What can we learn from the global spin alignment of ϕ mesons in heavy-ion collisions?

We propose that a significant positive deviation from $1/3$ for the spin density matrix element ${\ensuremath{\rho}}_{00}$ of the $\ensuremath{\phi}$ meson may indicate the existence of a mean field of the $\ensuremath{\phi}$ meson generated in heavy-ion collisions. This explains why STAR preliminary data for the $\ensuremath{\phi}$ meson's ${\ensuremath{\rho}}_{00}$ are much larger than $1/3$, while the data of $\mathrm{\ensuremath{\Lambda}}$ and $\overline{\mathrm{\ensuremath{\Lambda}}}$ polarization seem not to allow such a significant and positive deviation. The contribution is from the polarization of the strange quark and antiquark through the spin-orbit interaction in the $\ensuremath{\phi}$ field, a similar interaction that is responsible for nuclear shell structure at the nucleon level. We show that ${\ensuremath{\rho}}_{00}$ for the $\ensuremath{\phi}$ meson is a good analyzer for fields even if they may strongly fluctuate in space-time.