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The development of polarization profiles are the primary reason for the loss of average polarization. Polarization profiles have been parametrized with a Gaussian distribution. We derive the effect of 3-dimensional polarization profiles on the measured polarization in polarimeters, as well as the observed polarization and the figure of merit in single and double spin experiments. Examples from RHIC are provided. The Relativistic Heavy Ion Collider (RHIC) is the only collider of spin polarized protons. During beam acceleration and storage profiles of the polarization P develop, which affect the polarization measured in a polarimeter, and the polarization and figure of merit (FOM) in colliding beam experiments. We calculate these for profiles in all dimensions, and give examples for RHIC. Like in RHIC we call the two colliding beams Blue and Yellow. We use the overbar to designate intensity-weighted averages in polarimeters (e.g. {bar P}), and angle brackets to designate luminosity-weighted averages in colliding beam experiments (e.g. ).

Effect of 3D Polarization profiles on polarization measurements and colliding beam experiments