Measuring spin correlation between quarks during QCD confinement

TL;DR

The study probes how quark confinement and spontaneous chiral-symmetry breaking in QCD manifest in hadronisation by tracking spin correlations from vacuum $s\bar{s}$ pairs to final-state $\Lambda\bar{\Lambda}$ hyperons in $\sqrt{s}=200$ GeV $p+p$ collisions. Using STAR at RHIC, the authors reconstruct $\Lambda$ hyperons, extract spin correlations from decay kinematics with mixed-event corrections, and compare to SU(6) and Burkardt–Jaffe models while accounting for feed-down effects. They observe a significant positive spin correlation for short-range pairs, $P_{\Lambda\bar{\Lambda}} = 0.181 \pm 0.035_{\mathrm{stat}} \pm 0.022_{\mathrm{sys}}$ (4.4σ), consistent with 100% initial $s\bar{s}$ spin alignment in the vacuum, and see decoherence at larger pair separations. This provides a novel hadron-level probe of QCD vacuum structure and confinement dynamics, offering a new bridge between nonperturbative QCD, lattice studies, and quantum-information-inspired perspectives on hadronisation.

Abstract

The vacuum is now understood to possess a rich and complex structure, characterized by fluctuating energy fields and a condensate of virtual quark-antiquark pairs. The spontaneous breaking of the approximate chiral symmetry, signaled by the nonvanishing quark condensate $\langle q\bar{q}\rangle$, is dynamically generated through topologically nontrivial gauge configurations such as instantons. The precise mechanism linking the chiral symmetry breaking to the mass generation associated with quark confinement remains a profound open question in Quantum Chromodynamics (QCD) - the fundamental theory of strong interaction. High energy proton-proton collisions could liberate virtual quark-antiquark pairs from the vacuum that subsequently undergo confinement to form hadrons, whose properties could serve as probes into QCD confinement and the quark condensate. Here, we report evidence of spin correlations in $Λ\barΛ$ hyperon pairs inherited from spin-correlated strange quark-antiquark virtual pairs. Measurements by the STAR experiment at the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory reveal a relative polarization signal of $(18 \pm 4)\%$ that links the virtual spin-correlated quark pairs from the QCD vacuum to their final-state hadron counterparts. Crucially, this correlation vanishes when the hyperon pairs are widely separated in angle, consistent with the decoherence of the quantum system. Our findings provide a new experimental paradigm for exploring the dynamics and interplay of quark confinement and entanglement.

Figures (6)

• Figure 1: Illustration of tracing the QCD evolution of the spin of a strange quark-antiquark pair to a $\Lambda\bar{\Lambda}$ hyperon pair and how it can be measured by the STAR experiment at RHIC. See (a)-(e) in text for details.
• Figure 2: $\mathrm{d}N/\mathrm{d}\cos\theta^\star$ distributions of decay (anti-)protons for $\Lambda\bar{\Lambda}$, $\Lambda\Lambda$, and $\bar{\Lambda}\bar{\Lambda}$ hyperon pairs measured at mid-rapidity ($|y| < 1$). Panel a) shows the short-range pairs ($|\Delta y| < 0.5$ and $|\Delta \phi| < \pi/3$) and panel b) shows the long-range pairs. Statistical uncertainties are denoted by the error bars. The fits to the data represented by lines are used to demonstrate the magnitude of the spin-spin correlation.
• Figure 3: Spin correlation $P_\mathrm{\Lambda_1\Lambda_2}$ of short-range (left) and long-range (right) $\Lambda\bar{\Lambda}$, $\Lambda\Lambda$, and $\bar{\Lambda}\bar{\Lambda}$ hyperon pairs. The hyperon pair $P_\mathrm{\Lambda_1\Lambda_2}$ is compared to $K^0_\mathrm{S}K^0_\mathrm{S}$ measurements and PYTHIA 8.3 predictions. Statistical uncertainties are denoted by the error bars, and the systematic uncertainties are represented by the shaded boxes.
• Figure 4: Spin correlation $P_\mathrm{\Lambda_1\Lambda_2}$ as a function of pair separation $\Delta R$. The data are compared with predictions from the SU(6) quark model su6:model and the Burkardt-Jaffe model Burkardt:1993zh. Statistical uncertainties are denoted by the error bars, and the systematic uncertainties are represented by the shaded boxes. The blue and yellow arrows are used to illustrate the separation of the $\Lambda\bar{\Lambda}$ pairs.
• Figure 5: 3D and 2D invariant mass distributions of $p\pi^-$ pairs, paired with $\bar{p}\pi^+$ pairs are shown in the top left and top right panels, respectively. The projections of the multi-dimensional distributions to $p\pi^-$ and $\bar{p}\pi^+$ are shown in the bottom left and bottom right panels, respectively.