(B) Three-neutrino mixing parameters

$\Delta $m${}^{2}_{32}$ INSPIRE search

The sign of $\Delta $m${}^{2}_{32}$ is not known at this time. If given, values are shown separately for the normal and inverted mass ordering. Unless otherwise specified, the ranges below correspond to the projection onto the $\Delta $m${}^{2}_{32}$ axis of the 90$\%$ CL contours in the sin$^2(2\theta _{23})$ $−$ $\Delta $m${}^{2}_{32}$ plane presented by the authors. If uncertainties are reported with the value, they correspond to one standard deviation uncertainty.

VALUE ($ 10^{-3} $ eV${}^{2}$) DOCUMENT ID TECN  COMMENT
$\bf{ -2.56 \pm0.04}$ OUR FIT  Assuming inverted mass hierarchy
$\bf{ 2.51 \pm0.05}$ OUR FIT  Error includes scale factor of 1.1.  Assuming normal mass hierarchy
$2.54$ $\pm0.08$ 1
ABE
2017F
T2K Normal mass ordering with neutrinos and antineutrinos
$-2.51$ $\pm0.08$ 1
ABE
2017F
T2K Inverted mass ordering with neutrinos and antineutrinos
$2.67$ $\pm0.11$
ADAMSON
2017A
NOVA 3${{\mathit \nu}}$ osc; normal mass ordering
$-2.72$ $\pm0.11$
ADAMSON
2017A
NOVA 3${{\mathit \nu}}$ osc; inverted mass ordering
$2.45$ $\pm0.06$ $\pm0.06$ 2
AN
2017A
DAYA 3${{\mathit \nu}}$ osc; normal mass ordering
$-2.56$ $\pm0.06$ $\pm0.06$ 2
AN
2017A
DAYA 3${{\mathit \nu}}$ osc; inverted mass ordering
$2.56$ ${}^{+0.21}_{-0.23}$ ${}^{+0.12}_{-0.13}$ 3
CHOI
2016
RENO 3${{\mathit \nu}}$ osc; normal mass ordering
$-2.69$ ${}^{+0.23}_{-0.21}$ ${}^{+0.13}_{-0.12}$ 3
CHOI
2016
RENO 3${{\mathit \nu}}$ osc; inverted mass ordering
$2.72$ ${}^{+0.19}_{-0.20}$ 4
AARTSEN
2015A
ICCB 3${{\mathit \nu}}$ osc; normal mass ordering
$-2.73$ ${}^{+0.21}_{-0.18}$ 4
AARTSEN
2015A
ICCB 3${{\mathit \nu}}$ osc; inverted mass ordering
$2.37$ $\pm0.09$ 5
ADAMSON
2014
MINS 3${{\mathit \nu}}$ osc., accel., atmospheric; normal mass ordering
$-2.41$ ${}^{+0.09}_{-0.12}$ 5
ADAMSON
2014
MINS 3${{\mathit \nu}}$ osc., accel., atmsopheric; inverted mass ordering
• • • We do not use the following data for averages, fits, limits, etc. • • •
$2.53$ ${}^{+0.15}_{-0.13}$
ABE
2017C
T2K normal mass ordering with neutrinos
$2.55$ ${}^{+0.33}_{-0.27}$
ABE
2017C
T2K normal mass ordering with antineutrinos
