On the interpretation of $\Lambda$ spin polarization measurements

The physics interpretation of the recent measurements of the spin polarization of $\Lambda$ hyperons produced in relativistic heavy-ion collisions is discussed. We suggest that the polarization measured in the $\Lambda$ rest frame should be projected along the direction of the total angular momentum that is first transformed to the same frame, and only then averaged over $\Lambda$'s with different momenta in the center-of-mass frame. As this improved procedure is not expected to significantly change the present results regarding the global spin polarization, it may affect the estimates of the magnitude of the polarization and its energy dependence. Such a treatment is also generally more appropriate whenever directions in the $\Lambda$ rest frame and in the center-of-mass frame are compared. Throughout the paper we deliver explicit expressions for various boosts, rotations, and transformations of angular distributions, which may help to compare model predictions with the experimental results.