Segment Finding Algorithm

The offline segment finding algorithm uses a three-cell mask as this contains all possible patterns of track segments with eight hits. The mask is stepped around a complete superlayer two cells at a time forming overlapping regions. This method is not suitable for the trigger as we do not need to find all segments. Furthermore, to get all hits from three cells in a complete superlayer together would require too large a communication overhead given the sector organisation of the readout.

Since 90% of all segments in NC and CC events are contained in one or two cells in a superlayer [2] a one- or two-cell mask should be sufficient for online segment finding. At present our SLT segment finding algorithm is based on a single-cell mask. This choice of mask is simple and has the advantage of requiring little data to be transferred and no co-ordinate transformations. Since we are concerned with the r- projection, only the axial superlayers are searched for track segments.

The segment finding algorithm uses a track following method that looks for straight lines in local non-orthogonal (LNO) cell co-ordinates. In this co-ordinate system one axis (u) is defined to lie in the sense wire plane perpendicular to the CTD z-axis and the other axis (v) is parallel to the the drift lines in the planar drift approximation. In the algorithm we choose the co-ordinates along the u-axis as the wire numbers and along the v-axis as the drift distances. This system has the advantage of describing the geometry of a single cell by only the spacing between the sense wires (which is constant in a given superlayer). Little geometry is required and no co-ordinate transformations are needed during segment finding in a one-cell mask.

The present road following method works as follows.

• Initialise a segment road by taking the first two positive signed hits (seed pairs) on consecutive wires to define a direction.
• Using the road, predict the drift distance to the next sense wire.
• If a hit is found within a cut then the hit is stored and the procedure is repeated using the last two hits on the road to predict the drift distance to the next wire.
• If no hit is found the predicted drift distance is used to follow the road and predict the drift distance to the next wire.
• But if again no hit is found within a cut then a new seed pair is tried; a gap of one non-hit wire is allowed.
• The routine gives up entirely after seven successive sets of seed pairs fail.
• Forward-following as well as backward-following are performed.

At least three hits are required to define a segment and hits are used only once. In practice the minimum number of hits required is one of the parameters of the algorithm and can vary between three and eight. The average number of hits on a MC segment in one cell is five [2]. We have used four hits to define a segment (See section 5.1 for more details on this choice.).

The road width is calculated from the expected nominal drift distance resolution of 130  m. The one standard deviation error on the predicted drift distance by the algorithm is normally 2.5 times the drift distance resolution. If we have missed a hit and are allowing a gap of one wire, the standard deviation on the prediction increases by 1.5. In each case the road width is taken to be three standard deviations (  mm).

The algorithm finds both a segment and its mirror (the segment formed from the other sign of the ambiguous drift directions). We have exploited the design of the CTD cell to reduce the number of wrong choices of the segment ambiguity. The sense wire planes of the CTD are not radial but at 45 to a radius, and hence, to the direction of high \ tracks. In most cells the correct segment will cross the sense wire plane and point roughly towards the bunch-crossing point, whereas the wrong segment will have a large angle with the radius vector to the segment centre. Only one solution is taken to define the vector hit and that is the one that points most directly at the bunch-crossing point.