Optimal b-Flavour and b-Hadron Reconstruction

Abstract

Without the luxury of a fully reconstructed b-hadron state, to make progress in b-physics, one is at the mercy of detector design and performance. As we have seen, precision tracking and a particle identification capability are prerequisites to be able to reconstruct the underlying physics event from the particles that make it through the detection-reconstruction chain. The experimenter must use the detector information available to make a selection of the particles that are most likely to be involved in the process of interest. This selection procedure could take the form of simply cutting away those particles whose parameter values fall outside of predetermined bounds. This cut-based approach has been traditionally the main technique of data analysis in high energy physics and its simplicity can produce measurements that are well ‘understood’ i.e. with a low systematic uncertainity. However, the performance of this method is best when applied to variables that (a) provide excellent discrimination and (b) are uncorrelated. This follows since cutting on a variable that shows only a weak discrimination will lead to a low selection efficiency and high background, whereas highly correlated variables bring no extra information to an analysis and so cannot improve the performance. Furthermore, rejecting particles from an analysis in this way assumes that they are all independent of each other which is often not the case e.g. measurements of track impact parameters, referenced to the reconstructed primary vertex position, are correlated between those tracks that formed part of the primary vertex fit. For these reasons, cut-based analyses tend to be restricted to the use of a few, high performance, variables that have small correlations between them.