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Vacuum was once thought to be just space that filled with nothing. Quite the contrary, vacuum possess intricate structure that associated with energy, and a sea of virtual particle pairs known as the quark condensate. These pairs cause the spontaneous chiral symmetry breaking, a fundamental phenomenon responsible for generating over 99% of mass in the visible universe. However, the precise mechanism linking the chiral symmetry breaking to the mass generation associated with quark confinement remains one of the most profound open questions in physics. Here, we investigate the high energy proton-proton collisions at the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory, where those collisions could liberate virtual quark-antiquark pairs from the vacuum. These virtual pairs, specifically the strange quark pairs, are quantum spin entangled to begin with, and later undergo the process of quark confinement to form hadron, such as Lambda hyperons. In this Letter, we report the first evidence of spin correlation of Lambda-Lambda-bar hyperon pairs measured by the STAR experiment at RHIC - a result that traces virtual quark pairs from the Quantum Chromodynamic (QCD) vacuum to their final-state hadron counterparts. Our findings provide a new experimental paradigm for exploring the intricate dynamics and interplay of confinement and entanglement, offering new insights into one of QCD's most fundamental phenomena.

Conclusions:

We present the first evidence of spin correlations for Lambda hyperon pairs in high-energy p+p collisions at RHIC, measured across different kinematic regimes. Notably, among all possible combinations of Lambda hyperon pairs, short-range Lambda-Lambda-bar pairs exhibit a significant positive relative polarization, P_LL = (0.32 +- 0.06_stat +- 0.02_sys), with a statistical significance of 5.1 standard deviations. As the distance between the pair increases, the spin correlation is found to be significantly less, which could be weaken by quantum decoherence. By probing the QCD evolution of a strange quark-antiquark pair that is expected to be spin-aligned, this new measurement on the hadron level provides crucial insights into the underlying mechanisms of QCD confinement. The observation of this pronounced relative polarization, alongside the methodology established for spin correlation measurements of hyperon pairs, paves the way for a transformative approach to understanding the complex dynamics of QCD.

Paper draft

The latest paper draft is available here and below in the attachments of this page.

Previous draft versions: v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12

Method

Latest version of the Method is available here.

Previous versions: v1, v2, v3, v4, v5, v6

Dedicated page to the Method can be found here.

Analysis note

The analysis note is available here and below in the file attachments of this page.

Analysis codes

Available on CVS: cvs checkout offline/paper/psn0848

Answers to Spin PWG Comments

File with replies to Spin PWG comments is available here.

Answers to GPC comments

File with replies to GPC comments is available here.

Answers to Collaboration review comments:

04/01/2024:

Figures:

Figure 0: Illustration of tracing the QCD evolution of the spin of a strange quark-antiquark pair to a L-Lbar hyperon pair, measured by the STAR experiment at RHIC.

Figure 2: dN/dcos(theta*) distributions of decay (anti-)protons for LLbar, LL, and LbarLbar 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. The fits to the data are used to extract the corresponding spin-spin correlation values P_L1L2.

Figure 3: Spin-spin correlation P_L1L2 of short-range (a)) and long-range (b)) LLbar, LL, and LbarLbar hyperon pairs. The hyperon pair P_L1L2 is compared to K0sK0s and PYTHIA baseline.

Figure 4: Spin correlation P_L1L2 as a function of angular separation Delta R. Data are compared with predictions from SU(6) quark model and Burkardt-Jaffe model. Statistical uncertainties are denoted by the error bars, and the systematic uncertainties are represented by the shaded boxes. The blue and yellow arrows are illustration of the spatial separation of L-Lbar pairs.

GPC meetings:

11/18/2024: Slides
12/02/2024: Slides
12/16/2024: Slides
01/13/2025: Slides
01/27/2025: Slides
02/03/2025: Slides
02/18/2025: Slides
02/24/2025: Slides
03/05/2025 (offline): Slides
03/06/2025 (offline): Slides
03/11/2025 (offline): Slides

PWGC preview:

08/09/2024: Slides

Spin PWG presentations:

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