$2.55$ ${}^{+0.08}_{-0.08}$
ABE
2017C
T2K Normal mass ordering with neutrinos and antineutrinos
$-2.63$ ${}^{+0.08}_{-0.08}$
ABE
2017C
T2K Inverted mass ordering with neutrinos and antineutrinos
$2.51$ ${}^{+0.29}_{-0.25}$ 6
ABE
2016D
T2K 3${{\mathit \nu}}$ osc.; normal mass ordering; ${{\overline{\mathit \nu}}}$ beam
$2.52$ ${}^{+0.20}_{-0.18}$ 7
ADAMSON
2016A
NOVA 3${{\mathit \nu}}$ osc; normal mass ordering
$-2.56$ $\pm0.19$ 7
ADAMSON
2016A
NOVA 3${{\mathit \nu}}$ osc; inverted mass ordering
$\text{2.0 - 5.0}$ 8
AGAFONOVA
2015A
OPER 90$\%$ CL, 5 events
$2.37$ $\pm0.11$ 9
AN
2015
DAYA 3${{\mathit \nu}}$ osc.; normal mass ordering
$-2.47$ $\pm0.11$ 9
AN
2015
DAYA 3${{\mathit \nu}}$ osc.; inverted mass ordering
$2.51$ $\pm0.10$ 10
ABE
2014
T2K 3${{\mathit \nu}}$ osc.; normal mass ordering
$-2.56$ $\pm0.10$ 10
ABE
2014
T2K 3${{\mathit \nu}}$ osc.; inverted mass ordering
$2.54$ ${}^{+0.19}_{-0.20}$ 11
AN
2014
DAYA 3${{\mathit \nu}}$ osc.; normal mass ordering
$-2.64$ ${}^{+0.20}_{-0.19}$ 11
AN
2014
DAYA 3${{\mathit \nu}}$ osc.; inverted mass ordering
$2.48$ ${}^{+0.05}_{-0.07}$ 12
FORERO
2014
FIT 3${{\mathit \nu}}$; normal mass ordering
$-2.38$ ${}^{+0.06}_{-0.05}$ 12
FORERO
2014
FIT 3${{\mathit \nu}}$; inverted mass ordering
$2.457$ $\pm0.047$ 13, 14
GONZALEZ-GARC..
2014
FIT Normal mass ordering; global fit
$-2.449$ ${}^{+0.047}_{-0.048}$ 13
GONZALEZ-GARC..
2014
FIT Inverted mass ordering; global fit
$2.3$ ${}^{+0.6}_{-0.5}$ 15
AARTSEN
2013B
ICCB DeepCore, 2${{\mathit \nu}}$ oscillation
$2.44$ ${}^{+0.17}_{-0.15}$ 16
ABE
2013G
T2K 3${{\mathit \nu}}$ osc.; normal mass ordering
$2.41$ ${}^{+0.09}_{-0.10}$ 17
ADAMSON
2013B
MINS 2${{\mathit \nu}}$ osc.; beam + atmospheric; identical ${{\mathit \nu}}$ $\&$ ${{\overline{\mathit \nu}}}$
$\text{2.2 - 3.1}$ 18
ABE
2012A
T2K off-axis beam
$2.62$ ${}^{+0.31}_{-0.28}$ $\pm0.09$ 19
ADAMSON
2012
MINS ${{\overline{\mathit \nu}}}$ beam
$\text{1.35 - 2.55}$ 20, 21
ADAMSON
2012B
MINS MINOS atmospheric
$\text{1.4 - 5.6}$ 20, 22
ADAMSON
2012B
MINS MINOS pure atmospheric ${{\mathit \nu}}$
$\text{0.9 - 2.5}$ 20, 22
ADAMSON
2012B
MINS MINOS pure atmospheric ${{\overline{\mathit \nu}}}$
$\text{1.8 - 5.0}$ 23
ADRIAN-MARTIN..
