Atmospheric Neutrino Experiments

To be able to compare between the various experiments while taking into account the different detection efficiencies, the experimental results are expressed as a ``ratio of ratios'':

$$R_{atm} = \frac{\left(\nu_{\mu}+ \overline{\nu_{\mu}} / \nu_{e}+ ... ...eft(\nu_{\mu}+ \overline{\nu_{\mu}} / \nu_{e}+ \overline{\nu_{e}} \right)_{MC}}$$ (3.39)

• Fréjus
  

  The Fréjus detector, located near the center of the Fréjus tunnel in South-East France, was a high-resolution iron calorimeter of 900 ton mass. Datataking started in February 1984 with a mass of 240 ton and ended in September 1988. The detector mass had been gradually upgraded to reach 900 ton in June 1985. The total exposure corresponds to 2.0 kton-year.

  The trigger requirements imposed a threshold of about 200 MeV in electromagnetic energy. This led to an average trigger rate of about 45 events per hour, of which half were due to atmospheric muons while the rest was induced by local radioactivity and electronic noise. Atmospheric neutrinos produced about one event per week.

  The total data sample consists of 216 events. The events are fully compatible with neutrino interactions and do not resemble for example neutrons coming from the surrounding rock. After classification into electron-like, muon-like and neutral-current like events [Ber89], the result obtained is [Dau95]:

  $$R_{atm}^{Fr\acute{e}jus} = 1.00 \pm 0.15 (stat.) \pm 0.08 (syst)$$ (3.40)

  
  
  which is in excellent agreement with the theoretical prediction.

  Note that the Fréjus experiment does not restrict its analysis to quasi-elastic events like the other experiments do.

• Soudan 2
  

  Soudan 2 is also a tracking calorimeter. Its total mass is 963 tons, mainly provided by corrugated steel. The data considered in the most recent published analysis [All97] have been collected between April 1989 and December 1993, corresponding to an exposure of 1.52 kton-year.

  The analysis method has been chosen to emulate the analysis used for the water Cerenkov detectors (see below), such that only single track (muon) and single shower (electron) events are used. A future analysis using the track reconstruction and separation properties of the detector is foreseen.

  After correcting for the background produced by photons and neutrons originating in the rock around the detector, 86.4 events are kept, yielding the result

  $$R_{atm}^{Soudan 2} = 0.72 \pm 0.19 (stat.) \ ^{+0.05}_{-0.07} (syst)$$ (3.41)

  
  

  A new result has been presented at the 1997 EPS conference [Nak97] for a total exposure of 2.83 kton-year:

  $$R_{atm}^{Soudan 2} = 0.61 \pm 0.14 (stat.) \ ^{+0.05}_{-0.07} (syst)$$ (3.42)

  
  

• IMB
  

  The IMB detector is an 8 kton water Cerenkov detector located in the Morton Salt Mine near Cleveland, Ohio. For the atmospheric neutrino study, data collected from May 1986 to March 1991 was considered, using a fiducial volume of 3.3 kton for a total exposure of 7.7 kton-year.

  The event selection threshold is about $50 \ MeV$ (70 photomultiplier tubes to be precise). Analysis of the geometry and intensity of the Cerenkov hit pattern provides a fairly reliable means of particle identification, but since the aim is to determine the neutrino flavor, only single-ring events (quasi-elastics) are used to achieve maximal purity. Electron-like events produce a diffuse showering pattern associated with the electron (or positron), while muon-like events result in a much sharper, nonshowering pattern. The correlation between $\nu_{e}(\nu_{\mu})$-induced events and single-ring (non)-showering events is found to be $87 \pm 1 (stat) \% \ (92 \pm 1 (stat) \%)$.

  The result for the ratio is [Bec92]:

  $$R_{atm}^{IMB} = 0.54 \pm 0.05 (stat.) \pm 0.11 (syst)$$ (3.43)

  
  
  But this significantly low ratio seems to be independent of the zenith angle, suggesting it is not related to the distance from the neutrino production point.

• (Super-)Kamiokande
  

  We have already described the (Super-)Kamiokande detector in section 3.3.2.

