Atmospheric Charged K/πK/\pi Ratio and Measurement of Muon Annual Modulation with a Liquid Scintillation Detector at Soudan

We report a measurement of muon annual modulation in a 12-liter liquid scintillation detector with a live-time of more than 4 years at the Soudan Underground Laboratory. Muon minimum ionization in the detector is identified by its observed pulse shape and large energy deposition. The measured muon rate in the detector is 28.69$\pm$2.09 muons per day with a modulation amplitude of 2.66$\pm$ 1.0\% and a phase at Jul 22 $\pm$ 36.2 days. This annual modulation is correlated with the variation of the effective atmospheric temperature in the stratosphere. The correlation coefficient, $\alpha_{T}$, is determined to be $0.898 \pm 0.025$. This can be interpreted as a measurement of the atmospheric charged kaon to pion ($K$/$\pi$) ratio of 0.094$^{+0.044}_{-0.061}$ for $E_{p} >$ 7 TeV, consistent with the measurement from the MINOS far detector. To further constrain the value of $K$/$\pi$ ratio, a Geant4 simulation of the primary cosmic-ray protons with energy up to 100 TeV is implemented to study the correlation of $K$/$\pi$ ratio and the muon annual modulation for muon energy greater than 0.5 TeV. We find out that a charged $K$/$\pi$ ratio of 0.1598, greater than the upper bound (0.138) from this work at the production point 30 km above the Earth surface in the stratosphere cannot induce muon annual modulation at the depth of Soudan.Comment: 6 pages and 11 figure