Timing layers, 4-and 5-dimension tracking

The combination of precision space and time information in particle tracking, the so called 4D tracking, is being considered in the upgrade of the ATLAS, CMS and LHCb experiments at the High-Luminosity LHC, set to start data taking in 2024-2025. Regardless of the type of solution chosen, space-time tracking brings benefits to the performance of the detectors by reducing the background and sharpening the resolution; it improves tracking performances and simplifies tracks combinatorics. Space-time tracking also allows investigating new physics channels, for example it opens up the possibilities of new searches in long-living particles by measuring accurately the time of flight between the production and the decay vertexes. The foreseen applications of 4D tracking in experiments with very high acquisition rates, for example at HL-LHC, add one more dimension to the problem, increasing dramatically the complexity of the read-out system and that of the whole detector design: we call 5D tracking the application of 4D tracking in high rate environments.