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, has collected over $67\times {10}^6$ 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 ${\alpha }_T=0.873\pm 0.009(\mathrm{stat})\pm 0.010(\mathrm{syst})$. 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 $E_p\gtrsim 7\mathrm{TeV}$ of ${0.12}_{-0.05}^{+0.07}$, consistent with the expectation from collider experiments.

Figure 1

The 5 yr average temperature at various pressure levels (solid line). The range is from 1000 hPa ($1\mathrm{hPa}=1.019\mathrm{g}/{\mathrm{cm}}^2$), near the Earth’s surface, to 1 hPa (nearly 50 km), near the top of the stratosphere. The height axis on the right represents the average log-pressure height corresponding to the average temperatures plotted here. The dashed line is the weight as a function of pressure level ($X$) used to find $T_{\mathrm{eff}}$. The weights are determined by Eq. (8), normalized to one.

Figure 2

The time between consecutive cosmic ray muon arrivals, fit with a Poisson distribution. The fit gives ${\chi }^2/N_{\mathrm{d}.\mathrm{o}.\mathrm{f}.}=55.2/68$; $⟨R_{\mu }⟩=0.4692\pm 0.0001\mathrm{Hz}$ (from slope). The Poissonian nature of the muon arrival times demonstrates the absence of short time scale systematic effects on the data.

Figure 3

A plot of the energy spectra observed in the far detector. The dashed line is $E_{\mathrm{th}}\cos \theta$, which was used to determine the value used in Eq. (8). The solid line is the distribution of muon surface energies, $E_{\mu }$ in far detector. Also shown are $E_{\mathrm{th}}\cos \theta (\mathrm{CS})$ (dot-dashed line), the distribution of $E_{\mathrm{th}}\cos \theta$ after charge-separation cuts have been applied, and $E_{\mu }(\mathrm{CS})$ (dotted line), the distribution of $E_{\mu }$ after the charge-separation cuts (see Sec. 2c) have been applied. Note that the charge-separation cuts have been applied, but the distributions shown include both muon species.

Figure 4

The daily deviation from the mean rate of cosmic ray muon arrivals from 8/03–8/08, shown here with statistical error bars. The periodic fluctuations have the expected maxima in August, minima in February. The hatched region indicates the period of time when the detector ran with the magnetic field reversed from the normal configuration.

Figure 5

The daily deviation from the mean effective temperature over a period of five years, beginning when the far detector was complete, 08/03–08/08. The hatched region indicates the period of time when the detector ran with the magnetic field reversed from the normal configuration.

Figure 6

A plot of $\Delta R_{\mu }/⟨R_{\mu }⟩$ as a function of $\Delta T_{\mathrm{eff}}/⟨T_{\mathrm{eff}}⟩$ for single muons, fit by a line with the $y$ intercept fixed at 0. The fit has a ${\chi }^2/N_{\mathrm{d}.\mathrm{o}.\mathrm{f}.}=1959/1797$, and the slope is ${\alpha }_T=0.873\pm 0.009$.

Figure 7

The theoretical prediction for ${\alpha }_T$ as a function of detector depth. The dashed (top) curve is the prediction using the pion-only model (of MACRO) and the dotted (bottom) curve is the prediction using a kaon-only model. The solid (middle) curve is the new prediction including both $K$ and $\pi$. These curves are illustrative only as the definition of effective temperature used to calculate the experimental values also depends on the $K/\pi$ ratio. The data from other experiments are shown for comparison only, and are from Barrett  1, 2 [2], AMANDA [4], MACRO [11], Torino [12], Sherman [15], Hobart [16] and Baksan [17].

Figure 8

The MINOS experimental ${\alpha }_T$ as a function of the $K/\pi$ ratio (dot-dashed line), with its error given by the crosshatched region, on the same axes as the theoretical ${\alpha }_T$ as a function of the $K/\pi$ ratio (dashed line), with its error given by the hatched region. The error on the experimental ${\alpha }_T$ (from Table 2 $E_{\mathrm{th}}\cos \theta$, $B_{\pi ,K}^1$ and $⟨T_{\mathrm{eff}}⟩$) plus statistical error is $\pm 0.012$, and the theoretical ${\alpha }_T$ error (from ${ϵ}_{\pi ,K}$ and the rock map, Table 3) is $\pm 0.013$ at the best fit point. The intersection is at $K/\pi ={0.12}_{-0.05}^{+0.07}$. The solid line denotes the $1\sigma$ contour around the best fit.

Figure 9

A compilation of selected measurements of $K/\pi$ for various center of mass energies. The STAR value was from $\mathrm{Au}+\mathrm{Au}$ collisions at RHIC [28], the NA49 measurement was from $\mathrm{Pb}+\mathrm{Pb}$ collisions at SPS [29, 30], and the E735 measurement was from $p+\overline{p}$ collisions at the Tevatron [31].