Track Timing at $e^{+}e^{-}$ Linear Colliders with a Silicon Drift Detector Main Tracker

The track timing capabilities of a silicon drift detector based tracker for a future linear electron-positron collider are evaluated. We show such a detector can time tracks at the nanosecond, and for high-$P_{T}$, sub-nanosecond level. This implies that, even for collider designs with the bunch spacing at 1.4 ns, every track can be assigned to a particular bunch crossing at a confidence level of up to two standard deviations. We suggest a choice for the drift axes in the tracker layers to simultaneously optimize the momentum resolution and track timing.