Observation of Global Spin Alignment of $\phi$ and $K^{*0}$ Vector Mesons in Nuclear Collisions

The collaboration
Nature 614 (2023) 244-248, 2023.

Abstract (data abstract)
Notwithstanding decades of progress since Yukawa first developed a description of the force between nucleons in terms of meson exchange, a full understanding of the strong interaction remains a major challenge in modern science. One remaining difficulty arises from the non-perturbative nature of the strong force, which leads to the phenomenon of quark confinement at distances on the order of the size of the proton. Here we show that in relativistic heavy-ion collisions, where quarks and gluons are set free over an extended volume, two species of produced vector (spin-1) mesons, namely $\phi$ and $K^{*0}$, emerge with a surprising pattern of global spin alignment. In particular, the global spin alignment for $\phi$ is unexpectedly large, while that for $K^{*0}$ is consistent with zero. The observed spin-alignment pattern and magnitude for the $\phi$ cannot be explained by conventional mechanisms, while a model with a connection to strong force fields, i.e. an effective proxy description within the Standard Model and Quantum Chromodynamics, accommodates the current data. This connection, if fully established, will open a potential new avenue for studying the behaviour of strong force fields.

• #### Figure 3 (phi)

Data from Figure 3 (phi)

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Global spin alignment of $\phi$ and $K^{*0}$ vector mesons in heavy-ion collisions. The measured matrix element $\rho_{00}$ as a function...

• #### Figure 3 (K*0)

Data from Figure 3 (k*0)

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Global spin alignment of $\phi$ and $K^{*0}$ vector mesons in heavy-ion collisions. The measured matrix element $\rho_{00}$ as a function...

• #### Extended Figure 1a

Data from Extended Figure 1a

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Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$...

• #### Extended Figure 1b

Data from Extended Figure 1b

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Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$...

• #### Extended Figure 1c

Data from Extended Figure 1c

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Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$...

• #### Extended Figure 1d

Data from Extended Figure 1d

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Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$...

• #### Extended Figure 2

Data from Extended Figure 2

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Efficiency corrected $\phi$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.1 in the method section.

• #### Extended Figure 3

Data from Extended Figure 3

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Efficiency and acceptance corrected $K^{*0}$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.4 in the method section.

• #### Extended Figure 4

Data from Extended Figure 4

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$\phi$-meson $\rho_{00}$ obtained from 1st- and 2nd-order event planes. The red stars (gray squares) show the $\phi$-meson $\rho_{00}$ as a...

• #### Extended Figure 5

Data from Extended Figure 5

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$\phi$-meson $\rho_{00}$ with respect to different quantization axes. $\phi$-meson $\rho_{00}$ as a function of beam energy, for the out-of-plane direction...

• #### Extended Figure 6a (1st EP)

Data from Extended Figure 6 (11.5 GeV & 1st EP)

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$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are...

• #### Extended Figure 6a (2nd EP)

Data from Extended Figure 6 (11.5 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are...

• #### Extended Figure 6b (1st EP)

Data from Extended Figure 6 (19.6 GeV & 1st EP)

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$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are...

• #### Extended Figure 6b (2nd EP)

Data from Extended Figure 6 (19.6 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are...

• #### Extended Figure 6c (1st EP)

Data from Extended Figure 6 (27.0 GeV & 1st EP)

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$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are...

• #### Extended Figure 6c (2nd EP)

Data from Extended Figure 6 (27.0 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are...

• #### Extended Figure 6d (1st EP)

Data from Extended Figure 6 (39.0 GeV & 1st EP)

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$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are...

• #### Extended Figure 6d (2nd EP)

Data from Extended Figure 6 (39.0 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are...

• #### Extended Figure 6e (1st EP)

Data from Extended Figure 6 (62.4 GeV & 1st EP)

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$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are...

• #### Extended Figure 6e (2nd EP)

Data from Extended Figure 6 (62.4 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are...

• #### Extended Figure 6f (1st EP)

Data from Extended Figure 6 (200.0 GeV & 1st EP)

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$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are...

• #### Extended Figure 6f (2nd EP)

Data from Extended Figure 6 (200.0 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are...

• #### Extended Figure 7a (2nd EP)

Data from Extended Figure 7 (11.5 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

• #### Extended Figure 7b (2nd EP)

Data from Extended Figure 7 (14.5 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

• #### Extended Figure 7c (2nd EP)

Data from Extended Figure 7 (19.6 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

• #### Extended Figure 7d (2nd EP)

Data from Extended Figure 7 (27.0 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

• #### Extended Figure 7e (2nd EP)

Data from Extended Figure 7 (39.0 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

• #### Extended Figure 7f (2nd EP)

Data from Extended Figure 7 (54.4 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

• #### Extended Figure 7g (2nd EP)

Data from Extended Figure 7 (200.0 GeV & 2nd EP)

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$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

• #### Extended Figure 8a

Data from Extended Figure 8 (27.0 GeV)

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$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are...

• #### Extended Figure 8b

Data from Extended Figure 8 (39.0 GeV)

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$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are...

• #### Extended Figure 8c

Data from Extended Figure 8 (62.4 GeV)

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$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are...

• #### Extended Figure 8d

Data from Extended Figure 8 (200.0 GeV)

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$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are...

• #### Extended Figure 8e

Data from Extended Figure 8 (39 GeV)

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$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are...

• #### Extended Figure 8f

Data from Extended Figure 8 (54.4 GeV)

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$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are...

• #### Extended Figure 8g

Data from Extended Figure 8 (200.0 GeV)

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$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are...

• #### Extended Figure 9 (phi)

Data from Extended Figure 9 (phi)

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Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and...

• #### Extended Figure 9 (K*0)

Data from Extended Figure 9 (K*0)

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Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and...