Review of opportunities for new long-lived particle triggers in Run 3 of the Large Hadron Collider

Long-lived particles (LLPs) are highly motivated signals of physics Beyond the Standard Model (BSM) with great discovery potential and unique experimental challenges. The LLP search programme made great advances during Run 2 of the Large Hadron Collider (LHC), but many important regions of signal space remain unexplored. Dedicated triggers are crucial to improve the potential of LLP searches, and their development and expansion is necessary for the full exploitation of the new data. The public discussion of triggers has therefore been a relevant theme in the recent LLP literature, in the meetings of the LLP@LHC Community workshop and in the respective experiments. This paper documents the ideas collected during talks and discussions at these Workshops, benefiting as well from the ideas under development by the trigger community within the experimental collaborations. We summarise the theoretical motivations of various LLP scenarios leading to highly elusive signals, reviewing concrete ideas for triggers that could greatly extend the reach of the LHC experiments. We thus expect this document to encourage further thinking for both the phenomenological and experimental communities, as a stepping stone to further develop the LLP@LHC physics programme.