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Measurement of the flux and zenith-angle distribution of upward through-going muons by Super-Kamiokande

A total of 614 upward through-going muons of minimum energy 1.6 GeV are observed by Super-Kamiokande during 537 detector live days. The measured muon flux is 1.74+/-0.07(stat.)+/-0.02(sys.)x10^{-13}cm^{-2}s^{-1}sr^{-1} compared to an expected flux of 1.97+/-0.44(theo.)x10^{-13}cm^{-2}s^{-1}sr^{-1}. The absolute measured flux is in agreement with the prediction within the errors. However, the zenith angle dependence of the observed upward through-going muon flux does not agree with no-oscillation predictions. The observed distortion in shape is consistent with the \nu_\mu<->\nu_\tau oscillation hypothesis with \sin^22\theta>0.4 and 1x10^{-3}<\Delta m^2<1x10^{-1} eV^{2} at 90% confidence level.

Energetic atmospheric ν µ orν µ passing through the Earth interact with the rock surrounding the Super-Kamiokande ("Super-K") detector and produce muons via weak interactions. While those neutrinoinduced muons traveling downwards are impossible to differentiate from the constant rain of cosmic ray muons, upward-going muons are mostly ν µ orν µ induced, because upward-going cosmic ray muons cannot penetrate through the whole Earth and ν e andν e induced electrons and positrons shower and die out in the rock before reaching the detector. Those muons energetic enough to cross the entire detector are defined as "upward through-going muons". The mean energy of their parent neutrinos is approximately 100 GeV. Neutrinos arriving vertically travel roughly 13,000 km, while those coming from near the horizon originate only ∼500 km away.
Previously published results on atmospheric neutrinos with average energies below ∼10 GeV have indicated an anomalously low ν µ /ν e ratio [1][2][3][4] and have also reported a strong zenith angle dependence [2]. This has been interpreted as a possible signature of neutrino oscillations. Recent results from this experiment [5,6] have shown strong evidence for ν µ ↔ ν τ oscillations [7]. These results have reported on lower energy ν µ and ν e neutrinos which interacted in the water of the detector itself, hereafter referred to as "contained" events.
The oscillation hypothesis has also been suggested to explain the anomalous upward through-going muon zenith angle distributions observed by Kamiokande [8] and MACRO [9] as well as the low absolute upward-going muon flux seen in MACRO. However, the absolute upward-going muon fluxes measured in Kamiokande, IMB [10], and Baksan [11] were consistent with the no-oscillation expectations within the large errors present in the absolute flux predictions.
We make the first report on the measurement of upward through-going muon flux and its zenithangle distribution as observed by Super-K. The experimental site is located at the Kamioka Observatory, Institute for Cosmic Ray Research, the University of Tokyo, 1000 m underground in the Kamioka mine, Gifu prefecture, Japan.
The Super-K detector is a 50 kton cylindrical water Cherenkov calorimeter. The detector is divided by an optical barrier instrumented with photomultiplier tubes ("PMT"s) into a cylindrical primary detector region (the Inner Detector, or "ID") and a surrounding shell of water (the Outer Detector, or "OD") serving as a cosmic ray veto counter. Details of the detector can be found in reference [5].
The cosmic ray muon rate at Super-K is 2.2 Hz. The trigger efficiency for a muon entering the detector with momentum more than 200 MeV/c is ∼100% for all zenith angles. The nominal detector effective area for upward through-going muons with a track length > 7m in the ID is ∼1200 m 2 .
The data used in this analysis were taken from Apr. 1996 to Jan. 1998, corresponding to 537 days of detector livetime. Event reconstruction is made by means of the charge and timing information recorded by each hit PMT. The direction of a muon track is first reconstructed by several automated grid search methods, which find the track by minimizing the width of the residual distribution of the photon timeof-flight subtracted ID PMT times. Details of one such muon fitter are described elsewhere [12].
