Observation of muon intensity variations by season with the MINOS far detector

The temperature of the upper atmosphere affects the height of primary cosmic ray interactions and the production of high-energy cosmic ray muons which can be detected deep underground. The MINOS far detector at Soudan MN, USA, has collected over 67 million cosmic ray induced muons. The underground muon rate measured over a period of five years exhibits a 4% peak-to-peak seasonal variation which is highly correlated with the temperature in the upper atmosphere. The coefficient, $\alpha_T$, relating changes in the muon rate to changes in atmospheric temperature was found to be: $\alpha_T = 0.874 \pm 0.009$ (stat.) $\pm 0.010$ (syst.). Pions and kaons in the primary hadronic interactions of cosmic rays in the atmosphere contribute differently to $\alpha_T$ due to the different masses and lifetimes. This allows the measured value of $\alpha_T$ to be interpreted as a measurement of the K/$\pi$ ratio for $E_{p}\gtrsim$\unit[7]{TeV} of $0.13 \pm 0.08$, consistent with the expectation from collider experiments.