The MONUMENT Experiment: Ordinary Muon Capture studies for 0$\nu\beta\beta$ decay

The MONUMENT experiment measures ordinary muon capture (OMC) on isotopes relevant for neutrinoless double-beta (0$\nu\beta\beta$) decay and nuclear astrophysics. OMC is a particularly attractive tool for improving the theoretical description of 0$\nu\beta\beta$ decay. It involves similar momentum transfers and allows testing the virtual transitions involved in 0$\nu\beta\beta$ decay against experimental data. During the 2021 campaign, MONUMENT measured OMC on $^{76}$Se and $^{136}$Ba, the isotopes relevant for next-generation 0$\nu\beta\beta$ decay searches, like LEGEND and nEXO. The experimental setup has been designed to accurately extract the total and partial muon capture rates, which requires precise reconstruction of energies and time-dependent intensities of the OMC-related $\gamma$ rays. The setup also includes a veto counter system to allow selecting a clean sample of OMC events. This work provides a detailed description of the MONUMENT setup operated during the 2021 campaign, its two DAQ systems, calibration and analysis approaches, and summarises the achieved detector performance. Future improvements are also discussed.