($1.112 < M < 1.120 \text{ GeV}/c^2$) is $\sim 90\%$.
  • Jet Reconstruction: Anti-$k_T$ algorithm with radius parameter $R=0.6$. Inputs included TPC tracks, calorimeter towers, and reconstructed $\Lambda$ candidates. Jets were corrected for underlying event contributions.
• Polarization Extraction:
  • The polarization $P$ is extracted from the angular distribution of the daughter proton in the $\Lambda$ rest frame:
    $$\frac{dN}{d\cos\theta^*} \propto A(\cos\theta^*)(1 + \alpha_{\Lambda} P \cos\theta^*)$$
    where $\theta^*$ is the angle between the polarization axis ($\hat{S} = \vec{p}_{jet} \times \vec{p}_{\Lambda} / |\vec{p}_{jet} \times \vec{p}_{\Lambda}|$) and the daughter momentum, and $\alpha_{\Lambda} \approx 0.75$ is the decay asymmetry parameter.
• Analysis Techniques:
  • Mixed-Event (ME) Method: Used to correct for detector acceptance $A(\cos\theta^*)$. Real $\Lambda$ candidates were paired with jets from different events to remove physical correlations while preserving acceptance effects.
  • Background Subtraction: Side-band method applied to the mass spectrum.
  • Systematic Checks: Null tests performed using spin-0 $K_S^0$ mesons (yielding zero polarization). Closure tests using PYTHIA 6.4 simulations validated the ME correction and dilution factors.
  • Corrections: Data corrected from detector level to particle level. Dilution factors (0.86–0.94) were applied to account for jet axis resolution.

3. Key Contributions

1. First Measurement in $pp$ Jets: This is the first measurement of transverse $\Lambda/\bar{\Lambda}$ polarization specifically inside jets in unpolarized $pp$ collisions.
2. Gluon PFF Constraints: Unlike $e^+e^-$ data, $pp$ collisions at RHIC energies have substantial gluon-initiated subprocesses (up to 50% of $\Lambda$ yield). This measurement provides the first experimental constraints on the gluon Polarizing Fragmentation Function.
3. Universality Test: By comparing these results with $e^+e^-$ and DIS data, the study tests the universality of the PFF across different processes.
4. Kinematic Dependence: The study maps polarization as a function of:
   • Jet transverse momentum ($p_T^{jet}$).
   • Longitudinal momentum fraction ($z$).
   • Transverse momentum relative to the jet axis ($j_T$).

4. Key Results

• Dependence on Jet $p_T$:
  • $\Lambda$ Hyperons: Show a clear transition from negative polarization at low $p_T^{jet}$ to positive polarization at high $p_T^{jet}$. The average polarization is $0.24 \pm 0.19 (\text{stat}) \pm 0.09 (\text{sys})\%$.
  • $\bar{\Lambda}$ Hyperons: Remain predominantly negative across the entire measured $p_T^{jet}$ range. The average polarization is $-0.77 \pm 0.20 (\text{stat}) \pm 0.09 (\text{sys})\%$.
  • Interpretation: The sign change in $\Lambda$ is attributed to the varying parton flavor composition of jets. At low $p_T$, gluon fragmentation dominates; at high $p_T$, quark fragmentation (specifically $u$ and $d$ valence quarks) becomes more significant.
• Dependence on $z$ and $j_T$:
  • In low and medium $p_T^{jet}$ ranges, no clear dependence on $z$ or $j_T$ is observed for either species.
  • In the highest $p_T^{jet}$ range ($> 11.9$ GeV/c), $\Lambda$ and $\bar{\Lambda}$ show opposite signs in polarization as a function of $z$.
  • No significant $j_T$ dependence is observed, though the sign difference between $\Lambda$ and $\bar{\Lambda}$ persists at high $p_T$.
• Comparison with Theory:
  • Theoretical models (DGMZ scenarios) based on $e^+e^-$ data (BELLE) and assuming zero gluon PFF generally agree with data at low $p_T^{jet}$ but show sizable discrepancies at high $p_T^{jet}$ and in $j_T$ dependence.
  • Existing models significantly overestimate or underestimate the data when gluon contributions are not properly constrained, highlighting the necessity of the new $pp$ data.

5. Significance

• Solving the Polarization Puzzle: These results provide critical new inputs to understand the 50-year-old mystery of large transverse $\Lambda$ polarization in unpolarized collisions.
• QCD Dynamics: The data directly probe the non-perturbative hadronization mechanism, specifically the flavor and gluon dependence of the PFF.
• Future Impact:
  • Provides the first constraints on the gluon PFF, a previously unconstrained quantity.
  • Enables rigorous tests of TMD evolution and universality when combined with future data from the Electron-Ion Collider (EIC) and other facilities.
  • Demonstrates that the polarization inside a jet can be non-zero even at mid-rapidity, challenging previous assumptions that such polarization vanishes in these kinematic regions.

In conclusion, the STAR Collaboration has successfully measured the transverse polarization of hyperons inside jets, revealing a complex interplay between quark and gluon fragmentation that existing theoretical models cannot fully explain without incorporating the new constraints on the gluon PFF provided by this dataset.