# R(${{\boldsymbol \nu}_{{\mu}}}$) = (Measured Flux of ${{\boldsymbol \nu}_{{\mu}}}$) $/$ (Expected Flux of ${{\boldsymbol \nu}_{{\mu}}}$) INSPIRE search

VALUE DOCUMENT ID TECN  COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.84$ $\pm0.12$ 1
 2006
MINS MINOS atmospheric
$0.72$ $\pm0.026$ $\pm0.13$ 2
 2001
MCRO upward through-going
$0.57$ $\pm0.05$ $\pm0.15$ 3
 2000
MCRO upgoing partially contained
$0.71$ $\pm0.05$ $\pm0.19$ 4
 2000
MCRO downgoing partially contained + upgoing stopping
$0.74$ $\pm0.036$ $\pm0.046$ 5
 1998
MCRO Streamer tubes
6
 1991
IMB Water Cherenkov
7
 1989
NUSX
$0.95$ $\pm0.22$ 8
 1981
Baksan
$0.62$ $\pm0.17$
 1978
Case Western/UCI
1  ADAMSON 2006 uses a measurement of 107 total neutrinos compared to an expected rate of $127$ $\pm13$ without oscillations.
2  AMBROSIO 2001 result is based on the upward through-going muon tracks with $\mathit E_{{{\mathit \mu}}}>1$ GeV. The data came from three different detector configurations, but the statistics is largely dominated by the full detector run, from May 1994 to December 2000. The total live time, normalized to the full detector configuration, is $6.17$ years. The first error is the statistical error, the second is the systematic error, dominated by the theoretical error in the predicted flux.
3  AMBROSIO 2000 result is based on the upgoing partially contained event sample. It came from 4.1 live years of data taking with the full detector, from April 1994 to February 1999. The average energy of atmospheric muon neutrinos corresponding to this sample is 4$~$GeV. The first error is statistical, the second is the systematic error, dominated by the 25$\%$ theoretical error in the rate (20$\%$ in the flux and 15$\%$ in the cross section, added in quadrature). Within statistics, the observed deficit is uniform over the zenith angle.
4  AMBROSIO 2000 result is based on the combined samples of downgoing partially contained events and upgoing stopping events. These two subsamples could not be distinguished due to the lack of timing information. The result came from 4.1 live years of data taking with the full detector, from April 1994 to February 1999. The average energy of atmospheric muon neutrinos corresponding to this sample is 4$~$GeV. The first error is statistical, the second is the systematic error, dominated by the 25$\%$ theoretical error in the rate (20$\%$ in the flux and 15$\%$ in the cross section, added in quadrature). Within statistics, the observed deficit is uniform over the zenith angle.
5  AMBROSIO 1998 result is for all nadir angles and updates AHLEN 1995 result. The lower cutoff on the muon energy is 1$~$GeV. In addition to the statistical and systematic errors, there is a Monte Carlo flux error (theoretical error) of $\pm0.13$. With a neutrino oscillation hypothesis, the fit either to the flux or zenith distribution independently yields sin$^22\theta =1.0$ and $\Delta \mathit m{}^{2}\sim{}$ a few times $10^{-3}$ eV${}^{2}$. However, the fit to the observed zenith distribution gives a maximum probability for $\chi {}^{2}$ of only 5$\%$ for the best oscillation hypothesis.
6  CASPER 1991 correlates showering/nonshowering signature of single-ring events with parent atmospheric-neutrino flavor. They find nonshowering ($\approx{}{{\mathit \nu}_{{\mu}}}$ induced) fraction is $0.41$ $\pm0.03$ $\pm0.02$, as compared with expected $0.51$ $\pm0.05$ (syst).
7  AGLIETTA 1989 finds no evidence for any anomaly in the neutrino flux. They define $\rho$ = (measured number of ${{\mathit \nu}_{{e}}}$'s)/(measured number of ${{\mathit \nu}_{{\mu}}}$'s). They report $\rho$(measured)=$\rho$(expected) = $0.96$ ${}^{+0.32}_{-0.28}$.
8  From this data BOLIEV 1981 obtain the limit $\Delta \mathit m{}^{2}{}\leq{}$ $6 \times 10^{-3}$ eV${}^{2}$ for maximal mixing, ${{\mathit \nu}_{{\mu}}}$ $\nrightarrow$ ${{\mathit \nu}_{{\mu}}}$ type oscillation.
References:
PR D73 072002 First Observations of Separated Atmospheric ${{\mathit \nu}_{{\mu}}}$ and ${{\overline{\mathit \nu}}_{{\mu}}}$ Events in the MINOS Detector
 AMBROSIO 2001
PL B517 59 Matter Effects in Upward Going Muons and Sterile Neutrino Oscillations
 AMBROSIO 2000
PL B478 5 Low Energy Atmospheric Muon Neutrinos in MACRO
 AMBROSIO 1998
PL B434 451 Measurement of the Atmospheric Neutrino Induced Upgoing Muon Flux using MACRO
 CASPER 1991
PRL 66 2561 Measurement of Atmospheric Neutrino Composition with IMB-3
 AGLIETTA 1989
EPL 8 611 Experimental Study of Atmospheric Neutrino Flux in the NUSEX Experiment
 BOLIEV 1981
SJNP 34 787 Limitations on Parameters of Neutrino Oscillations According to Data of Baksan Underground Telescope
 CROUCH 1978
PR D18 2239 Cosmic Ray Muon Fluxes Deep Underground: Intensity vs Depth, and the Neutrino Induced Component