Consider a simple interpretation starting from the measured STXS and their uncertainties in terms of inclusive signal strength per production process (as a working example – no impact on what is written below).
What is the minimum information needed to be made public? Several options:
First case: everything can be considered Gaussian:
central values of the measured STXS
covariance matrices separately for statistical and experimental uncertainties, one covariance matrix for every theoretical uncertainty that one might want to correlate between the measurement and the interpretation, one covariance matrix for all remaining theoretical uncertainties
in this case, all NP are profiled and the matrices contain the impact of the uncertainties on the STXS
correlation between uncertainties in the measurement and the interpretation is only possible if the corresponding covariance matrices look like (Delta1^2 Delta1Delta2, Delta1Delta2 Delta2^2) (this would have to be checked)
for uncertainties one might want to correlate between measurement and interpretation, also the size of the uncertainties considered needs to be reported (e.g. the size of the alphas variation considered)
a somewhat finer splitting of the uncertainties could be useful, e.g. a split into uncertainties related to signal and to background (to be considered case-by-case)
Second case: keep some nuisance parameters unprofiled, but still everything can be considered Gaussian:
give the covariance matrices with impact of the profiled nuisance parameters on the STXS as above, and extend the vector of central values and the covariance matrices by the unprofiled parameters
this allows to share nuisance parameters between the measurement and interpretation also if the impact on the STXS does not have the simplest form as above
rest as above
Non-Gaussian case: uncertainties or one or few STXS cannot be considered Gaussian: