Spin versus Helicity Equilibration Times and Lagrangian for Strange Quarks in Rotating Quark-Gluon Plasma

Abstract: Measurements of the net polarization of $\Lambda$ and $\bar{\Lambda}$ hyperons at the Relativistic Heavy Ion Collider (RHIC) have stimulated much interest in how strange quarks might align their spin with the vorticity of the matter created in heavy ion collisions. We calculate the Lagrangian in the rest frame of a fluid element undergoing rotation with angular velocity $\omega$ including photon and gluon fields. There is an additional coupling between the quarks and the gauge fields proportional to $\omega$, but this vertex does not change the spin of the quarks. We also show that the times to equilibrate quark helicity and spin parallel to the vorticity are the same so long as $\omega$ is small compared to the temperature.