LHCb RICH: Potential physics performance

In Upgrade phases the PID performance are expected to be reduced by the high detector occupancy and large event multiplicity. The use of fast timing information can be one of the key element to restore and improve the performance of the current RICH detectors in these conditions. A detailed study of the potential physics performance that can be achieved in signal identification, by means of the fast timing information in the PID response, is reported in this note. In particular, the study involves the $B_{(s)}^0\to hh^{\prime}$ and $B_{(s)}^0\to p\bar{p}hh^{\prime}$ decay channels and takes into account three different time hypotheses applying window around the time-arrival of the tracks. A significant improvement up to 70% in the background reduction is observed when applying a time-window of 600 ps with respect to the performance with the no-time hypothesis.