Blind background prediction using a bifurcated analysis scheme

In this paper we describe a bifurcation analysis procedure for data driven background prediction under the conditions of a blinded signal box. The procedure uses the application of inverse cuts to properly measure the veto power of the different sets of cuts while not opening the signal box. This technique was first developed for a single background source in the stopped K experiments E787 and E949 at Brookhaven [? ]. The work in this paper was inspired by the use of the bifurcation technique in the E391 experiment [? ]. We begin with a derivation of the bifurcation analysis in the case of one background source and uncorrelated cuts. We then extend this to two background sources and a simple model of correlation between cuts. We cover the various derivations with a fair amount of algebraic detail. Throughout this paper the method will be applied to a toy model of a background prediction. We utilize the Mathematica software package to simulate this system [? ].