sunxuhit's blog

Notwithstanding decades of progress since Yukawa first developed a description of the force between nucleons in terms of meson exchange~\cite{Yukawa:1935xg}, 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\cite{Sheng:2019kmk,PhysRevD.105.099903,Sheng:2020ghv,Sheng:2022wsy,Sheng:2022ffb}, 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.

Figures in Main Text:

Figure 1:

caption: A schematic view of the coordinate setup for measuring global spin alignment in heavy-ion collisions. Two nuclei collide and a tiny exploding QGP fireball, only a few femtometers across, is formed in the middle. The direction of the orbital angular momentum ($\hat {L}$) is perpendicular to the reaction plane defined by the incoming nuclei when $b \neq 0$. The symbol $\vec{p}$ represents the momentum vector of a particle. At the top-left corner, a $\phi$ meson, made of $s$ and $\bar{s}$ quarks, is depicted separately as a particle decaying into a ($K^+$, \,$K^-$) pair. In this example, the quantization axis ($\hat{n}$) for study of the $\phi$ meson's global spin alignment is set to be the same as $\hat{L}$. $\theta^*$ is the polar angle between the quantization axis and the momentum direction of a particle in the decay's rest frame. A similar depiction can be found for a $K^{*0}$ meson at the bottom-left corner.

Figure 2:

caption: Schematic display of a single Au+Au collision at $\sqrt{s_{NN}} = 27$ GeV in STAR detector. A three-dimensional rendering of the STAR TPC, surrounded by the TOF barrel shown as the outermost cylinder. The beam pipe is shown in green and inside it, gold ions travel in opposite directions along the beam axis (brown). Ions collide at the centre of the TPC, and trajectories (gray lines) as well as TOF hits (blue squares) from a typical collision are shown. Reconstructed trajectories of a ($K^+$, $K^-$) pair originating from a $\phi$-meson decay, as well as a $K^+$ and $\pi^-$ from a $K^{*0}$-meson decay, are shown as highlighted tracks.

Figure 3:

caption: Global spin alignment of $\phi$ and $K^{*0}$ vector mesons in heavy-ion collisions. The measured matrix element $\rho_{00}$ as a function of beam energy for the $\phi$ and $K^{*0}$ vector mesons within the indicated windows of centrality, transverse momentum ($p_T$) and rapidity ($y$). The open symbols indicate ALICE results \cite{Acharya:2019vpe} for Pb+Pb collisions at 2.76 TeV at $p_{T}$ values of 2.0 and 1.4 GeV/c for the $\phi$ and $K^{*0}$ mesons, respectively, corresponding to the $p_{T}$ bin nearest to the mean $p_{T}$ for the 1.0 – 5.0 GeV/$c$ range assumed for each meson in the present analysis. The red solid curve is a fit to data in the range of $\sqrt{s_{NN}} = 19.6$ to 200 GeV, based on a theoretical calculation with a $\phi$-meson field \cite{Sheng:2019kmk}. Parameter sensitivity of $\rho_{00}$ to the $\phi$-meson field is shown in Ref.~\cite{Sheng:2022wsy}. The red dashed line is an extension of the solid curve with the fitted parameter $G_s^{(y)}$. The black dashed line represents $\rho_{00}=1/3.$

Ending Paragraph:
[pls. note that Nature does not encourage the usual summary in which authors repeat what has been said in the main text. Instead, the ending paragraph is a place for extending the meaning of the finding. ]

Measurements of the global spin alignment of vector mesons provide new knowledge about the vector meson fields. The vector meson fields are an essential part of the nuclear force that binds nucleons inside atomic nuclei \cite{Bryan:1969mp,Nagels:1977ze} and are also pivotal in describing properties of nuclear structure and nuclear matter \cite{Walecka:1974qa,Serot:1984ey}. The $\rho_{00}$ for the $\phi$ meson has a desirable feature in that all contributions depend on squares of field amplitudes; it can be regarded as a field analyzer \cite{Sheng:2019kmk} which makes it possible to extract the imprint of the $\phi$-meson field even if the field fluctuates strongly in space-time. Another important feature worthy of mention is that an essential contribution to the $\phi$-meson $\rho_{00}$ is from the term~\cite{Sheng:2019kmk} $\sim \mathbf{S}\cdot (\mathbf{E}_\phi \times \mathbf{p})$, where $\mathbf{E}_\phi$ is the electric part of the $\phi$-meson field induced by the local, net strangeness current density, and $\mathbf{S}$ and $\mathbf{p}$ are the spin and momentum of the strange (anti)quarks, respectively. Such a term is nothing but the quark version of the spin-orbit force which, at the nucleon level, plays a key role in the nuclear shell structure \cite{Mayer:1949pd,Haxel:1949fjd}. Our measurements of a signal based on global spin alignment for vector mesons reveal a surprising pattern and a value for $\phi$ meson that is orders of magnitude larger than can be explained by conventional effects. This work provides a potential new avenue for understanding the strong interaction at work at the sub-nucleon level.

Figures in Method:

Extended Data Figure 1:

caption: Example of combinatorial background subtracted invariant mass distribution and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ meson. a) example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; b) example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; c) extracted yields of $\phi$ as a function of $\cos \theta^*$; d) extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Extended Data Figure 2:

caption: Efficiency corrected $\phi$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.~\ref{eq:fitEqEffXAccpt_00} in method.

Extended Data Figure 3:

caption: Efficiency and acceptance corrected $K^{*0}$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.~\ref{eq:abservedRho_00} in method.

Extended Data Figure 4:

caption: $\phi$-meson $\rho_{00}$ obtained from 1st- and 2nd-order event plane. The red stars (gray squares) show the $\phi$-meson $\rho_{00}$ as a function of beam energy, obtained with 2nd-order (1st-order) EP.

Extended Data Figure 5:

caption: $\phi$-meson $\rho_{00}$ w.r.t different quantization axes. $\phi$-meson $\rho_{00}$ as a function of beam energy, for the out-of-plane direction (stars) and the in-plane direction (diamonds). Curves are fits based on theoretical calculations with a $\phi$-meson field~\cite{Sheng:2019kmk}. The corresponding $C_s^{(y)}$ values obtained from the fits are shown in the legend.

Extended Data Figure 6:

caption: $\rho_{00}$ as a function of transverse momentum for $\phi$. The gray squares and red stars are results obtained with 1st and 2nd order EP, respectively.

Extended Data Figure 7:

caption: $\rho_{00}$ as a function of transverse momentum for $K^{*0}$.

Extended Data Figure 8:

caption: $\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for $\phi$-meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with 2nd-order EP.

Extended Data Figure 9:

caption: Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.