Atmospheric neutrinos and the implications to cosmic ray interactions

Nuclear Physics B (Proc. Suppl.) 175–176 (2008) 301–306 www.elsevierphysics.com

Atmospheric neutrinos and the implications to cosmic ray interactions Takaaki Kajitaa a

Research center for Cosmic Neutrinos, Institute for Cosmic Ray Research, Univ. of Tokyo Kashiwa-no-ha 5-1-5, Kashiwa, Chiba 277-8582, Japan Atmospheric neutrinos have been used to study neutrino oscillations. Neutrino oscillation analyses with atmospheric neutrinos are discussed. With the increased statistics of the atmospheric neutrino data, it is more important to understand the atmospheric neutrino flux more accurately. Detailed calculations of the atmospheric neutrino fluxes calibrated by the atmospheric muon data show suggestions to the interaction of cosmic rays.

1. INTRODUCTION Atmospheric neutrinos have been used to study the neutrino oscillations [1,2]. Atmospheric neutrinos arise from the decay of secondaries (π, K and μ) produced by primary cosmic-ray interactions in the atmosphere. Muons and neutrinos have the same origin, and therefore the muon flux data are useful to get the information on the neutrino flux. Furthermore, it is possible to get information on hadronic interaction of cosmic ray particles using muon and neutrino data. In this article, we discuss the recent atmospheric neutrino data, some highlights in the oscillation analyses and the implications of the muon and neutrino data on high-energy cosmic ray interactions.

2. OBSERVATION OF ATMOSPHERIC NEUTRINOS Atmospheric neutrinos have been observed in underground experiments. Interactions of low energy neutrinos, around 1 GeV, have all of the final state particles “fully contained (FC)” in the detector. Higher energy charged current νμ interactions may result in the muon exiting the detector; these are referred to as “partially contained (PC)”. There is a third category of charged current νμ events, where the interaction occurs outside the detector, and the muon enters and either passes through the detector or stops in the detector. These are referred to as “upward-going 0920-5632/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2007.11.017

muons” because one generally requires they originate from below the horizon to discriminate them from the ordinary cosmic ray muons. The typical energy ranges for FC, PC, upward-stopping and upward through-going muon events are 1, 10, 10 and 100 GeV, respectively. Since the present statistics of the atmospheric neutrino data are dominated by those of SuperKamiokande (SK), we will mainly discuss the SK data and the oscillation analyses based on those data. The zenith angle distributions for e-like and μ-like events observed in SK (141 kton·yr) are shown in Fig.1. The μ-like data have exhibited a strong deficit of upward-going events, while no significant deficit has been observed in the e-like data. We notice that the observed number of events for upward through-going muons was slightly higher than the no-oscillation prediction. We come back to this issue later when we discuss the neutrino flux and cosmic ray interactions. 2.1. νμ ↔ ντ oscillation analysis Since μ-like events show the zenith angle and energy dependent deficit of events, while e-like events show no evidence for such effect, the dominant oscillation channel should be between νμ and ντ . In the analysis of the atmospheric neutrino data, a χ2 method that takes into account various systematic uncertainties is used. In the χ2 analysis, the events are divided to 760 bins (380 from both SK-I and SK-II) based on the event type, momentum and zenith angle. Dur-

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Figure 2. Allowed parameter regions of νμ → ντ oscillations from SK (141 kton·year).

ing the fit, the numbers of expected events for these bins are recalculated to account for neutrino oscillations, and systematic variations in the predicted rates due to uncertainties in the neutrino flux model, neutrino cross-section model, and detector response. In the present analysis, a total of 70 systematic errors are taken into account. The estimated oscillation parameters (sin2 2θ, Δm2 ) for two flavor νμ → ντ oscillation are shown in Fig. 2. The result from SK is; sin2 2θ > 0.93 and 1.9 × 10−3 < Δm2 < 3.1 × 10−3 eV2 at 90% C.L. Results from the other experiments are consistent with this result [3,5–7].

Figure 1. Zenith angle distributions observed in SK based on 141 kton·yr exposure for various data samples. CosΘ =1(−1) means down-going (up-going). The solid histograms show the prediction without neutrino oscillations. The dashed histograms show the prediction with νμ → ντ oscillations (Δm223 =2.5×10−3 eV2 , sin2 2θ23 =1.0). In the oscillation prediction, various uncertainty parameters such as the absolute normalization were adjusted to give the best fit to the data.

