CALCULATION OF TRACK AND VERTEX ERRORS FOR DETECTOR DESIGN STUDIES

The Kalman filter technique has come into wide use for charged track r econstruction in high-energy physics experiments. It is also well suit ed for detector design studies, allowing for the efficient estimation of optimal track covariance matrices without the need of a hit level M onte Carlo simulation. Although much has been published about the Kalm an filter equations, there is a lack of previous literature explaining how to implement the equations; In this paper, the operators necessar y to implement the Kalman filter equations for two common detector con figurations are worked out: a central detector in a uniform solenoidal magnetic field, and a fixed-target detector with no magnetic field in the region of the interactions. With the track covariance matrices in hand, vertex and invariant mass errors are readily calculable. These quantities are particularly interesting for evaluating experiments des igned to study weakly decaying particles which give rise to displaced vertices. The optimal vertex errors are obtained via a constrained ver tex fit. Solutions are presented to the constrained vertex problem wit h and without kinematic constraints. Invariant mass errors are obtaine d via propagation of errors; the use of vertex constrained track param eters is discussed. Many of the derivations are new or previously unpu blished.