Semi-analytic approach to the System8 method for efficiency determination with generic correlation factors

Methods using data as input constraints are often used in the determination of the performance of selection cuts. Usually they require solving a system of equations where the parameters of interest are a part of the set of unknowns. This paper discusses several aspects of such a method to determine selection efficiency. An analytical solution of the system of eight non-linear equations is developed up to a single polynomial equation and finally a semi-analytic solution that can be easily implemented is obtained. A realistic test is performed using random data to illustrate the utility of the method and its application to the determination of distribution shapes.