Eigenvector recomposition: a new method to correlate flavor-tagging systematic uncertainties across analyses

In order to simplify the treatment of the flavor-tagging scale factor uncertainties in physics analyses, their large number is currently significantly reduced using an eigenvector decomposition approach that preserves both the total size of the uncertainty and the underlying correlations. This method provides an effective way to reduce the number of uncertainties, while keeping the correlation information for further use in the analyses. However, when combining physics analyses with different flavour tagging setups -- i.e different taggers, working points, or jet collections -- the flavour tagging eigenvectors are in general not the same, so the uncertainties can not be directly correlated. This note introduces the eigenvector recomposition method to overcome this problem and enable the correlation of flavor-tagging systematic uncertainties across different setups. The tool is designed to transform the eigenvectors into the original set of flavor-tagging scale factor uncertainties, which can be safely correlated across different analyses. This note describes the method and gives practical examples about its usage in physics analyses, focusing on the $VH, H\rightarrow b\overline{b}$ analysis case.