A minimum track length cut of 7m (∼1.6 GeV) was applied. To reduce the abundant downward-going cosmic ray muons, events satisfying cos Θ < 0.1 are selected, where Θ is the zenith angle of the muon track, with cos Θ < 0 corresponding to upward-going events. Muons which leave both entrance and exit signal clusters in the OD are regarded as through-going. After a visual scan by two independent groups (event loss probability < 0.01%) and a final direction hand-fit, 614 upward through-going muon events with cos Θ < 0 are observed. Different hand fits are consistent with each other within 1.5 • . They are shown to be unbiased in blind tests using Monte-Carlo (MC) simulated events, with deviations between the reconstructed track direction and the real muon direction (∆θ rec ) estimated to be 1.4 • . Using this same MC, the directional correlation between a muon and its parent neutrino is estimated to be 4.1 • , including contributions from the muon production angle and from multiple Coulomb scatterings in the rock.
Due to the finite fitter resolution and multiple Coulomb scattering in the nearby rock, some down-going cosmic ray muons may appear to have cos Θ < 0. Figure 1 illustrates the estimation of this contamination. Assuming this background continues to fall exponentially as cos Θ decreases, the contribution to apparent upward-going muons is estimated to be 4.3±0.4 events, all contained in the −0.1 < cos Θ < 0 zenith angle bin. The contamination at the Kamioka site due to cosmic ray photoproduced upward-going pions [13] meeting the 7m track length requirement is estimated to be < 1%.
The total detection efficiency of the complete data reduction process for upward through-going muons is estimated by a Monte Carlo simulation to be >99% which is almost isotropic for −1 < cos Θ < 0. Using the upward/downward symmetry of the detector configuration, the validity of this Monte Carlo program has been checked by real cosmic ray downward through-going muons.
This analysis used a model which is a combination of the Bartol atmospheric neutrino flux model [14] and a neutrino interaction model composed of quasi-elastic scattering [15] + single-pion production [16] + deep inelastic scattering (DIS) multi-pion production. The DIS cross-section is based on the parton distribution functions (PDF) of GRV94DIS [17] with the additional kinematic constraint of W > 1.4 GeV/c 2 . Lohmann's muon energy loss formula in standard rock [18] is then employed to analytically calculate the expected muon flux at the detector. This flux is compared to three other analytic calculations to estimate the model-dependent uncertainties of the expected muon flux. The other flux calculations use the various pairs of the Bartol flux, the GRV94DIS PDF, the atmospheric neutrino flux model calculated by Honda et al [19], and the CTEQ3M [20]PDF. These comparisons yield ±10% of uncertainty for the absolute flux normalization and −3.7% to +1.6% for the bin-by-bin shape difference in the zenith-angle distribution. The shape difference is due mostly to the input flux models.
Given the detector live time T , the effective area for upward through-going muons S(Θ), and the detection efficiency ε(Θ), the upward through-going muon flux is calculated by the formula: where the suffix j represents each event number, 2π is the total solid angle covered by the detector for upward through-going muons, N corresponds to the total number of observed muon events (614). Subsequently, we subtract the cosmic ray muon contamination (4.3 events) from the most horizontal bin (-0.1<cos Θ<0). Conceivable experimental systematic errors are summarized in Table II. Including these experimental systematic errors, the observed upward through-going muon flux is: Φ obs = (1.74 ± 0.07(stat.) ± 0.02(sys.)) × 10 −13 cm −2 s −1 sr −1 . Fig. 2 shows the flux as a function of zenith angle. The shape of the distribution is not well represented by the theoretical prediction without neutrino oscillation, having a χ 2 /degrees of freedom (dof) = 18.7/9 corresponding to 2.8% probability. This shape comparison is done after multiplying the expected flux by a free-running normalization factor (1+α µ ), whose best fit value is α µ = −14%.