2012
ANTR atm. ${{\mathit \nu}}$ with deep see telescope
$\text{1.3 - 4.0}$ 24
ABE
2011C
SKAM atmospheric ${{\overline{\mathit \nu}}}$
$2.32$ ${}^{+0.12}_{-0.08}$
ADAMSON
2011
MINS 2${{\mathit \nu}}$ oscillation; maximal mixing
$3.36$ ${}^{+0.46}_{-0.40}$ 25
ADAMSON
2011B
MINS ${{\overline{\mathit \nu}}}$ beam
$\text{< 3.37}$ 26
ADAMSON
2011C
MINS MINOS
$\text{1.9 - 2.6}$ 27
WENDELL
2010
SKAM 3${{\mathit \nu}}$ osc.; normal mass ordering
$\text{-1.7 - -2.7}$ 27
WENDELL
2010
SKAM 3${{\mathit \nu}}$ osc.; inverted mass ordering
$2.43$ $\pm0.13$
ADAMSON
2008A
MINS MINOS
$\text{0.07 - 50}$ 28
ADAMSON
2006
MINS atmospheric ${{\mathit \nu}}$ with far detector
$\text{1.9 - 4.0}$ 29, 30
AHN
2006A
K2K KEK to Super-K
$\text{2.2 - 3.8}$ 31
MICHAEL
2006
MINS MINOS
$\text{1.9 - 3.6}$ 29
ALIU
2005
K2K KEK to Super-K
$\text{0.3 - 12}$ 32
ALLISON
2005
SOU2
$\text{1.5 - 3.4}$ 33
ASHIE
2005
SKAM atmospheric neutrino
$\text{0.6 - 8.0}$ 34
AMBROSIO
2004
MCRO MACRO
$1.9\text{ to }3.0 $ 35
ASHIE
2004
SKAM L/E distribution
$\text{1.5 - 3.9}$ 36
AHN
2003
K2K KEK to Super-K
$\text{0.25 - 9.0}$ 37
AMBROSIO
2003
MCRO MACRO
$\text{0.6 - 7.0}$ 38
AMBROSIO
2003
MCRO MACRO
$\text{0.15 - 15}$ 39
SANCHEZ
2003
SOU2 Soudan-2 Atmospheric
$\text{0.6 - 15}$ 40
AMBROSIO
2001
MCRO upward ${{\mathit \mu}}$
$\text{1.0 - 6.0}$ 41
AMBROSIO
2001
MCRO upward ${{\mathit \mu}}$
$\text{1.0 - 50}$ 42
FUKUDA
1999C
SKAM upward ${{\mathit \mu}}$
$\text{1.5 - 15.0}$ 43
FUKUDA
1999D
SKAM upward ${{\mathit \mu}}$
$\text{0.7 - 18}$ 44
FUKUDA
1999D
SKAM stop ${{\mathit \mu}}$ $/$ through
$\text{0.5 - 6.0}$ 45
FUKUDA
1998C
SKAM Super-Kamiokande
$\text{0.55 - 50}$ 46
HATAKEYAMA
1998
KAMI Kamiokande
$\text{4 - 23}$ 47
HATAKEYAMA
1998
KAMI Kamiokande
$\text{5 - 25}$ 48
FUKUDA
1994
KAMI Kamiokande
1  Supersedes ABE 2017C.
2  AN 2017A report results from combined rate and spectral shape analysis of 1230 days of data taken with the Daya Bay reactor experiment. The data set contains more than $2.5 \times 10^{6}$ inverse beta-decay events with neutron capture on ${}^{}\mathrm {Gd}$. The fit to the data gives $\Delta {}^{2}_{ee}=0.00250$ $\pm0.00006$ $\pm0.00006$ eV. Supersedes AN 2015 .
3  CHOI 2016 reports result of the RENO experiment from a rate and shape analysis of 500 days of data. A simultaneous fit to $\theta _{13}$ and $\Delta $m${}^{2}_{ee}$ yields $\Delta $m${}^{2}_{ee}$ = $0.00262$ ${}^{+.00021}_{-.00023}{}^{+.00012}_{-.00013}$ eV. We convert the results to $\Delta $m${}^{2}_{32}$ using PDG 2014 values of sin$^2({{\mathit \theta}_{{12}}})$ and $\Delta $m${}^{2}_{21}$.
4  AARTSEN 2015A obtains this result by a three-neutrino oscillation analysis using $10 - 100$ GeV muon neutrino sample from a total of 953 days of measurements with the low-energy subdetector DeepCore of the IceCube neutrino telescope.
5  ADAMSON 2014 uses a complete set of accelerator and atmospheric data. The analysis combines The analysis combines the ${{\mathit \nu}_{{\mu}}}$ disappearance and ${{\mathit \nu}_{{e}}}$ appearance data using three-neutrino oscillation fit. The fit results are obtained for normal and inverted mass ordering assumptions.
6  ABE 2016D reports oscillation results using ${{\overline{\mathit \nu}}_{{\mu}}}$ disappearance in an off-axis beam.
7  Superseded by ADAMSON 2017A.
8  AGAFONOVA 2015A result is based on 5 ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{\tau}}}$ appearance candidates with an expected background of $0.25$ $\pm0.05$ events. The best fit is for $\Delta $m${}^{2}_{32}=3.3 \times 10^{-3}$ eV${}^{2}$.
