The spin density matrix gives full information about the helicities of the W bosons and as seen in equations 3.33 and 3.38, certain elements can be used to calculate the polarised cross-section.
It has already been shown in chapter 6 that the SDM elements extracted directly from the data do not represent the true SDM elements, figure 6.1. This did not pose a problem when calculating the TGC values from the data because the data could be compared directly to fully simulated Monte Carlo. However, this does cause a problem when trying to calculate the polarised cross-sections. For these, the SDM elements corrected for detector, acceptance and background effects are required.