A set of neutrino oscillation hypotheses are then tested using the zenith angle distribution. The expected flux ((dΦ/dΩ) osc ) for a given set of ∆m 2 and sin 2 2θ is calculated and the same binning (dcosΘ=0.1) is applied to this flux as to the data. To test the validity of a given oscillation hypothesis, we minimize a χ 2 which is defined as: where σ stat,i (σ sys,i ) is the statistical (experimental systematic) error in the observed flux (dΦ/dΩ) i obs for the ith bin, and (1 + α µ ) is an absolute normalization factor of the expected flux. The absolute flux normalization error σ αµ is estimated to be ±22 % by adding in quadrature the bin-to-bin correlated experimental errors and theoretical uncertainties in Table I. Based on the bin-by-bin correlated systematic errors in Table II added in quadrature, we estimate σ sys,i to range from ±(0.3−3.8)%. Then, the minimum χ 2 (χ 2 min ) is searched for on the ∆m 2 − sin 2 2θ plane.
Assuming ν µ ↔ ν τ oscillations, χ 2 min (= 7.5/8 dof) occurs at (sin 2 2θ, ∆m 2 ) = (0.95, 5.9×10 −3 eV 2 ) and α µ = +12%, in good agreement with the overall normalization found in the contained event analysis [7], although the α µ of this analysis refers to the flux normalization of neutrino energies predominantly around 100 GeV. For the null oscillation case (sin 2 2θ=0), we obtain χ 2 of 19.2 at a best-fit α µ = −14% using the same χ 2 definition. The zenith angle distribution of (1 + α µ )(dΦ/dΩ) i osc for the best fit parameters is shown in Fig. 2 together with the data. Figure 3 shows the confidence intevals on the (sin 2 2θ, ∆m 2 ) plane for ν µ ↔ ν τ oscillations. The 90% C.L. contour marks the line of χ 2 min + 4.6. If we replace the Bartol neutrino flux [14] by Honda's [19] and/or the GRV94DIS parton distribution functions [17] by CTEQ3M [20], the allowed region contours are similar to those presented in Fig. 3. Consequently, we find that the zenith angle dependence is in favor of the ν µ ↔ ν τ oscillation hypothesis and supports the Super-K contained event analysis [5][6][7]. It is also consistent with the data presented in the Kamiokande [8] and MACRO [9] upward-going muon analyses. Interactions of ν τ in the rock below is estimated at less than a few percent and neglected in this analysis. Oscillation of ν µ to ν e in this range of parameter space has been ruled out by the CHOOZ experiment [22].
In conclusion, based on 614 upward through-going muon events during 537 detector live days, the flux of the upward through-going muons (>1.6 GeV) is measured with the Super-K detector: Φ obs = (1.74 ± 0.07(stat.) ± 0.02(sys.)) × 10 −13 cm −2 s −1 sr −1 . This is compared with the expected flux of Φ theo = (1.97 ± 0.44(theo.)) × 10 −13 cm −2 s −1 sr −1 . The absolute observed upward through-going muon flux is in agreement with the expected flux within the relatively large uncertainties in the theoretical calculations. We find that the zenith angle dependence does not agree with the theoretical expectation without neutrino oscillations at the 97% C.L. However, the ν µ ↔ ν τ oscillation hypothesis with sin 2 2θ > 0.4 and 1×10 −3 < ∆m 2 < 1 × 10 −1 eV 2 is consistent with the observed zenith angle shape at 90% C.L. This result supports the evidence for neutrino oscillations given by the analysis of the contained atmospheric neutrino events by Super-K.
We     Allowed region contours at 68% (dotted contour), 90% (thick solid), and 99% (dashed) C.L. obtained by the Super-K upward through-going muon analysis on the (sin 2 2θ,∆m 2 ) plane for the νµ ↔ ντ oscillation hypothesis. The star indicates the best fit point at (sin 2 2θ, ∆m 2 ) = (0.95, 5.9 × 10 −3 eV 2 ). Also shown is the allowed region contour (thin solid) at 90% C.L. by the Super-K contained event analysis. The allowed regions are to the right of the contours.