  In this paper we use detailed Monte Carlo simulations to demonstrate that
liquid xenon (LXe) can be used to build a Cherenkov-based TOF-PET, with an
intrinsic coincidence resolving time (CRT) in the vicinity of 10 ps. This
extraordinary performance is due to three facts: a) the abundant emission of
Cherenkov photons by liquid xenon; b) the fact that LXe is transparent to
Cherenkov light; and c) the fact that the fastest photons in LXe have
wavelengths higher than 300 nm, therefore making it possible to separate the
detection of scintillation and Cherenkov light. The CRT in a Cherenkov LXe
TOF-PET detector is, therefore, dominated by the resolution (time jitter)
introduced by the photosensors and the electronics. However, we show that for
sufficiently fast photosensors (e.g, an overall 40 ps jitter, which can be
achieved by current micro-channel plate photomultipliers) the overall CRT
varies between 30 and 55 ps, depending of the detection efficiency. This is
still one order of magnitude better than commercial CRT devices and improves by
a factor 3 the best CRT obtained with small laboratory prototypes.