9  AN 2015 uses all eight identical detectors, with four placed near the reactor cores and the remaining four at the far hall to determine prompt energy spectra. The results correspond to the exposure of $6.9 \times 10^{5}$ GW$_{th}$-ton-days. They derive $\Delta $m${}^{2}_{ee}$ = $0.00242$ $\pm0.00011$ eV${}^{2}$. Assuming the normal (inverted) ordering, the fitted $\Delta $m${}^{2}_{32}$ = $0.00237$ $\pm0.00011$ ($0.00247$ $\pm0.00011$) eV${}^{2}$. Superseded by AN 2017A.
10  ABE 2014 results are based on ${{\mathit \nu}_{{\mu}}}$ disappearance using three-neutrino oscillation fit. The confidence intervals are derived from one dimensional profiled likelihoods. In ABE 2014 the inverted mass ordering result is reported as $\Delta $m${}^{2}_{13}$ = $0.00248$ $\pm0.00010$ eV${}^{2}$ which we converted to $\Delta $m${}^{2}_{32}$ by adding PDG 2014 value of $\Delta $m${}^{2}_{21}$ = ($7.53$ $\pm0.18$) $ \times 10^{-5}$ eV${}^{2}$. Superseded by ABE 2017C.
11  AN 2014 uses six identical detectors, with three placed near the reactor cores (flux-weighted baselines of 512 and 561 m) and the remaining three at the far hall (at the flux averaged distance of 1579 m from all six reactor cores) to determine prompt energy spectra and derive $\Delta $m${}^{2}_{ee}$ = $0.00259$ ${}^{+.00019}_{-.00020}$ eV${}^{2}$. Assuming the normal (inverted) ordering, the fitted $\Delta $m${}^{2}_{32}$ = $0.00254$ ${}^{+.00019}_{-.00020}$ ($0.00264$ ${}^{+.00019}_{-.00020}$) eV${}^{2}$. Superseded by AN 2015 .
12  FORERO 2014 performs a global fit to $\Delta $m${}^{2}_{31}$ using solar, reactor, long-baseline accelerator, and atmospheric neutrino data.
13  GONZALEZ-GARCIA 2014 result comes from a frequentist global fit. The corresponding Bayesian global fit to the same data results are reported in BERGSTROM 2015 as $0.002460$ $\pm0.000046$ eV${}^{2}$ for normal and $0.002445$ ${}^{+.000047}_{-.000045}$ eV${}^{2}$ for inverted mass ordering.
14  The value for normal mass ordering is actually a measurement of $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$ which differs from $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ by a much smaller value of $\Delta {{\mathit m}^{2}}_{\mathrm {12}}$.
15  AARTSEN 2013B obtained this result by a two-neutrino oscillation analysis using $20 - 100$ GeV muon neutrino sample from a total of 318.9 days of live-time measurement with the low-energy subdetector DeepCore of the IceCube neutrino telescope.
16  Based on the observation of 58 ${{\mathit \nu}_{{\mu}}}$ events with $205$ $\pm17$(syst) expected in the absence of neutrino oscillations. Superseded by ABE 2014 .
17  ADAMSON 2013B obtained this result from ${{\mathit \nu}_{{\mu}}}$ and ${{\overline{\mathit \nu}}_{{\mu}}}$ disappearance using ${{\mathit \nu}_{{\mu}}}$ ($10.71 \times 10^{20}$ POT) and ${{\overline{\mathit \nu}}_{{\mu}}}$ ($3.36 \times 10^{20}$ POT) beams, and atmospheric (37.88 kton-years) data from MINOS. The fit assumed two-flavor neutrino hypothesis and identical ${{\mathit \nu}_{{\mu}}}$ and ${{\overline{\mathit \nu}}_{{\mu}}}$ oscillation parameters.
18  ABE 2012A obtained this result by a two-neutrino oscillation analysis. The best-fit point is $\Delta $m${}^{2}_{32}$ = $2.65 \times 10^{-3}$ eV${}^{2}$.
19  ADAMSON 2012 is a two-neutrino oscillation analysis using antineutrinos.
20  ADAMSON 2012B obtained this result by a two-neutrino oscillation analysis of the L/E distribution using 37.9 kton$\cdot{}$yr atmospheric neutrino data with the MINOS far detector.
