Manipulations of charged particle tracks in a uniform magnetic field are unavoidable part of everyday life of experimentalists working on collider experiment data. We usually fit set of hit points in a tracking device to a helix to determine the momentum of the track. We sometimes need to extrapolate it through some materials to connect it to the corresponding track segment detected in another tracking device, taking into account energy loss and multiple scattering. Tracks reconstructed this way are then combined to form primary and secondary vertices, and so on. These tasks often involve complicated numerical procedures such as track parameter transformations and error propagations. It is therefore highly desirable to formulate the problems in unified and consistent manner.
In this review, we present an introduction to helix manipulation techniques in as unified form as possible. We start with the helix parametrization of a track exploited throughout this review together with some comments on generalities of track fitting. We then discuss the extrapolation of the track to other detector regions through material media, where the track is expected to experience energy loss and multiple scattering. This enables us to link track segments reconstructed in different regions of a detector system to a single track, which will be our next topic. Vertexing of so reconstructed tracks follows it together with techniques to implement geometrical constraints. The results up to this point assume that original helix track segments are given numerically together with their error matrices and are applicable to any helix track regardless of its momentum. It is, however, useful to consider high momentum limit, since it allows us to calculate error matrices analytically and thus enables us to estimate the performance of a tracking device analytically. This will be the last topic of our review.