A method based on muon system to monitor LHCb luminosity

LHCb is one of the four main experiments running at the Large Hadron Collider (LHC) of the European Organization for Nuclear Research. Since 2010, it has been collecting data to study the Physics of b and c quarks. For the past three years, the experimental apparatus underwent significant upgrades to be ready for a new round of data collection, expected to start in June 2022. The new apparatus is designed to be able to run at an instantaneous luminosity five times larger than the previous one, which was 2.0 x 10(32) cm(-2) s(-1), and the whole detector readout will be at a 40 MHz rate. It is worth noticing that the luminosity at the LHCb interaction point, for the characteristics of the detector, needs to be reduced with respect to the luminosity provided by LHC. Major changes in the different subdetectors were required, along with complete modifications of the trigger schemes. The LHCb collaboration is developing and studying different methods for the on-line measurement of luminosity at the LHCb impact point, crucial for the monitoring of correct machine operation and for most experimental physics studies. The present work describes a procedure based on hit counting in the muon detector for an on-line luminosity monitor. The performance and the precision achieved with this method in tests carried out on past data collected are presented, together with proposals for future upgrades.