21  The 90$\%$ single-parameter confidence interval at the best fit point is $\Delta $m${}^{2}$ = $0.0019$ $\pm0.0004$ eV${}^{2}$.
22  The data are separated into pure samples of ${{\mathit \nu}}$s and ${{\overline{\mathit \nu}}}$s, and separate oscillation parameters for ${{\mathit \nu}}$s and ${{\overline{\mathit \nu}}}$s are fit to the data. The best fit point is ($\Delta $m${}^{2}$, sin$^22\theta $) = (0.0022 eV${}^{2}$, 0.99) and ($\Delta \bar m{}^{2}$, sin$^22{{\overline{\mathit \theta}}}$) = (0.0016 eV${}^{2}$, 1.00). The quoted result is taken from the 90$\%$ C.L. contour in the ($\Delta $m${}^{2}$, sin$^22\theta $) plane obtained by minimizing the four parameter log-likelihood function with respect to the other oscillation parameters.
23  ADRIAN-MARTINEZ 2012 measured the oscillation parameters of atmospheric neutrinos with the ANTARES deep sea neutrino telescope using the data taken from 2007 to 2010 (863 days of total live time).
24  ABE 2011C obtained this result by a two-neutrino oscillation analysis with separate mixing parameters between neutrinos and antineutrinos, using the Super-Kamiokande-I+II+III atmospheric neutrino data. The corresponding 90$\%$ CL neutrino oscillation parameter range obtained from this analysis is $\Delta {{\mathit m}^{2}}_{\mathrm {}}$ = $1.7 - 3.0$ eV${}^{2}$.
25  ADAMSON 2011B obtained this result by a two-neutrino oscillation analysis of antineutrinos in an antineutrino enhanced beam with $1.71 \times 10^{20}$ protons on target. This results is consistent with the neutrino measurements of ADAMSON 2011 at 2$\%$ C.L.
26  ADAMSON 2011C obtains this result based on a study of antineutrinos in a neutrino beam and assumes maximal mixing in the two-flavor approximation.
27  WENDELL 2010 obtained this result by a three-neutrino oscillation analysis with one mass scale dominance ($\Delta $m${}^{2}_{21}$ = 0) using the Super-Kamiokande-I+II+III atmospheric neutrino data, and updates the HOSAKA 2006A result.
28  ADAMSON 2006 obtained this result by a two-neutrino oscillation analysis of the L/E distribution using 4.54 kton yr atmospheric neutrino data with the MINOS far detector.
29  The best fit in the physical region is for $\Delta \mathit m{}^{2}$ = $2.8 \times 10^{-3}$ eV${}^{2}$.
30  Supercedes ALIU 2005 .
31  MICHAEL 2006 best fit is $2.74 \times 10^{-3}$ eV${}^{2}$. See also ADAMSON 2008 .
32  ALLISON 2005 result is based on an atmospheric neutrino observation with an exposure of 5.9 kton yr. From a two-flavor oscillation analysis the best-fit point is $\Delta \mathit m{}^{2}$ = 0.0017 eV${}^{2}$ and sin$^22 \theta $ = 0.97.
33  ASHIE 2005 obtained this result by a two-neutrino oscillation analysis using 92 kton yr atmospheric neutrino data from the complete Super-Kamiokande I running period. The best fit is for $\Delta $ = $2.1 \times 10^{-3}$ eV${}^{2}$.
34  AMBROSIO 2004 obtained this result, without using the absolute normalization of the neutrino flux, by combining the angular distribution of upward through-going muon tracks with ${{\mathit E}_{{\mu}}}$ $>$ 1 GeV, N$_{low}$ and N$_{high}$, and the numbers of InDown + UpStop and InUp events. Here, N$_{low}$ and N$_{high}$ are the number of events with reconstructed neutrino energies $<$ 30 GeV and $>$ 130 GeV, respectively. InDown and InUp represent events with downward and upward-going tracks starting inside the detector due to neutrino interactions, while UpStop represents entering upward-going tracks which stop in the detector. The best fit is for $\Delta \mathit m{}^{2}$ = $2.3 \times 10^{-3}$ eV${}^{2}$.
