Measurements of muons at sea level

Transcription

1 J. Phys. G: Nucl. Part. Phys. 24 (1998) Printed in the UK PII: S (98) Measurements of muons at sea level Shuhei Tsuji, Toshikazu Katayama, Kazuhide Okei, Tomonori Wada, Isao Yamamoto and Yoshihiko Yamashita Department of Physics, Faculty of Science, Okayama University, Tsushimanaka Okayama , Japan Okayama University of Science, 1-1 Ridaicho Okayama , Japan Received 12 March 1998, in final form 12 May 1998 Abstract. We measure muon intensities at sea level by using the OKAYAMA cosmic-ray telescope in detail. Measured muons are also contained in the low-momentum region where they are strongly affected by geomagnetic field effects including the east west effect. We report the zenith and azimuthal angular dependence of conventional muons in the momentum range GeV/c in the zenith angular range Introduction Much experimental work has been reported on muon intensities at sea level, since they are important astrophysical standards and contain information concerning cosmic-ray interaction processes. The controversial issue lies in the significant difference in the muon/electron neutrino ratios, between the calculations [1 5] and some experiments [10 12]. Such a difference should be attributed to either neutrino oscillation or misidentification of the particles concerned. There are many calculations [1 9] along these lines and their validity should be finally examined for the comparison momentum spectrum of the cosmic-ray muons and/or its charge ratio. However, almost all previous experiments were performed and reported in narrow zenith angular ranges, in the near vertical or near horizontal directions [13 23]. The OKAYAMA telescope [24] (hereafter paper I), is suitable for the measurement of wider zenith or azimuthal angular dependence of muon intensities at sea level, for various reasons. (A) It moves by a servo-motor mechanism thus allowing any azimuthal and zenith angles to be used. (B) It measures the incoming direction, the momentum and the charge sign of an incident cosmic-ray muon. First, the zenith angular dependence of cosmic-ray muon fluxes was measured. Then, we compared our results taken from the near-vertical and near-horizontal region with the other experimental results [14, 15, 22, 23]. In medium zenith angular regions (30 75 ), we compared our results with theoretical models [25, 26] as the measurements of muons have rarely been reported in this angular region. In addition, positive and negative muon fluxes at a zenith angle of 75 were measured and compared with the theoretical model taking into account the geomagnetic field. The azimuthal angular dependence of cosmic-ray muon fluxes were measured at zenith angles 20 and 40. These muon data were also analysed taking account of the geomagnetic field, including the east west effect [27] /98/ $19.50 c 1998 IOP Publishing Ltd 1805

2 1806 S Tsuji et al Table 1. Geographical environment Location Height Geomagnetic field 34 N latitude, E longitude 5.3 m above sea level N inclination, 6 52 W declination horizontal component T Properties of the telescope Opening angle 15.5 Trigger counters scintillation counters (40 50 cm) 2 S1, S2 Position chambers a drift chambers (40 40 cm 2, unit cell: mm 3 ) PC1X (3 layers) PC1Y (2 layers) PC2X (3 layers) PC2Y (2 layers) PC3X (8 layers) PC3Y (2 layers) Zenith angle (movable) 0 80 Azimuthal angle (movable) Solid iron magnet data Useful magnetic volume cm 3 Current, coil 350 A, 15 turns Magnetic induction 18 ± 0.4 kg Cutt-off momentum by the magnetic material 0.43 GeV/c Maximum detectable momentum (maximum value) 270 GeV/c Geometrical acceptance solid angle 16.9 cm 2 sr ( 5 GeV/c, the distance between the top of PC1 and the bottom of PC3) Coulomb scattering effect 0.37 a In detail in paper I [24]. In this paper, we mainly present the zenith and azimuthal angular dependence of muon fluxes in the momentum range, GeV/c, in the zenith angular range, 0 81,in the observation period from September 1992 to December 1997, using the OKAYAMA cosmic-ray telescope. The results of muon measurements will be compared with those of other experimental and theoretical results. 2. Apparatus and operation The OKAYAMA cosmic-ray telescope is installed in the building of Okayama University at sea level. The main characteristics of the OKAYAMA telescope are summarized in table 1. The telescope is movable in all directions for the azimuthal angle and up to 80 for the zenith angle with each servo-motor mechanism; it measures not only the incoming direction but also the momentum and the charge sign of any cosmic-ray muon incident on the solid iron magnet. The telescope was described in detail in paper I. The OKAYAMA telescope has been in operation for some time and data for the analyses of the zenith angular dependence of muons were accumulated in the observation period from 27 September 1992 to 8 September The effective observation times are 5025 h in the vertical measurement and h in the moving measurements from 6.1 to 80 in the zenith angles for tracing Cygnus X-3. The data for the analyses of the azimuthal angular dependence of muons at zenith angles of 20 and 40 was accumulated in the observation period from 3 June 1997 to 17 December The effective observation times are 3258 h

