Spin alignment of $K^{\ast }$ induced by strange-baryon density inhomogeneity

Abstract

The difference between the spin alignments of $K^{\ast }$ and those of $\varphi$ at the low collision energies is a puzzle raised by the recent experiments. Unlike $\varphi$ meson, $K^{\ast }$, carrying a unit strange charge, should react to strange chemical potential ${\mu }_S$. In this paper, we shall first convince you that ${\mu }_S$ is not small in a brayon-rich medium for keeping strange neutrality, and then derive the spin alignment induced by the gradient of ${\mu }_S$, and hence of baryon chemical potential ${\mu }_B$, using linear response theory, with the transport coefficients expressed, without any approximation, in terms of the $K^{\ast }$'s in-medium spectral properties by employing Ward-Takahashi identity. It turns out that such an effect applies mainly to the particles whose longitudinal and transverse modes diverge, and induces only the local spin alignment in a static medium. The magnitudes of these coefficients will be further estimated under the quasi-particle approximation.

arXiv comment10 pages, 3 figures

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• Vector and Tensor Spin Polarization for Vector Bosons at Local Equilibrium