35  ASHIE 2004 obtained this result from the L(flight length)/E(estimated neutrino energy) distribution of ${{\mathit \nu}_{{\mu}}}$ disappearance probability, using the Super-Kamiokande-I 1489 live-day atmospheric neutrino data. The best fit is for $\Delta \mathit m{}^{2}$ = $2.4 \times 10^{-3}$ eV${}^{2}$.
36  There are several islands of allowed region from this K2K analysis, extending to high values of $\Delta \mathit m{}^{2}$. We only include the one that overlaps atmospheric neutrino analyses. The best fit is for $\Delta \mathit m{}^{2}$ = $2.8 \times 10^{-3}$ eV${}^{2}$.
37  AMBROSIO 2003 obtained this result on the basis of the ratio R = N$_{low}/N_{high}$, where N$_{low}$ and N$_{high}$ are the number of upward through-going muon events with reconstructed neutrino energy $<$ 30 GeV and $>$ 130 GeV, respectively. The data came from the full detector run started in 1994. The method of FELDMAN 1998 is used to obtain the limits. The best fit is for $\Delta \mathit m{}^{2}$ = $2.5 \times 10^{-3}$ eV${}^{2}$.
38  AMBROSIO 2003 obtained this result by using the ratio R and the angular distribution of the upward through-going muons. R is given in the previous note and the angular distribution is reported in AMBROSIO 2001 . The method of FELDMAN 1998 is used to obtain the limits. The best fit is for $\Delta \mathit m{}^{2}$ = $2.5 \times 10^{-3}$ eV${}^{2}$.
39  SANCHEZ 2003 is based on an exposure of 5.9 kton yr. The result is obtained using a likelihood analysis of the neutrino L/E distribution for a selection ${{\mathit \mu}}$ flavor sample while the ${{\mathit e}}$-flavor sample provides flux normalization. The method of FELDMAN 1998 is used to obtain the allowed region. The best fit is for $\Delta \mathit m{}^{2}$ = $5.2 \times 10^{-3}$ eV${}^{2}$.
40  AMBROSIO 2001 result is based on the angular distribution of upward through-going muon tracks with ${{\mathit E}_{{\mu}}}$ $>$ 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 best fit is obtained outside the physical region. The method of FELDMAN 1998 is used to obtain the limits.
41  AMBROSIO 2001 result is based on the angular distribution and normalization of upward through-going muon tracks with ${{\mathit E}_{{\mu}}}$ $>$ 1 GeV. See the previous footnote.
42  FUKUDA 1999C obtained this result from a total of 537 live days of upward through-going muon data in Super-Kamiokande between April 1996 to January 1998. With a threshold of ${{\mathit E}_{{\mu}}}$ $>$ 1.6 GeV, the observed flux is ($1.74$ $\pm0.07$ $\pm0.02$) $ \times 10^{-13}$ cm${}^{-2}$s${}^{-1}$sr${}^{-1}$. The best fit is for $\Delta \mathit m{}^{2}$ = $5.9 \times 10^{-3}$ eV${}^{2}$.
43  FUKUDA 1999D obtained this result from a simultaneous fitting to zenith angle distributions of upward-stopping and through-going muons. The flux of upward-stopping muons of minimum energy of 1.6 GeV measured between April 1996 and January 1998 is ($0.39$ $\pm0.04$ $\pm0.02$) $ \times 10^{-13}$ cm${}^{-2}$s${}^{-1}$sr${}^{-1}$. This is compared to the expected flux of ($0.73$ $\pm0.16$ (theoretical error))${\times }10^{-13}$ cm${}^{-2}$s${}^{-1}$sr${}^{-1}$. The best fit is for $\Delta \mathit m{}^{2}$ = $3.9 \times 10^{-3}$ eV${}^{2}$.
44  FUKUDA 1999D obtained this result from the zenith dependence of the upward-stopping/through-going flux ratio. The best fit is for $\Delta \mathit m{}^{2}$ = $3.1 \times 10^{-3}$ eV${}^{2}$.
