Characterization of the varying flux of atmospheric muons measured with the Large Volume Detector for 24 years

The Large Volume Detector (LVD), hosted in the INFN Laboratori Nazionali del Gran Sasso, is triggered by atmospheric muons at a rate of $\sim 0.1$~Hz. The data collected over almost a quarter of century are used to study the muon intensity underground. The 50-million muon series, the longest ever exploited by an underground instrument, allows for the accurate long-term monitoring of the muon intensity underground. This is relevant as a study of the background in the Gran Sasso Laboratory, which hosts a variety of long-duration, low-background detectors. We describe the procedure to select muon-like events as well as the method used to compute the exposure. We report the value of the average muon flux measured from 1994 to 2017: $\mathrm{I_{\mu}^0 = 3.35 \pm 0.0005^{stat}\pm 0.03^{sys} \cdot 10^{-4} ~m^{-2} s^{-1}}$. We show that the intensity is modulated around this average value due to temperature variations in the stratosphere. We quantify such a correlation by using temperature data from the European Center for Medium-range Weather Forecasts: we find an effective temperature coefficient $\mathrm{\alpha_{T}} = 0.94\pm0.01^{stat} \pm0.01^{sys}$, in agreement with other measurements at the same depth. We scrutinise the spectral content of the time series of the muon intensity by means of the Lomb-Scargle analysis. This yields the evidence of a 1-year periodicity, as well as the indication of others, both shorter and longer, suggesting that the series is not a pure sinusoidal wave. Consequently, and for the first time, we characterise the observed modulation in terms of amplitude and position of maximum and minimum on a year-by-year basis.