2.2. L/E analysis SK has updated the L/E analysis [3] including the SK-II data. Figure 3 shows the ratio of the data over non-oscillated MC as a function of L/E together with the best-fit expectation for 2-flavor νμ ↔ ντ oscillations with systematic errors.. A dip, which should correspond to the first oscillation minimum, is observed around L/E = 500 km/GeV. Also shown in Fig. 3 are the L/E distributions for the best-fit expectation for the neutrino decay [8] and decoherence [9] models, which are proposed to explain the zenith angle distribution of the data. Since these models cannot predict the dip observed in the data, the χ2 values for these models were worse. The neutrino decay and decoherence models were disfa-

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vored at 4.8 and 5.3 standard deviation levels, respectively (preliminary). The observed L/E distribution clearly shows that the neutrino flavor transition probability obeys the sinusoidal function as predicted by neutrino oscillations. 2.3. Detecting CC ντ events If νμ → ντ is the dominant oscillation channel, about one CC ντ event per kiloton year exposure is expected to occur in an atmospheric neutrino detector. The low event rate is due to the threshold effect of the τ production process which requires a ντ energy of at least 3.5 GeV to produce a τ lepton. These τ typically decay to hadrons (branching ratio is 64%) within 1 mm from the vertex point. These events should be upward-going but otherwise similar to energetic NC events, hence it is difficult to isolate ντ events in the on-going atmospheric neutrino experiments. SK searched for CC ντ events. The candidate ντ events were selected by a maximum likelihood or a neural network method. Various kinematical information were used as the inputs to

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Figure 4. Zenith angle distribution for the candidate tau neutrino interactions observed in SK (92 kton·yr). The gray and while regions show the fitted tau neutrino contribution and the non-tau atmospheric neutrino interactions, respectively.

these analyses. Even with these information, the signal to noise ratio was about 10%. However, the zenith-angle distribution can be used to estimate the number of ντ events statistically, because both the ντ signal and background events have accurately predicted zenith angle distributions. See Fig. 4. The best fit number of ντ interactions that occurred in the fiducial volume of the detector during the 92 kton·yr exposure was 138±48(stat.)+15 −32 (syst.). The expected number was 78±26. The observed number of ντ interactions was consistent with the νμ → ντ expectation. Zero CC ντ assumption is excluded at 2.4 standard deviation level. 3. ATMOSPHERIC NEUTRINOS AND HIGH-ENERGY COSMIC RAY INTERACTIONS The fluxes of muons and neutrinos are strongly correlated, except for an uncertainty coming from that in the π/K production ratio,. Therefore, it is important to calibrate the neutrino flux calculation using the muon flux data. In our previous flux calculation [10], we compare the muon data [11] at the balloon altitude and simulated the muon flux using several hadronic interaction models. The typical muon energies were from less

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K yields at xF ∼ 0.1 without changing the multiplicities. (Hence, the quantum numbers are conserved automatically.) We assign a modification parameter to a valence quark of the projectile, and consider the same magnitude of modification for the secondary particles which have the same valence quark as the projectile. In p + Air interactions, the change of average energy are assigned as:

Figure 5. The muon fluxes measured by the BESS experiment at Tsukuba (Sept. 2002) [12] and on Mt. Norikura (Oct. 1999) [13], and by the L3+C experiment [14] are compared with the calculated muon fluxes with the model of Ref. [10].

than 1 GeV to about 10 GeV. DPMJET-III [15] was selected for our calculation of the neutrino flux. However, the muon data at the balloonaltitude were limited to the GeV regions. High quality muon data at the ground level are available [12–14]. The energy range covers from less than 1 GeV to about 1 TeV. Figure 5 compares the observed and calculated muon fluxes. They agree reasonably well in the energy range below 10 GeV. However, in the higher energy range, there is a systematic difference in the observed and calculated fluxes. The difference gets larger with the increasing muon energies. Due to the accuracy of the recent measurement of the primary cosmic ray fluxes, this discrepancy cannot be explained by the uncertainty in the observed primary cosmic ray fluxes. Therefore, we conclude that the modification of the model (DPMJET-III) for the cosmic ray interactions at high energy is needed. 3.1. Modification of the interaction models We modified [16] the hadronic interaction model based on cosmic-ray muon data. The region of xF ∼ 0.1 (where xF is the Feyman x) in the π and K production is most relevant to the atmospheric muons and neutrino fluxes. We modify the secondary spectra to change the π and

< Eπ+ >= (1 + cu ) < Eπ0 + > < Eπ− >= (1 + cd ) < Eπ0 − > < Eπ0 >= (1 + (cu + cd )/2) < Eπ0 0 > 0 < EK + >= (1 + cu ) < EK + > 0 > < EK − >=< EK − 0 < EK 0 >= (1 + cd ) < EK 0 > 0 >=< E > < EK ¯0 ¯0 K