3 Table 2. Zenith angular dependence of the differential intensities. Momentum Zenith P = 12.5 ± 2.5 GeV/c P = 22.5 ± 2.5 GeV/c P = 45.0 ± 5.0 GeV/c angle Measured Intensity Measured Intensity Measured Intensity (degree) number [cm 2 sr 1 s 1 (GeV/c) 1 ] number [cm 2 sr 1 s 1 (GeV/c) 1 ] number [cm 2 sr 1 s 1 (GeV/c) 1 ] (8.37 ± 0.17) (2.04 ± 0.09) (3.21 ± 0.28) ± (8.22 ± 0.15) (2.00 ± 0.08) (2.97 ± 0.24) ± (8.90 ± 0.17) (1.94 ± 0.09) (2.84 ± 0.27) ± (8.78 ± 0.18) (2.02 ± 0.09) (3.20 ± 0.29) ± (7.78 ± 0.17) (1.88 ± 0.09) (2.66 ± 0.28) ± (8.52 ± 0.19) (2.08 ± 0.10) (3.15 ± 0.30) ± (8.58 ± 0.19) (1.91 ± 0.09) (2.90 ± 0.30) ± (8.52 ± 0.19) (2.030 ±.10) (3.03 ± 0.31) ± (7.98 ± 0.18) (1.92 ± 0.10) (2.66 ± 0.29) ± (8.17 ± 0.19) (1.91 ± 0.09) (3.27 ± 0.32) ± (8.31 ± 0.27) (1.88 ± 0.13) (3.37 ± 0.46) ± (7.24 ± 0.25) (1.89 ± 0.13) (2.98 ± 0.43) ± (8.44 ± 0.27) (2.23 ± 0.15) (3.34 ± 0.47) ± (7.37 ± 0.25) (1.94 ± 0.14) (2.04 ± 0.35) ± (7.43 ± 0.26) (2.01 ± 0.14) (3.07 ± 0.45) ± (6.37 ± 0.23) (1.71 ± 0.13) (2.35 ± 0.38) ± (6.82 ± 0.24) (1.54 ± 0.12) (2.72 ± 0.41) ± (7.07 ± 0.24) (1.67 ± 0.12) (2.41 ± 0.40) ± (7.08 ± 0.25) (1.76 ± 0.13) (2.17 ± 0.38) 10 6 Measurements of muons at sea level 1807

4 Table 2. (Continued) Momentum Zenith P = 12.5 ± 2.5 GeV/c P = 22.5 ± 2.5 GeV/c P = 45.0 ± 5.0 GeV/c angle Measured Intensity Measured Intensity Measured Intensity (degree) number [cm 2 sr 1 s 1 (GeV/c) 1 ] number [cm 2 sr 1 s 1 (GeV/c) 1 ] number [cm 2 sr 1 s 1 (GeV/c) 1 ] 1808 S Tsuji et al 44 ± (7.04 ± 0.25) (1.68 ± 0.13) (3.24 ± 0.45) ± (6.38 ± 0.23) (1.93 ± 0.14) (2.13 ± 0.38) ± (6.27 ± 0.23) (1.81 ± 0.13) (2.87 ± 0.42) ± (6.25 ± 0.23) (1.66 ± 0.13) (2.36 ± 0.37) ± (5.52 ± 0.22) (1.57 ± 0.12) (2.60 ± 0.40) ± (5.37 ± 0.21) (1.37 ± 0.12) (2.09 ± 0.36) ± (5.33 ± 0.21) (1.38 ± 0.11) (2.08 ± 0.34) ± (4.97 ± 0.21) (1.54 ± 0.13) (1.94 ± 0.35) ± (4.81 ± 0.21) (1.19 ± 0.11) (1.79 ± 0.35) ± (4.11 ± 0.19) (1.21 ± 0.11) (2.11 ± 0.36) ± (3.65 ± 0.18) (1.20 ± 0.11) (1.64 ± 0.33) ± (3.68 ± 0.18) (1.20 ± 0.11) (2.21 ± 0.36) ± (3.39 ± 0.17) (1.27 ± 0.11) (2.41 ± 0.39) ± (2.86 ± 0.15) (1.02 ± 0.10) (1.88 ± 0.34) ± (2.60 ± 0.15) (9.97 ± 0.94) (1.50 ± 0.29) ± (2.36 ± 0.14) (7.79 ± 0.83) (1.79 ± 0.32) ± (1.64 ± 0.11) (7.01 ± 0.79) (1.34 ± 0.27) ± (1.36 ± 0.10) (4.80 ± 0.62) (1.24 ± 0.27) ± 1 81 (1.13 ± 0.13) (4.99 ± 0.87) (1.37 ± 0.35) 10 6

