Abstract
We calculate the contribution to the polarization of Lambda hyperons in relativistic nuclear collisions at high energy from the decays of Sigma ^{*}(1385) and Sigma ^0, which are the predominant sources of Lambda production besides the primary component, as a function of the Lambda momentum. Particularly, we estimate the longitudinal component of the mean spin vector as a function of the azimuthal angle in the transverse plane, assuming that primary Sigma ^{*} and Sigma ^0 polarization follow the predictions of local thermodynamic equilibrium in a relativistic fluid. Provided that the rapidity dependence around midrapidity of polarization is negligible, we find that this component of the overall spin vector has a very similar pattern to the primary one. Therefore, we conclude that the secondary decays cannot account for the discrepancy in sign between experimental data and hydrodynamic model predictions of the longitudinal polarization of Lambda hyperons recently measured by the STAR experiment at RHIC.
Highlights
The model is very successful for the global polarization, that is for the mean spin vector of the hyperon, which is parallel to the overall angular momentum of the colliding nuclei, at several energies
The oscillations of the longitudinal polarization of as a function of the azimuthal angle have been observed by the STAR experiment [12], yet with a flipped sign with respect to the thermodynamic-hydrodynamic calculations
For strong and electromagnetic decays with parity conservation, it is readily found that the first term containing δλλ does not give any contribution to the mean spin vector because λ2 = λ2 implies λ1 = λ1 and one is left with a vanishing trace of DS1(Jν) in (20)
Summary
The model is very successful for the global polarization, that is for the mean spin vector of the hyperon, which is parallel to the overall angular momentum of the colliding nuclei, at several energies. It was observed that the longitudinal – that is, along the beam line – component of the mean spin vector shows a very similar pattern to that of the azimuthal particle spectra, the so-called elliptic flow [3,7]. This feature and more characteristics of the longitudinal component of the polarization were analyzed and discussed in Refs. The three-momentum is denoted by the roman font, i.e., “P” and “p” for the Mother and Daughter, respectively
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