Explicit covariance matrix for particle measurement precision

We derive explicit and precise formulae for 3 x 3 error matrix of particle transverse momentum, direction and impact parameter. The error matrix elements are expressed as functions of up to fourth order statistical moments of the measured coordinates. The formulae are valid for any curvature and track length in case of negligible multiple scattering. The calculation is compared with formulae derived by Gluckstern for curvature and direction. We show that Gluckstern formulation is valid at the limit of small L/R, ratio between the track length and radius of curvature. (C) 1998 Elsevier Science B.V. All rights reserved.