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A first look at strange-quark polarization in top-quark decays with CMS Open Data

Using 16.39 fb⁻¹ of public CMS data from 13 TeV proton-proton collisions, this study presents the first measurement of strange-quark polarization in top-quark decays by analyzing the longitudinal polarization of $\Lambda$ baryons in hadronic $W \to c\bar{s}$ jets, finding results consistent with zero or LEP-inferred transfer values while projecting future statistical reach for the full LHC dataset.

Original authors: Yevgeny Kats

Published 2026-11-02

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yevgeny Kats

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Inside the heart of every atom, protons and neutrons are built from smaller particles called quarks. These quarks are not just static building blocks; they possess a fundamental property called spin, which acts like a tiny internal compass needle. For decades, physicists have understood how quarks behave when they are free or moving at high speeds, but a major mystery remains: how does this spin survive when quarks crash together and stick to other particles to form new, heavier objects called hadrons? This process, known as fragmentation, is governed by the strong nuclear force, a complex interaction that is notoriously difficult to calculate. While we know that heavy quarks, like those in the bottom or charm families, tend to keep their spin direction as they form new particles, the behavior of the strange quark is much less certain. Because the strange quark is relatively light, its spin might be scrambled or lost entirely during the chaotic formation of new matter. Understanding this transfer of spin is crucial not only for mapping the fundamental rules of the universe but also for developing a new way to measure the spin of quarks in any high-energy collision.

A researcher has taken the first step toward solving this puzzle by looking at the decay of top quarks, the heaviest known elementary particles. In a recent study using public data from the Large Hadron Collider, they focused on a specific scenario where a top quark pair decays, and one of the resulting particles, a W boson, breaks apart into a charm quark and a strange quark. Because of the way the weak nuclear force works, the strange quark produced in this specific decay is born with its spin fully aligned in one direction, like a perfectly spun top. The researcher then watched as this polarized strange quark traveled a microscopic distance before fragmenting into a jet of particles, eventually forming a specific type of hadron called a Lambda baryon. By measuring the direction in which the Lambda baryon decays, they could determine whether the original spin of the strange quark had survived the journey or if it had been washed out.

The study utilized a dataset of proton-proton collisions recorded in 2016, analyzing 16.39 inverse femtobarns of data. The researcher first identified events containing a single electron or muon, a signature that indicated a top quark pair had been created. They then reconstructed the complex debris of the collision to find the specific jet containing the strange quark, using a technique that identified its partner charm quark to ensure they were looking at the right pair. Within these jets, they hunted for Lambda baryons, which are unstable particles that travel a short distance before decaying into a proton and a pion. The key to the measurement lay in the angle at which the proton was emitted during this decay. If the strange quark's spin had been preserved, the protons would emerge at a preferred angle relative to the original direction of the strange quark. If the spin had been lost, the protons would fly off in random directions.

After carefully filtering through millions of collision events to isolate the relevant signals, the researcher found that the data was consistent with two possibilities: either the spin was completely lost, or it was transferred to the Lambda baryon at a level similar to what was observed in older experiments at the LEP collider. The statistical precision of this first attempt was not yet high enough to distinguish between these two scenarios. The measured polarization was effectively zero within the margins of error, meaning they could not yet confirm how much of the original spin survived. However, the study successfully validated the entire method, proving that it is possible to identify the strange quark's partner, isolate the correct jet, and measure the decay angles of the resulting Lambda baryons in a real-world detector environment.

The researcher also noted that the data contained more soft, low-energy Lambda baryons than their computer simulations predicted. The simulation under-produced these particles, with 259 simulated compared to 356 observed in the data. These extra particles appeared to come from pileup interactions, where multiple collisions happen at the same time, rather than from the primary top quark decay. While these extra particles did not bias the measurement, they highlighted a need for better modeling of the detector environment in future studies. The researcher projected that with the full dataset from the current and future runs of the Large Hadron Collider, including the High-Luminosity upgrade, the statistical uncertainty will shrink dramatically. This will allow for a definitive measurement of the spin transfer, potentially revealing whether the strange quark retains its spin direction as it transforms into matter.

This work represents a foundational step in a new field of particle physics. By demonstrating that the strange quark's spin can be tracked through the chaotic process of hadron formation, the study opens the door to a more detailed understanding of the strong force. The technique developed here could eventually be applied to other types of quarks, allowing physicists to decompose the spin structure of matter with unprecedented clarity. While the current results are a starting point, the path forward is clear: with more data and refined analysis tools, the mystery of how the spin of a single quark shapes the matter around it is within reach of being solved.

Technical Summary: A First Look at Strange-Quark Polarization in Top-Quark Decays with CMS Open Data

Problem and Motivation
The mechanism by which quark spin is transferred to the hadrons produced during fragmentation remains one of the least tested aspects of Quantum Chromodynamics (QCD). While heavy quarks ( $b$ and $c$ ) offer favorable conditions for spin preservation due to their large masses, the strange quark ( $s$ ), with a mass comparable to $\Lambda_{QCD}$ , presents a more challenging case where polarization survival is not guaranteed. Previous measurements at LEP established that energetic $\Lambda$ baryons retain a significant fraction of the longitudinal polarization of strange quarks produced in $Z \to s\bar{s}$ decays. However, these measurements were inclusive, averaging over all quark flavors and requiring model-dependent unfolding to isolate the strange-sector contribution.