45  FUKUDA 1998C obtained this result by an analysis of 33.0 kton yr atmospheric neutrino data. The best fit is for $\Delta \mathit m{}^{2}$ = $2.2 \times 10^{-3}$ eV${}^{2}$.
46  HATAKEYAMA 1998 obtained this result from a total of 2456 live days of upward-going muon data in Kamiokande between December 1985 and May 1995. With a threshold of ${{\mathit E}_{{\mu}}}$ $>$ 1.6 GeV, the observed flux of upward through-going muons is ($1.94$ $\pm0.10$ ${}^{+0.07}_{-0.06}$) $ \times 10^{-13}$ cm${}^{-2}$s${}^{-1}$sr${}^{-1}$. This is compared to the expected flux of ($2.46$ $\pm0.54$ (theoretical error))${\times }10^{-13}$ cm${}^{-2}$s${}^{-1}$sr${}^{-1}$. The best fit is for $\Delta \mathit m{}^{2}$ = $2.2 \times 10^{-3}$ eV${}^{2}$.
47  HATAKEYAMA 1998 obtained this result from a combined analysis of Kamiokande contained events (FUKUDA 1994 ) and upward going muon events. The best fit is for $\Delta \mathit m{}^{2}$ = $13 \times 10^{-3}$ eV${}^{2}$.
48  FUKUDA 1994 obtained the result by a combined analysis of sub- and multi-GeV atmospheric neutrino events in Kamiokande. The best fit is for $\Delta \mathit m{}^{2}$ = $16 \times 10^{-3}$ eV${}^{2}$.
  Conservation Laws:
LEPTON FAMILY NUMBER
  References:
ABE 2017C
PR D96 011102 Updated T2K Measurements of Muon Neutrino and Antineutrino Disappearance using $1.5 \times 10^{21}$ Protons on Target
ABE 2017F
PR D96 092006 Measurement of Neutrino and Antineutrino Oscillations by the T2K Experiment Including a New Additional Sample of ${{\mathit \nu}_{{e}}}$ Interactions at the Far Detector
ADAMSON 2017A
PRL 118 151802 Measurement of the Neutrino Mixing Angle $\mathit \theta _{23}$ in NOvA
AN 2017A
PR D95 072006 Measurement of Electron Antineutrino Oscillation Based on 1230 Days of Operation of the Daya Bay Experiment
ABE 2016D
PRL 116 181801 Measurement of Muon Antineutrino Oscillations with an Accelerator-Produced Off-Axis Beam
ADAMSON 2016A
PR D93 051104 First easurement of Muon-Neutrino Disappearance in NOvA
CHOI 2016
PRL 116 211801 Observation of Energy and Baseline Dependent Reactor Antineutrino Disappearance in the RENO Experiment
AARTSEN 2015A
PR D91 072004 Determining Neutrino Oscillation Parameters from Atmospheric Muon Neutrino Disappearance with Three Years of IceCube DeepCore Data
AGAFONOVA 2015A
PRL 115 121802 Discovery of ${{\mathit \tau}}$ Neutrino Appearance in the CNGS Neutrino Beam with the OPERA Experiment
AN 2015
PRL 115 111802 A New Measurement of Antineutrino Oscillation with the Full Detector Configuration at Daya Bay
ABE 2014
PRL 112 181801 Precise Measurement of the Neutrino Mixing Parameter ${{\mathit \theta}_{{23}}}$ from Muon Neutrino Disappearance in an Off-Axis Beam
ADAMSON 2014
PRL 112 191801 Combined Analysis of ${{\mathit \nu}_{{\mu}}}$ Disappearance and ${{\mathit \nu}_{{\mu}}}\rightarrow{{\mathit \nu}_{{e}}}$ Appearance in MINOS using Accelerator and Atmospheric Neutrinos
AN 2014
PRL 112 061801 Spectral Measurement of Electron Antineutrino Oscillation Amplitude and Frequency at Daya Bay
FORERO 2014
PR D90 093006 Neutrino Oscillations Refitted
GONZALEZ-GARCIA 2014
JHEP 1411 052 Updated Fit to Three Neutrino Mixing: Status of Leptonic $\mathit CP$ Violation
AARTSEN 2013B
PRL 111 081801 Measurement of Atmospheric Neutrino Oscillations with IceCube