5 Table 3. The differential intensities at each zenith angle. Zenith angle (degree) ± 1 80 ± 1 Momentum Measured Intensity Measured Intensity Measured Intensity GeV/c number [cm 2 sr 1 s 1 (GeV/c) 1 ] number [cm 2 sr 1 s 1 (GeV/c) 1 ] number [cm 2 sr 1 s 1 (GeV/c) 1 ] (1.51 ± 0.03) (1.21 ± 0.02) (7.93 ± 0.12) (2.22 ± 0.10) (1.85 ± 0.39) (5.73 ± 0.10) (1.91 ± 0.09) (8.14 ± 2.35) (3.93 ± 0.08) (1.42 ± 0.08) (1.29 ± 0.32) (3.01 ± 0.07) (1.07 ± 0.07) (1.15 ± 0.28) (2.30 ± 0.06) (9.94 ± 0.65) (2.07 ± 0.38) (1.78 ± 0.05) (8.01 ± 0.58) (8.88 ± 2.37) (1.38 ± 0.05) (6.35 ± 0.53) (6.23 ± 1.97) (8.37 ± 0.17) (4.71 ± 0.20) (1.12 ± 0.12) (3.75 ± 0.12) (2.35 ± 0.14) (6.07 ± 0.95) (2.04 ± 0.09) (1.18 ± 0.11) (4.95 ± 0.86) (1.17 ± 0.07) (7.46 ± 0.86) (2.92 ± 0.73) (6.12 ± 0.37) (4.08 ± 0.47) (1.79 ± 0.39) (3.21 ± 0.28) (1.78 ± 0.34) (1.24 ± 0.33) (1.39 ± 0.20) (1.64 ± 0.32) (1.40 ± 1.40) (8.68 ± 1.64) (1.08 ± 0.31) (3.82 ± 1.91) (8.07 ± 1.68) (2.19 ± 1.27) (1.17 ± 1.17) (3.73 ± 1.18) (4.26 ± 2.13) (1.69 ± 0.85) (2.38 ± 1.37) (1.12 ± 1.12) (1.00 ± 0.32) (7.37 ± 4.26) (1.01 ± 0.71) (2.84 ± 2.01) (1.17 ± 0.83) (3.59 ± 2.54) (3.49 ± 3.49) Measurements of muons at sea level 1809

