Review Document: Full Software Trigger

This document presents a trigger system for the upgraded LHCb detector, scheduled to begin operation in 2020. This document serves as input for the internal review towards the "DAQ, online and trigger TDR". The proposed trigger system is implemented entirely in software. In this document we show that track reconstruction of a similar quality to that available in the offline algorithms can be performed on the full inelastic $pp$-collision rate, without prior event selections implemented in custom hardware and without relying upon a partial event reconstruction. A track finding efficiency of 98.8 % relative to offline can be achieved for tracks with $p_T >$ 500 MeV/$c$. The CPU time required for this reconstruction is about 40 % of the available budget. Proof-of-principle selections are presented which demonstrate that excellent performance is achievable using an inclusive beauty trigger, in addition to exclusive beauty and charm triggers. Finally, it is shown that exclusive beauty and charm selections that do not introduce lifetime biases can be performed at the full input rate.