Polarization profile

From RHIC Spin Group

Measuring Beam Polarization Profile with p-Carbon Polarimeters

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Two-dimensional case

Let's assume the polarization and intensity profiles have a gaussian shape:

Since we are interested only in the width of the polarization profile with respect to the intensity one we can use the following relations:

Integrating from to over both dimensions we get for the polarization weighted with intensity of either one or both beams:

As we normaly measure the average polarization given by it is trivial to get the equations for re-weighting factors and :

where

It is interesting to study the difference between the scale factors and . To make things easier we assume the same value for all 's which is .

where the last term gives a correction on the order of . Therefore, with good precision we have


Time dependent P_SSA