¯ (ud) (d¯ u) ¯ ((u¯ u − dd)/2) (u¯ s) ¯ (sd) (d¯ s) ¯ (sd)

Here, cu and cd are the modification parameters assigned to the u and d quarks respectively, and the < Ei0 > is the average energy in the original DPMJET-III for the i particle. The modification of the nucleon spectra is determined after the modification for mesons are determined, so that the total energy is conserved to be equal to that of the projectile. These assumptions and parameterization naturally relate the K and π productions through the parameters assigned for the u and d quarks. For the n + Air interactions, we assume iso-symmetry. We tuned the cu ’s and cd ’s to minimize the difference between calculations and observations. In this study, we used the muon flux data from L3+C above 60 GeV/c, and BESS at Tsukuba for all the momentum region. We found that cu and cd shown in Fig. 6(top) give the best result. The kinks seen at around 10 GeV are due to the connection to the NUCRIN interaction model at the lower energies. The difference between cu and cd results from a requirement that the calculated muon charge ratio should agree with the data. We call thus modified interaction model as “modified DPMJETIII”. We compared the energy distributions of the secondary particles for the original and modified DPMJET-III in Fig. 6(bottom). We notice that the energy fraction carried by π + , π − and K + for the modified DPMJET-III increases gradually with the increasing projectile energy. As a result, the energy fraction carried by p and n decreases with the increasing projectile energy.

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Figure 6. Top: The best modification parameters for DPMHET-III [15], as a function of Eproj . Bottom: The ratio of the average energy of secondary particles to the projectile energy. The dashed and solid lines show the results from the original and modified DPMJET-III, respectively.

Figure 7 compares the observed and calculated muons fluxes based on the modified interaction model. We carried out the same procedure using different interaction models (Fluka97 [17] and Fritiof7.02 [18]). The calculated muon fluxes based on these modified interaction models agree well with the data. 3.2. Neutrino flux Atmospheric neutrino flux is calculated [19] based on the modified DPMJET-III. Since the original flux calculation predicted too low muon flux above a few tens of GeV, the calculated neutrino flux reported in Ref. [10] must have predicted too low neutrino flux at the high energies. Figure 8 compares the neutrino fluxes before and after the modification of the hadronic

interaction model. As expected the calculation with the modified interaction model predicts the higher neutrino flux above ∼10 GeV. The (νμ /ν μ ) and (νe /ν e ) flux ratios are also changed due to the modification of the interaction model to reproduce the observed μ+ /μ− ratio. We notice that the predicted flux of upward through going muons in the previous calculation was too low as seen in Fig. 1. It seems that this problem is fixed by calibrating the hadronic interaction model based on the muon data. Finally, we discuss the systematic uncertainty in the absolute flux based on the present calculation. The main source of the uncertainty is the error in the experimental muon flux. Also, the uncertainty due to that of the (K/π) production ratio in the hadronic interaction must be separately evaluated. In order to estimate the uncertainty due to the uncertainty in the (K/π) production ratio, we simply compared the 3 calculated neutrino fluxes based on different modified interaction models [15,17,18]. These 3 modified interaction models reproduce the observed muon fluxes equally well. Therefore the difference in the neutrino flux for these 3 models should be mostly due to the difference in the K production. The uncertainty in the absolute flux is rather small in the 1 to 10 GeV energy region (about 7 to 8 %).

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ACKNOWLEDGEMENTS The author would like to thank the colleagues in the Super-Kamiokande collaboration for discussions on the neutrino data. The author would like to thank M.Honda, T.Sanuki, K.Kasahara and S.Midorikawa for many useful comments. This work was partly supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology and by the Japan Society for the Promotion of Science. REFERENCES

Figure 8. Left: The comparison of the atmospheric neutrino fluxes calculated with modified and original DPMJET-III. The denominator is the original DPMJET-III. Right: Flux ratios calculated with modified DPMJET-III (solid line) and original DPMJET-III (dashed line).

Figure 9. The estimated uncertainty in the absolute flux together with the error sources [19].

4. SUMMARY Present atmospheric neutrino data are consistently explained by νμ ↔ ντ oscillations. The efforts to improve the flux calculation are continuing. Especially recent high precision cosmic ray muon data are very useful to constrain the hadronic interactions around TeV. Present work suggests that calibrating the hadronic interactions with the atmospheric muons is a powerful method. The uncertainty in the absolute atmospheric neutrino flux is reduced substantially.

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