6 1810 S Tsuji et al Figure 1. The zenith angular dependence of the absolute differential muon fluxes for each momentum, 12.5±2.5, 22.5±2.5 and 45.0±5.0 GeV/c., present flux;, observed flux by DEIS [14];, observed flux in Nottingham [15];, observed flux by Kiel-Desy [22]; full curves, theoretical spectra by Smith and Duller [25]; broken curves, theoretical spectra by Maeda [26]. Figure 2. The absolute differential muon fluxes for each zenith angle (0,60,80 )., present flux at ;, present flux at 60 ± 1 ;, present flux at 80 ± 1 ; full curves, theoretical spectra by Smith and Duller [25]; broken curves, theoretical spectra by Maeda [26]. in the azimuth measurements. The total number of events is passed through the limited area, cm 2 of the instrument. The polarity of the field in the solid iron magnet was changed once during the observed running time to avoid systematic asymmetry in the measurements. The muon fluxes were analysed following the methods in [28]. 3. Results of the measurements of cosmic-ray muons 3.1. The absolute differential muon fluxes at various zenith angles The absolute differential muon fluxes are compared with the results of other experiments in the vertical [15] and near the horizon [14, 22], and the theoretical models [25, 26] in other zenith angular regions. They are presented in table 2 and plotted in figure 1 for three momentum regions. The muon events in this analysis were used with the incident angles θ x 1.0 and θ y 5.0 and with the following momentum regions: 12.5±2.5, 22.5±2.5 and 45.0 ± 5.0 GeV/c. The data sets were binned according to the interval of the zenith angle 2. The error bars show statistical errors only. The plotted experimental data consist of Nottingham [15] in the vertical, DEISE [14] and Kiel-Desy [22] near the horizon. The lines represent the theoretical models of a muon intensity studied by Smith and Duller [25] and by Maeda [26]. Their models were adopted as atmospheric muons were produced

7 Measurements of muons at sea level 1811 Table 4. The differential intensity in the zenith angle 30 ± 4. Momentum Measured Intensity (GeV/c) number [cm 2 sr 1 s 1 (GeV/c) 1 ] (9.57 ± 0.11) (6.85 ± 0.09) (4.95 ± 0.07) (3.70 ± 0.06) (2.74 ± 0.05) (2.06 ± 0.05) (1.61 ± 0.04) (1.37 ± 0.04) (7.74 ± 0.13) (3.61 ± 0.09) (1.88 ± 0.07) (1.17 ± 0.05) (5.72 ± 0.29) (2.79 ± 0.21) (1.57 ± 0.17) (8.42 ± 1.31) (5.97 ± 1.15) (5.20 ± 1.13) (2.16 ± 0.76) (8.10 ± 2.25) (4.29 ± 1.92) (1.31 ± 1.31) 10 8 only by pions, since pions strongly dominate over kaons. In the calculations of Smith and Duller s model, the parameters in this intensity curve are applied to the same value as in their paper [25]. In the calculations of Maeda s model, we use the isothermal atmospheric model with the constant scale height, 8.4 km. Muons are assumed to be produced from an atmospheric depth of 160 g cm 2. For the other hypothesis, we used the constant power index of the primary nucleon, 2.7 and the attenuation mean free path of primary particles and the nuclear absorption mean free path of pions, 120 g cm 2. The lines are normalized to P = 10 GeV/c at the zenith angle 0. The results measured by the telescope approximately agree with other experimental results and theoretical models. The differential muon spectra are compared with the theoretical models [25, 26] at each zenith angle 0 + 1,60 ±1 and 80 ± 1. They are presented in table 3 and plotted in figure 2. At the zenith angles, 0 and 60, the fluxes agree with the theoretical models. At the zenith angle 80, the fluxes do not correspond with the model of the calculation by Maeda using the above assumed parameters concerned with the muon productions. In the calculation of Smith and Duller s model, the fluxes are not concentrated on the theoretical model to less than 10 GeV/c. It can be explained that the muon events at large zenith angles are affected by the geomagnetic field. The effect of the geomagnetic field is described in detail in a later section. Comparable fluxes of the other experiments at some zenith angular regions, Kiel- Desy [22] and Brookhaven [23] were reported. The Kiel-Desy group observed atmospheric muons at the zenith angle 75 ±7 and the Brookhaven group at the zenith angles, 30 ±4.1 and 75 ± 4.1. Our data binned together the zenith angles, 30 ± 4 and 75 ± 6. The absolute differential muon fluxes at the zenith angle 30 ± 4 are presented in table 4 and

