Geometrical optimization of interaction vertices in spark chamber analysis

Abstract

In spark chamber experiments, where there is difficulty in measuring directly the interaction vertices of multiprong events, use can be made of over-determination in linear track measurements to determine the best values of vertex co-ordinates. The method used is that of least-squares fit with constraints. An iterative procedure is used and the appropriate expressions for improving the fit at each stage are developed together with the error matrix for the fitted variables; means of generating the starting values are also discussed. The flow diagram for a computer programme, VTXFTN, performing the fit for a variable number of measurements is given, as well as the detailed coding, in FORTRAN, for forming the residuals and derivative matrices.