Measurement of the atmospheric muon charge ratio at TeV energies with the MINOS detector

The 5.4 kton MINOS far detector has been taking charge-separated cosmic ray muon data since the beginning of August, 2003 at a depth of 2070 m.w.e. in the Soudan Underground Laboratory, Minnesota, USA. The data with both forward and reversed magnetic field running configurations were combined to minimize systematic errors in the determination of the underground muon charge ratio. When averaged, two independent analyses find the charge ratio underground to be $N_{{\mu }^{+}}/N_{{\mu }^{-}}=1.374\pm 0.004(\mathrm{stat}{)}_{-0.010}^{+0.012}(\mathrm{sys})$. Using the map of the Soudan rock overburden, the muon momenta as measured underground were projected to the corresponding values at the surface in the energy range 1–7 TeV. Within this range of energies at the surface, the MINOS data are consistent with the charge ratio being energy independent at the 2 standard deviation level. When the MINOS results are compared with measurements at lower energies, a clear rise in the charge ratio in the energy range 0.3–1.0 TeV is apparent. A qualitative model shows that the rise is consistent with an increasing contribution of kaon decays to the muon charge ratio.

Figure 1

The coordinate system for the MINOS cosmic ray analysis. The octagonal steel and scintillator planes of the MINOS far detector are 8 m across. The detector is 30 m long. The central hole is for the magnet coil. The $+z$-axis is along the long axis of the detector and points toward detector north (N). Detector south (S) points back toward Fermilab. The $y$-axis is directed toward the zenith. The $x$-axis direction is chosen to make a right-handed coordinate system. The origin of the coordinate system is the center of the south face of the detector. Detector north (N) is rotated from true north by an angle $\alpha =26.5548°$ about the $y$-axis as measured by a gyro-theodolite; detector north therefore points along an azimuthal angle of 333.4452°. Alternating planes of scintillator strips are oriented along either the $u$ or $v$ axis directions, a coordinate system in which the $x–y$ plane is rotated by $+45°$ about the $z$-axis.

Figure 2

Finite element analysis model for the toroidal magnetic field in a plane of MINOS steel. The coordinate system for the field map is shown in Fig. 1. In this map, the detector plane is being viewed from detector north.

Figure 3

Distribution of ${\chi }_{\mathrm{fit}}^2/ndf$ for the fits to cosmic muon tracks. The cut was made at ${\chi }_{\mathrm{fit}}^2/ndf>1.5$. The shaded region shows the excluded tracks.

Figure 4

Muon rates per day as a function of day number from the start of data-taking with the complete and magnetized detector after the preanalysis cuts and analysis cuts 1–4. The shaded area shows the period of reverse field running.

Figure 5

The $N_{{\mu }^{+}}/N_{{\mu }^{-}}$ ratio for reconstructed muon tracks as a function of $(q/p)/{\sigma }_{q/p}$ after all other cut: (a) data forward data distribution; (b) data reverse data distribution. As indicated, the cut was chosen at $(q/p)/{\sigma }_{q/p}>2.2$ for both data sets, where $(q/p)/{\sigma }_{q/p}$ becomes asymptotically flat. The figures are labeled with the fits to a constant $N_{{\mu }^{+}}/N_{{\mu }^{-}}$ ratio for the cut at $(q/p)/{\sigma }_{q/p}>2.2$. The fits are superposed onto the data as horizontal lines.

Figure 6

The muon charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$ for (a) the DF and (b) the DR data sets as a function of fit momentum as the number of planes of track information within 3.5 m of the detector center is varied from 0 (no cut) to 100 planes.

Figure 7

The charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$ as a function of BdL. The errors shown are statistical. Superposed is the fit to a constant charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$ for $BdL>12$.

Figure 8

The charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$ as a function of fit momentum for (a) the DF data set and (b) the DR data set. For this figure, the data set was selected using the MIC cut. Superposed on both are the fits to a constant charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$.

Figure 9

The charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$ as a function of fit momentum, ${\mathrm{p}}_{\mathrm{fit}}$. For this figure, the data set was generated using the MIC cut. The errors shown are statistical. Superposed is the fit to a constant charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$.

Figure 10

The charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$ as a function of $\cos \theta$, where $\theta$ is the zenith angle. The errors shown are statistical. Superposed is the fit to a constant charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$.

Figure 11

The charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$ as a function of azimuthal angle $\varphi$. The errors shown are statistical. The gaps are due to acceptance effects resulting from the planar nature of the detector. Muons with azimuths $<60°$ have had 360° added to their azimuth so that there is a continuous distribution of muons from the north (270°–420°). Superposed is the fit to a constant charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$.

Figure 12

The vertical muon intensity in the MINOS far detector hall. Shown as solid circles are the vertical intensity data which have been normalized to the Crouch all-world average vertical intensity for standard rock [18]. Overlaid onto the solid circles is the Crouch average. Shown as x’s is the vertical intensity for the MINOS far detector hall corrected for Soudan rock.

Figure 13

The charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$ as a function of slant depth in Soudan rock. The errors shown are statistical. Superposed is the fit to a constant charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$.

Figure 14

The distribution of muon energies projected back to the surface for three slant depth bins of width 100 m.w.e. used in the computation of the vertical intensity in Fig. 12. These projections were made with Eq. (13) and Soudan rock parameters. The median value of the muon energy $⟨E_{\mu ,0}{⟩}_{\mathrm{med}}$ on the surface for these three bins is shown.

Figure 15

The muon charge ratio $N_{{\mu }^{+}}/N_{{\mu }^{-}}$ at the Earth’s surface. The errors shown are statistical.

Figure 16

The $\pi K$ model discussed in the text superposed onto the MINOS and $\mathrm{L}3+\mathrm{C}$ data sets. The MINOS charge ratio data are from Table 5 with a systematic error of $\pm 0.011$ that has been added in quadrature to the statistical error for each data point. The $\mathrm{L}3+\mathrm{C}$ data are taken from [3].

Figure 17

A compilation of muon charge ratio data from 0.1 to 7 TeV. The MINOS data have been taken from Table 5. Other data: $\mathrm{L}3+\mathrm{C}$ [3], Baxendale [35], CosmoALEPH [36], Matsuno [14], and Rastin [37]. The $\pi K$ model is superposed.