ABE 2013G
PRL 111 211803 Measurement of Neutrino Oscillation Parameters from Muon Neutrino Disappearance with an Off-Axis Beam
ADAMSON 2013B
PRL 110 251801 Measurement of Neutrino and Antineutrino Oscillations Using Beam and Atmospheric Data in MINOS
ABE 2012A
PR D85 031103 First Muon-Neutrino Disappearance Study with an Off-Axis Beam
ADAMSON 2012
PRL 108 191801 Improved Measurement of Muon Antineutrino Disappearance in MINOS
ADAMSON 2012B
PR D86 052007 Measurements of Atmospheric Neutrinos and Antineutrinos in the MINOS Far Detector
ADRIAN-MARTINEZ 2012
PL B714 224 Measurement of Atmospheric Neutrino Oscillations with the ANTARES Neutrino Telescope
ABE 2011C
PRL 107 241801 Search for Differences in Oscillation Parameters for Atmospheric Neutrinos and Antineutrinos at Super-Kamiokande
ADAMSON 2011B
PRL 107 021801 First Direct Observation of Muon Antineutrino Disappearance
ADAMSON 2011C
PR D84 071103 Search for the Disappearance of Muon Antineutrinos in the NuMI Neutrino Beam
ADAMSON 2011
PRL 106 181801 Measurement of the Neutrino Mass Splitting and Flavor Mixing by MINOS
WENDELL 2010
PR D81 092004 Atmospheric Neutrino Oscillation Analysis with Subleading Effects in Super-Kamiokande I, II, and III
ADAMSON 2008A
PRL 101 131802 Measurement of Neutrino Oscillations with the MINOS Detectors in the NuMI Beam
ADAMSON 2006
PR D73 072002 First Observations of Separated Atmospheric ${{\mathit \nu}_{{\mu}}}$ and ${{\overline{\mathit \nu}}_{{\mu}}}$ Events in the MINOS Detector
AHN 2006A
PR D74 072003 Measurement of Neutrino Oscillation by the K2K Experiment
MICHAEL 2006
PRL 97 191801 Observation of Muon Neutrino Disappearance with the MINOS Detectors in the NuMI Neutrino Beam
ALIU 2005
PRL 94 081802 Evidence for Muon Neutrino Oscillation in an Accelerator-Based Experiment
ALLISON 2005
PR D72 052005 Neutrino Oscillation Effects in Soudan 2 Upward-Stopping Muons
ASHIE 2005
PR D71 112005 Measurement of Atmospheric Neutrino Oscillation Parameters by Super-Kamiokande I
AMBROSIO 2004
EPJ C36 323 Measurements oa Atmospheric Muon Neutrino Oscillations, Global Analysis of the Data Collected with MACRO Detector
ASHIE 2004
PRL 93 101801 Evidence for an Oscillatory Signature in Atmospheric Neutrino Oscillation
AHN 2003
PRL 90 041801 Indications of Neutrino Oscillation in a 250 km Long Baseline Experiment
AMBROSIO 2003
PL B566 35 Atmospheric Neutrino Oscillations from Upward through Going Muon Multiple Scattering in MACRO
SANCHEZ 2003
PR D68 113004 Measurement of the Distributions of Atmospheric Neutrinos in SOUDAN2 and their Interpretation as Neutrino Oscillations
AMBROSIO 2001
PL B517 59 Matter Effects in Upward Going Muons and Sterile Neutrino Oscillations
FUKUDA 1999C
PRL 82 2644 Measurement of the Flux and Zenith Angle Distribution of Upward Through Going Muons by Super-Kamiokande
FUKUDA 1999D
PL B467 185 Neutrino Induced Upward Stopping Muons in Super-Kamiokande
FUKUDA 1998C
PRL 81 1562 Evidence for Oscillation of Atmospheric Neutrinos
HATAKEYAMA 1998
PRL 81 2016 Measurement of the Flux and Zenith Angle Distribution of Upward Through-Going Muons in Kamiokande II + III
FUKUDA 1994
PL B335 237 Atmospheric ${{\mathit \nu}_{{\mu}}}/{{\mathit \nu}_{{e}}}$ Ratio in the Multi-GeV Energy Range