This paper addresses the need for a direct, flavor-tagged measurement of strange-quark polarization. The author proposes utilizing the hadronic decay of the $W$ boson in semileptonic top-quark pair ( $t\bar{t}$ ) events ( $W \to c\bar{s}$ ). In this topology, the strange quark is produced with a known, nearly maximal longitudinal polarization ( $P(s) \approx -1$ ). By identifying the strange jet via its partner charm jet and measuring the polarization of $\Lambda$ baryons within it, one can directly probe the spin-dependent fragmentation function $\Delta D_{\Lambda/s}(z)$ without the flavor-averaging ambiguities of inclusive LEP analyses.

Methodology
The analysis utilizes 16.39 fb $^{-1}$ of proton-proton collision data at $\sqrt{s} = 13$ TeV from the CMS Open Data portal (Run 2016). The methodology proceeds through the following stages:

Event Selection and Reconstruction:
- Events are selected in the single-lepton channel (muon or electron) with at least four jets and two $b$ -tagged jets.
- A hadronic top quark is reconstructed by minimizing a $\chi^2$ variable combining the dijet mass ( $m_{jj}$ ) and the trijet mass ( $m_{jjb}$ ) against the known $W$ and top masses.
- The hadronic $W$ boson is reconstructed from the two non- $b$ jets in the top triplet.
Flavor Tagging:
- The strange jet is identified by charm-tagging its partner jet in the $W \to c\bar{s}$ decay. A custom working point on the DEEPJET $c$ -vs-light and $c$ -vs-bottom discriminants is used to select the charm jet. The recoiling jet is treated as the strange-jet candidate.
$\Lambda$ Reconstruction and Selection:
- $\Lambda \to p\pi^-$ (and charge conjugate) decays are reconstructed as displaced $V^0$ vertices within $\Delta R < 0.4$ of the strange jet axis.
- Candidates are required to have an invariant mass within 6 MeV of the $\Lambda$ mass and pass a $K_S^0$ veto.
- Crucially, the baryon number of the candidate is matched to the lepton charge: an $\ell^+$ (from $W^+ \to \ell^+\nu$ ) implies a hadronic $W^- \to \bar{c}s$ , expecting a $\Lambda$ ; an $\ell^-$ implies a $\bar{\Lambda}$ . This "right-sign" selection suppresses background from secondary strange quarks and combinatorial pairs.
Polarimetry and Analysis:
- The polarization is extracted from the angular distribution of the decay proton in the $\Lambda$ rest frame relative to the $\Lambda$ flight direction in the $W$ rest frame: $d\Gamma/d\cos\theta \propto 1 + \alpha_\Lambda P \cos\theta$ .
- Acceptance Correction: The simulation initially assumes isotropic $\Lambda$ decays, but the detector acceptance is highly non-uniform, particularly rejecting events where the soft pion falls below momentum thresholds. The data and simulation $p_T$ spectra also differ significantly. To correct for this, the simulation is reweighted to match the data's $\Lambda$ $p_T$ distribution in a control region (candidates in any top-triplet jet).
- Estimator: An unbinned maximum-likelihood fit is performed on the $\cos\theta$ distribution using templates generated by weighting the unpolarized simulation with $1 + \alpha_\Lambda P \cos\theta$ .

Key Contributions

First Realization: This work presents the first end-to-end realization of strange-quark polarimetry in top-quark decays using collider data.
Validation of the Chain: It validates the full analysis chain, including the reconstruction of the hadronic top, flavor tagging via charm-jet identification, and the extraction of polarization from $\Lambda$ decay angles in a high-multiplicity environment.
Systematic Identification: The paper identifies and quantifies the dominant systematic uncertainties, specifically the mismatch between data and simulation in the $\Lambda$ transverse momentum spectrum and the resulting acceptance bias. It demonstrates that reweighting the simulation to the data spectrum is essential to avoid fake polarization signals.
Purity Analysis: It quantifies the "charge-correlated purity" (the fraction of candidates carrying the primary strange quark), showing it rises from $\sim 6\%$ inclusively to $\sim 27\%$ (data) and $\sim 43\%$ (simulation) in the high-momentum fraction region ( $z > 0.3$ ).

Results
The analysis measures the longitudinal polarization $P_\parallel$ of $\Lambda$ baryons in the strange jet for the region $z > 0.3$ :
$P_\parallel = +0.04 \pm 0.45 \text{ (stat.)} \pm 0.06 \text{ (syst.)}$

The result is consistent with zero.
It is also consistent with the expected value of $-0.28$ to $-0.37$, which is derived from LEP-inferred polarization transfer factors applied to the fully polarized strange quarks of $W$ decays.
The two transverse polarization components are consistent with zero, as expected for a longitudinally polarized source.
The statistical uncertainty is currently the limiting factor, dominated by the small number of signal events in the 16.39 fb $^{-1}$ dataset.

Significance and Claims
The paper modestly claims that the current precision is insufficient to test the polarization transfer mechanism or distinguish between different fragmentation models. The primary significance of the work lies in:

Establishing the Methodology: Providing a validated framework for measuring strange-quark polarization in $t\bar{t}$ events.
Quantifying Dilutions: Identifying the specific dilution mechanisms (soft fragmentation, pileup, wrong-sign backgrounds) that must be controlled for a precise measurement.
Projections: The author projects that with the full Run-2, Run-3, and HL-LHC datasets, the statistical uncertainty could reach $\sim 0.05$ , comparable to the precision of the original LEP measurements. They suggest that future measurements should employ a pointing requirement to remove pileup-induced $\Lambda$ candidates and utilize joint fits of right-sign and wrong-sign samples to constrain acceptance asymmetries.

The work serves as a proof-of-concept, demonstrating that the unique topology of $t\bar{t}$ events offers a clean environment to isolate strange jets and measure their polarization, a capability not available in flavor-inclusive LEP analyses.

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