On new physics searches with multidimensional differential shapes

In the context of upcoming new physics searches at the LHC, we investigate the impact of multidimensional differential rates in typical LHC analyses. We discuss the properties of shape information, and argue that multidimensional rates bring limited information in the scope of a discovery, but can have a large impact on model discrimination. We also point out subtleties about systematic uncertainties cancellations and the Cauchy-Schwarz bound on interference terms.