Local spin alignment of vector mesons in relativistic heavy-ion collisions

We investigate the spin alignment of vector mesons arising from locally polarized quarks and anti-quarks (local spin alignment) in heavy-ion collisions. We find that $\rho_{00}\neq 1/3$ does not necessarily signal the global polarization of quarks and anti-quarks along the orbital angular momentum of the system, but may also originate from their local spin polarization. Such local spin polarization could be induced by local vorticity arising from the anisotropic expansion of the fireball. We further propose experimental observables that can distinguish between the local and the global spin alignments. Measurements of these observables in heavy-ion collisions can probe the vorticity pattern and shed light on the puzzles of $\phi$ and $K^{*0}$ spin alignments.