Real-time exclusive selection for the $\tau^- \to \phi\mu^-$ search with the LHCb Upgrade I detector

The LHCb Upgrade I trigger system provides full upfront charged-particle reconstruction at the 30 MHz bunch-crossing rate, enabling, for the first time, the deployment of exclusive selections directly at the first trigger stage (HLT1). A novel real-time exclusive trigger strategy for selecting the $\tau^{-}\to \phi \mu^-$ decay during Run 3 (2022-2026) proton-proton data taking is presented, together with the first analysis framework developed for this search at a hadron collider. This exclusive selection doubles the signal-event yield with respect to other general-purpose HLT1 selections in Run 3, while the total signal-selection efficiency is increased by about a factor of six relative to Run 2 (2015-2018). The selection algorithm yields an output rate of 1.7 kHz, corresponding to about 0.1% of the total HLT1 output rate, and has operated stably since the start of the 2025 data taking period. As the first exclusive HLT1 trigger for a τ rare-decay channel at LHCb, it establishes a proof of concept for future decay-specific real-time selections at the high-intensity frontier.