8 1812 S Tsuji et al Figure 3. The differential muon fluxes in the zenith angle 30 ±4., present flux in 30 ±4 ;, observed flux in Brookhaven [23] in 30 ± 4.1. plotted in figure 3. Our results are consistent with the results of the Brookhaven group. The absolute differential muon fluxes at the zenith angle 75 ± 6 are presented in table 5 and plotted in figure 4. Above 27.5 GeV/c in figure 4, the fluxes are consistent with other experiments. However, the fluxes below 27.5 GeV/c are not in alignment with the Kiel- Desy group findings. The disagreement is explained by the geomagnetic field effect caused by the spectrometer which when used by Kiel-Desy pointed in the east direction (azimuth: 288 ), on the other hand, our telescope pointed in a north-west direction (azimuth: 130 ). A low-momentum muon in the atmosphere is deflected by the geomagnetic field at large zenith angle θ. The deflection angle is given by φ = l r where l is the path length of a muon, r is the radius of curvature of a muon. In our experiment, a positive muon has a shorter path length than a negative one in a large zenith angular region. So the zenith angle θ of an incident positive muon is replaced thus becoming θ φ and the zenith angle θ of an incident negative muon is replaced to become θ + φ at the production of a muon [29]. We applied the muon spectra at the zenith angle 75 ± 6 calculated by Smith and Duller with this phenomenon. The applied spectra of the negative and positive muons are drawn in figure 5. The full curves contain the effect of the geomagnetic field and are drawn replacing the zenith angle θ with θ ± 0.5φ, because

9 Measurements of muons at sea level 1813 Figure 4. The absolute differential muon fluxes in the zenith angle 75 ± 6., present flux in 75 ± 6 ;, observed flux by Kiel-Desy [22] in 75 ± 7 ;, observed flux in Brookhaven [23] in 75 ± 4.1. Figure 5. The absolute differential positive and negative muon fluxes in the zenith angle 75 ± 6., present flux of positive muons in 75 ± 6 ;, present flux of negative muons in 75 ± 6 ; full curves, theoretical spectra of positive (heavy curve) and negative muons by Smith and Duller [25] at 75 ± 6 considering the geomagnetic field.

10 1814 S Tsuji et al Table 5. The differential intensity in the zenith angle 75 ± 6. Momentum Measured Intensity (GeV/c) number [cm 2 sr 1 s 1 (GeV/c) 1 ] (4.59 ± 0.19) (4.16 ± 0.17) (3.67 ± 0.16) (3.33 ± 0.15) (2.97 ± 0.14) (2.76 ± 0.14) (2.43 ± 0.13) (1.98 ± 0.05) (1.09 ± 0.04) (7.14 ± 0.33) (4.82 ± 0.29) (2.51 ± 0.15) (1.50 ± 0.12) (7.19 ± 0.93) (4.77 ± 0.78) (2.79 ± 0.62) (2.43 ± 0.61) (2.26 ± 0.60) (8.98 ± 1.96) (1.27 ± 0.90) (4.43 ± 1.67) 10 8 θ ± 0.5φ is the median angle between θ at the observed point and θ ± φ at the production point of a muon. The heavy curves show the theoretical positive muon spectra under this effect and the other curves show the theoretical negative one. These spectra are normalized at the momentum P = 10 GeV/c at the zenith angle 0. The fluxes of the positive and negative muons in the zenith angle 75 ±6 are plotted as open and closed circles in figure 5 and presented in table 6. The spectrum of positive muons in the low-momentum region agrees with the full curve. The spectrum of negative ones does not agree with the full curve. Multiple scattering in the atmosphere causes the discrepancy between the plots and the full curve for the negative muons with low momentum in this large zenith angular region The muon charge ratio The charge ratios for measured muons are presented in figure 6 as a function of muon momentum for each zenith angle. The collected data are divided into seven different zenith angular-regions between 34 and 84 with the momentum from GeV/c and with an acceptance angle of θ x 4.0 and θ y 5.0. The values of the muon charge ratio shown with broken lines are the measurements by Burnett et al [30] above 50 GeV/c. The errors quoted correspond to one standard deviation σ and have been determined by the following equation, σ = f + ( 1 f N + 1 ) 1/2 + N where f +, f, N + and N show the flux and number of positive and negative muons respectively.

