What can we learn from global spin alignment of $\varphi$ meson in heavy-ion collisions?

Abstract

We propose that a significant positive deviation from 1/3 for the spin density matrix element ${\rho }_{00}$ of the $\varphi$ meson may indicate the existence of a mean field of the $\varphi$ meson generated in heavy-ion collisions. This explains why STAR preliminary data for the $\varphi$ meson's ${\rho }_{00}$ are much larger than 1/3 while the data of $\Lambda$ and $\bar{\Lambda }$ polarization seem not to allow such a significant and positive deviation. The contribution may be from the polarization of the strange quark and antiquark through the $\varphi$ field, an effective mode of the gluon field in strong interaction. We show that ${\rho }_{00}$ for the $\varphi$ meson is a good analyzer for fields even if they may strongly fluctuate in space-time.

ReVTex 4, 8 pages, 1 figure. A sign error in the polarization formula for the anti-quark is corrected, related discussions are changed accordingly. The results for the case with the quark polarization along all directions are added as an appendix

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