Here, we follow closely the discussion of the resolution and uncertainty along the padrow given in the previous Section.
The first term in Equation 15 is independent of crossing angle. This is the component of the resolution that the cluster/hitfinder estimates in TPHIT.DZ. Figure 27 shows the average residual and estimated uncertainty as a function of for non-overlapping hits in a Au+Au event. The residual approaches the estimated uncertainty for small , but crossing angle effects dominate the resolution otherwise.
Figure 27: Average value of the residual (solid crosses) and estimated uncertainty calculated by the hifinder (dashed lines) as a function of crossing angle for isolated hits in a Au+Au event. For large , crossing angle effects dominate the effects of noise.
In Figure 28, it is seen that those hits with large energy loss show the fastest increase with crossing angle, similar to the large- effect discussed above.
Figure 28: Average value of the residual as a function of crossing angle for isolated hits of varying amplitude in a Au+Au event. Large-amplitude hits show increased degradation in resolution with crossing angle.
For the tracker to update the uncertainty in the time direction according to Equation 15, the constants and must be determined. As in the case with the resolution along the padrow, the coefficient corresponding the magnitude of finite electron statistics distortions, , vanishes with the current slow simulator. Fits of the width of the residual distribution for non-overlapping hits from Au+Au collisions, for various cuts on and , show best fit for for the outer sector and for the inner. Again, the values of these numbers may change as the configuration paramters of the simulator and hitfinder change.
As an example, the z-resolution of hits from a Au+Au event, integrating over dE/dx and crossing angles, is RMS=2.4 mm, =1.5 mm, while selecting hits with crossing angles gives =219 m.