Vector-Meson Spin Alignment from Anisotropic Quark or Hadron Coalescence

The distribution of particles is highly anisotropic in the initial stage of a heavy-ion collision. In this paper we demonstrate that this anisotropy induces a sizable effect on the spin alignment of vector mesons. We study two different production mechanisms for $\phi$ and $K^{\ast 0}$ mesons, on one hand the coalescence of quarks and on the other that of pseudoscalar mesons. In the quark-coalescence picture where $\phi$ and $K^{\ast 0}$ are produced via a bare vector coupling to quarks, a negative $\delta {\rho }_{00}^y$ of order ${10}^{-3}$ is observed. In contrast, when $\phi$ and $K^{\ast 0}$ are produced via quark coalescence with a vertex with spin-orbit coupling, or when they are produced via pseudoscalar-meson coalescence, a positive $\delta {\rho }_{00}^y$ emerges. In all cases, the magnitude of the spin alignment is directly proportional to the degree of anisotropy. The sign difference between the cases provides a possibility to clarify the production mechanism for vector mesons.