11 Measurements of muons at sea level 1815 Table 6. The differential intensities of and µ + in the zenith angle 75 ± 6. Charged muon µ + µ Momentum Measured Intensity Measured Intensity (GeV/c) number [cm 2 sr 1 s 1 (GeV/c) 1 ] number [cm 2 sr 1 s 1 (GeV/c) 1 ] (2.86 ± 0.15) (1.74 ± 0.12) (2.69 ± 0.14) (1.47 ± 0.10) (2.39 ± 0.13) (1.28 ± 0.10) (2.04 ± 0.12) (1.28 ± 0.10) (1.85 ± 0.11) (1.12 ± 0.09) (1.64 ± 0.11) (1.12 ± 0.09) (1.42 ± 0.10) (1.01 ± 0.08) (1.10 ± 0.04) (8.78 ± 0.35) (6.06 ± 0.30) (4.84 ± 0.27) (3.77 ± 0.24) (3.37 ± 0.23) (2.23 ± 0.19) (2.59 ± 0.21) (1.27 ± 0.11) (1.25 ± 0.10) (1.00 ± 0.10) (4.91 ± 0.69) (3.91 ± 0.69) (3.28 ± 0.62) (2.55 ± 0.57) (2.22 ± 0.54) (1.95 ± 0.54) (8.49 ± 3.21) (1.85 ± 0.51) (5.77 ± 3.33) (1.23 ± 0.47) (1.02 ± 0.39) (4.13 ± 1.31) (4.85 ± 1.46) (6.58 ± 6.58) (6.13 ± 6.13) ( ) (2.11 ± 1.22) 10 8 The plots of more than 100 GeV/c fluctuate owing to insufficient data. Our analysed result of these muon data over the momentum range GeV/c approximately agrees with Burnett et al s findings Azimuthal angular dependence of muon intensity The muon fluxes of various azimuthal angles are presented in figure 7 at the zenith angle 20 ± 5 and in figure 8 at the zenith angle 40 ± 5. The plots show the fluxes of total, positive and negative muons. They are fitted by sine curves. In the low-momentum region, GeV/c, at the zenith angle 20, total and positive muon fluxes in the east are found less than the fluxes in other directions. On the other hand, negative muon flux in the east is slightly more than the fluxes in the other directions. In the high-momentum region, 3.5 GeV 100 GeV/c, they are almost flat. In the zenith angle 40, the fluxes in the low-momentum region, GeV/c, also fluctuate more than in the high-momentum region, GeV/c. The positive excess of these muon fluxes are shown in figure 9 (zenith angle 20 ) and figure 10 (zenith angle 40 ). The positive excess has been defined as follows, positive excess 2 f + f f + + f where f + and f show the flux of positive and negative muons. The errors, one standard

12 Table 7. The azimuth dependence of the muon intensities in the zenith angle 20 ± GeV/c Azimuthal angle 0 ± 5 45 ± 5 90 ± ± ± ± ± ± 5 South West North East 1816 S Tsuji et al µ + and µ measured number flux ( 10 3 )[cm 2 sr 1 s 1 ] 1.13 ± ± ± ± ± ± ± ± 0.04 µ + measured number flux ( 10 4 )[cm 2 sr 1 s 1 ] 6.40 ± ± ± ± ± ± ± ± 0.28 µ measured number flux ( 10 3 )[cm 2 sr 1 s 1 ] 4.93 ± ± ± ± ± ± ± ± GeV/c µ + and µ measured number flux ( 10 3 )[cm 2 sr 1 s 1 ] 4.07 ± ± ± ± ± ± ± ± 0.07 µ + measured number flux ( 10 3 )[cm 2 sr 1 s 1 ] 2.17 ± ± ± ± ± ± ± ± 0.05 µ measured number flux ( 10 3 )[cm 2 sr 1 s 1 ] 1.89 ± ± ± ± ± ± ± ± 0.05

13 Table 8. The azimuth dependence of the muon intensities in the zenith angle 40 ± GeV/c Azimuthal angle 0 ± 5 45 ± 5 90 ± ± ± ± ± ± 5 South West North East µ + and µ measured number flux ( 10 4 )[cm 2 sr 1 s 1 ] 6.98 ± ± ± ± ± ± ± ± 0.19 µ + measured number flux ( 10 4 )[cm 2 sr 1 s 1 ] 3.75 ± ± ± ± ± ± ± ± 0.14 µ measured number flux ( 10 4)[cm 2 sr 1 s 1 ] 3.23 ± ± ± ± ± ± ± ± GeV/c µ + and µ measured number flux ( 10 3 )[cm 2 sr 1 s 1 ] 2.95 ± ± ± ± ± ± ± ± 0.04 µ + measured number flux ( 10 3 )[cm 2 sr 1 s 1 ] 1.60 ± ± ± ± ± ± ± ± 0.03 µ measured number flux ( 10 3 )[cm 2 sr 1 s 1 ] 1.34 ± ± ± ± ± ± ± ± 0.03 Measurements of muons at sea level 1817