  For the atmospheric neutrino analysis, the Kamiokande group has divided the data in two samples: the sub-GeV sample contains events with a visible energy $< 1.33 \ GeV$, while the multi-GeV sample contains the events with visible energy $> 1.33 \ GeV$. They have also considered two different types of events: fully contained and partially contained. To improve the purity of the partially contained sample, only muon-like events are considered. The total exposure time is 8.2 kton-year for the fully contained sample and 6.0 kton-year for the partially contained sample (the fiducial volume is slightly smaller for the latter).

  As opposed to IMB, the Kamiokande group has used about 30 % of the multiple ring events for the study of the muon-like to electron-like ratio. They require that 80 % of the total visible energy be seen in one ring to be able to identify the neutrino flavor. Note that this is only done for fully contained events.

  These are the results obtained by Kamiokande [Fuk94]:
  

  $$R_{atm}^{Kamiokande}(sub-GeV) = 0.60 \ ^{+0.06}_{-0.05} (stat.) \pm 0.05 (syst)$$ (3.44)

  $$R_{atm}^{Kamiokande}(multi-GeV) = 0.57 \ ^{+0.08}_{-0.07} (stat.) \pm 0.07 (syst)$$ (3.45)

  
  
  We see that like IMB this result is significantly lower than expectation.
  

  Table 3.3: Distribution of fully contained, multi-GeV Kamiokande events between single ring (SR) and multiple ring (MR) for data and two Monte Carlo simulations (the numbers between brackets come from the second simulation). The difference between the two Monte Carlo simulations is the predicted neutrino flux.

  	Data SR	Data MR	MC SR	MC MR
  $e$-like	73	25	45.9 (49.1)	20.7 (21.6)
  $\mu$-like	21	10	25.8 (27.3)	12 (13.2)
  Total	195		181.0 (189.1)

  
  But we'd like to draw the attention of the reader to table (3.3) where the distribution of fully contained, Multi-GeV events between the various categories is given. Compared to the simulation, there is an excess of electron-like events, but this excess is only significant in the single ring events. For the multiple ring events, the excess seems to be about 10 %, well within the statistical error.

  The Kamiokande group has also studied the angular dependence of the ratio [Fuk94]. Whereas the sub-GeV sample looks perfectly flat, the multi-GeV sample seems to exhibit a clear angular dependence, with a strong suppression for upward-going events and no suppression for downward-going neutrinos. The Kamiokande Collaboration claimed that their data excluded independence of angle at the 99 % C.L., but a reanalysis of the errors by D. Saltzberg [Sal95] showed that this is really only 95 %.

  At the 1997 summer conferences, preliminary data from a 20.1 kt-year exposure of Super-Kamiokande were shown for the first time [Nak97,Tot97]. Although a paper is not yet available, we can cite the results assuming the analysis is very similar to the Kamiokande analysis:
  

  $$R_{atm}^{Super-K}(sub-GeV) = 0.64 \pm 0.04 (stat.) \pm 0.05 (syst)$$ (3.46)

  $$R_{atm}^{Super-K}(multi-GeV) = 0.60 \pm 0.05 (stat.) \pm 0.07 (syst)$$ (3.47)

  
  
  These numbers are fully compatible with the earlier results of Kamiokande.

  Angular dependence plots were also shown and now the multi-GeV data does not exhibit a clear angular dependence anymore while the sub-GeV data on the other hand appears to follow a slight slope. But the data is presented in a histogram ranging from $cos\theta = -1$ to $cos\theta = 1$^3.4 divided in 5 bins. Since the angular correlation between the neutrino direction and the charged lepton has an r.m.s. $\approx 60^{o}$ for the sub-GeV data [Fuk94], neighboring bins cannot have very different values and much care has to be taken before drawing any conclusions.

  O. Ryazhskaya suggested [Rya94] that electron neutrino interactions could be faked by the reaction $n + A \rightarrow \pi^{0} + X$, where the neutron is produced in a muon interaction in the rock surrounding the detector. A study from the Kamiokande Collaboration has since then showed [Fuk96b] that this contamination is lower than 1.2 %.