14 1818 S Tsuji et al Figure 6. Measured muon charge ratios at different zenith angles, plotted as a function of muon momentum. The broken lines represent the averaged muon charge ratio (>50 GeV/c) measured by Burnett et al [30]. deviation σ, have been determined by following equation, σ = 4 ((N + ) 2 N + (N ) 2 N + ) 1/2 (N + + N ) 2 where N + and N show the number of positive and negative muons. The theoretical positive excess at the zenith angles 20 ± 5 and 40 ± 5 employed the calculations of Smith and Duller [25] in the geomagnetic field effects [29] are drawn as broken curves. The ratios of theoretical positive and negative fluxes are assumed as being average charge ratios of the results found within each momentum region. The chain lines show average values of positive excess. The plots at a zenith angle of 20 fluctuate largely in the low-momentum range, GeV/c, but do not fluctuate in the high-momentum range, GeV/c. The plots at a zenith angle of 40 fluctuate more than those in the zenith angle 20 in each momentum region. The results agree with the theoretical positive excess. Kamiya et al reported the azimuthal angular dependence of the positive excess at sea level for the zenith angle 78 for three energy ranges [31]. Our results show the same tendency of the Kamiya et al s results. These fluctuations of muon fluxes are known as the east

15 Measurements of muons at sea level 1819 Figure 7. The azimuthal angular dependence of the muon fluxes in the zenith angle 20 ± 5 for each momentum region, GeV/c, GeV/c., total muon flux;, positive muon flux;, negative muon flux; broken curves, sine curves fitted by each of the fluxes. Figure 8. The azimuthal angular dependence of the muon fluxes in the zenith angle 40 ± 5 for each momentum region, GeV/c, GeV/c., total muon flux;, positive muon flux;, negative muon flux; broken curves, sine curves fitted by each of the fluxes.

16 1820 S Tsuji et al Figure 9. The azimuthal angular dependence of the positive excess of muon in the zenith angle 20 ± 5 for each momentum region, GeV/c, GeV/c., positive excess of muon; broken curves, theoretical positive excesses calculated by Smith and Duller [25] considering geomagnetic field; chain lines, average ratio of positive excess. west effect of the geomagnetic field. The fluxes of our results are tabulated in tables 7 and Conclusion We have described: absolute differential fluxes and charge ratios of muons in each zenith angular regions, the fluxes and the positive excesses of muons in each azimuthal angular region. The measurements of muons in various zenith angular regions, differential fluxes and charge ratios, are consistent with the other experimental and theoretical results. As for the azimuthal angular dependence of muons, muon fluxes in the low-momentum region are strongly affected by the east west effect of the geomagnetic field and the results of positive excess are also consistent with theoretical results. We have further observed azimuthal angular dependence of muons at various zenith angles to investigate the anisotropy of atmospheric muons. We hope that the results of muon

17 Measurements of muons at sea level 1821 Figure 10. The azimuthal angular dependence of the positive excess of muon in the zenith angle 40 ± 5 for each momentum region, GeV/c, GeV/c., positive excess of muon; broken curves, theoretical positive excesses calculated by Smith and Duller [25] considering geomagnetic field; broken lines, average ratio of positive excess. fluxes will be useful for the studies of the cosmic-ray interaction process and calculations of the atmospheric neutrino flux. Acknowledgments We would like to thank Mr Kohji Kohno, Mr Hidemasa Asada, Mr Kohji Noda, Mr Eiji Kawabe, Mr Shinsuke Tagashira Mr Hironori Takei Mr Satoshi Tate, Mr Noriaki Sakurai and Mr Akihisa Yamamoto for their maintenance of the telescope and for their useful advice about the analyses. We also wish to thank Mr Hiroshi Miyai, Mr Manabu Yamamoto and Mr Makoto Nishiyama for making an improvement to the telescope thus allowing it to move up to a zenith angle of 80 and for the preliminary analyses of this work. Special thanks are extended to Dr Morihiro Honda for suggesting the importance of measurements of muon fluxes for the examinations of the neutrino flux calculations. This work was supported by a Grant-in-Aid for General Scientific Research Fund from the Japan Ministry of Education, Science and Culture.

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