$\bf{
0.547 \pm0.021}$

OUR FIT
Assuming inverted mass ordering

$\bf{
0.545 \pm0.021}$

OUR FIT
Assuming normal mass ordering

$0.56$ ${}^{+0.04}_{0.03}$ 
^{ 1} 

NOVA 
$0.56$ ${}^{+0.04}_{0.03}$ 
^{ 1}^{, 2} 

NOVA 
$0.51$ ${}^{+0.07}_{0.09}$ 
^{ 3} 

ICCB 
$0.588$ ${}^{+0.031}_{0.064}$ 
^{ 4} 

SKAM 
$0.575$ ${}^{+0.036}_{0.073}$ 
^{ 4} 

SKAM 
$0.526$ ${}^{+0.032}_{0.036}$ 
^{ 5} 

T2K 
$0.530$ ${}^{+0.030}_{0.034}$ 
^{ 5} 

T2K 
$0.41$ ${}^{+0.23}_{0.06}$ 
^{ 6} 

MINS 
$0.41$ ${}^{+0.26}_{0.07}$ 
^{ 6} 

MINS 
• • • We do not use the following data for averages, fits, limits, etc. • • • 
$0.455$ 
^{ 7} 

ICCB 
$0.58$ ${}^{+0.04}_{0.13}$ 
^{ 8} 

ICCB 
$0.48$ ${}^{+0.04}_{0.03}$ 
^{ 1}^{, 2} 

NOVA 
$0.47$ ${}^{+0.04}_{0.03}$ 
^{ 1}^{, 2} 

NOVA 
$0.49$ ${}^{+0.30}_{0.28}$ 


OPER 
$0.50$ ${}^{+0.20}_{0.19}$ 
^{ 9} 

ANTR 
$0.587$ ${}^{+0.036}_{0.069}$ 
^{ 10} 

SKAM 
$0.551$ ${}^{+0.044}_{0.075}$ 
^{ 10} 

SKAM 
$0.56$ $\pm0.04$ 
^{ 11} 

NOVA 
$0.47$ $\pm0.04$ 
^{ 11} 

NOVA 
$0.547$ ${}^{+0.020}_{0.030}$ 


FIT 
$0.551$ ${}^{+0.018}_{0.030}$ 


FIT 
$0.532$ ${}^{+0.061}_{0.087}$ 
^{ 12} 

T2K 
$0.534$ ${}^{+0.061}_{0.087}$ 
^{ 12} 

T2K 
$0.51$ ${}^{+0.08}_{0.07}$ 


T2K 
$0.42$ ${}^{+0.25}_{0.07}$ 


T2K 
$0.52$ ${}^{+0.075}_{0.09}$ 


T2K 
$0.55$ ${}^{+0.05}_{0.09}$ 
^{ 12} 

T2K 
$0.55$ ${}^{+0.05}_{0.08}$ 
^{ 12} 

T2K 
$0.404$ ${}^{+0.022}_{0.030}$ 
^{ 13} 

NOVA 
$0.624$ ${}^{+0.022}_{0.030}$ 
^{ 13} 

NOVA 
$0.398$ ${}^{+0.030}_{0.022}$ 
^{ 13} 

NOVA 
$0.618$ ${}^{+0.022}_{0.030}$ 
^{ 13} 

NOVA 
$0.45$ ${}^{+0.19}_{0.07}$ 
^{ 14} 

T2K 
$0.38\text{ to }0.65 $ 
^{ 15} 

NOVA 
$0.37\text{ to }0.64 $ 
^{ 15} 

NOVA 
$0.53$ ${}^{+0.09}_{0.12}$ 
^{ 16} 

ICCB 
$0.51$ ${}^{+0.09}_{0.11}$ 
^{ 16} 

ICCB 
$0.514$ ${}^{+0.055}_{0.056}$ 
^{ 17} 

T2K 
$0.511$ $\pm0.055$ 
^{ 17} 

T2K 
$0.567$ ${}^{+0.032}_{0.128}$ 
^{ 18} 

FIT 
$0.573$ ${}^{+0.025}_{0.043}$ 
^{ 18} 

FIT 
$0.452$ ${}^{+0.052}_{0.028}$ 
^{ 19} 

FIT 
$0.579$ ${}^{+0.025}_{0.037}$ 
^{ 19} 

FIT 
$0.24\text{ to }0.76 $ 
^{ 20} 

ICCB 
$0.514$ $\pm0.082$ 
^{ 21} 

T2K 
$0.388$ ${}^{+0.051}_{0.053}$ 
^{ 22} 

MINS 
$0.3\text{ to }0.7 $ 
^{ 23} 

T2K 
$0.28\text{ to }0.72 $ 
^{ 24} 

MINS 
$0.25\text{ to }0.75 $ 
^{ 25}^{, 26} 

MINS 
$0.27\text{ to }0.73 $ 
^{ 25}^{, 27} 

MINS 
$0.21\text{ to }0.79 $ 
^{ 25}^{, 27} 

MINS 
$0.15\text{ to }0.85 $ 
^{ 28} 

ANTR 
$0.39\text{ to }0.61 $ 
^{ 29} 

SKAM 
$0.34\text{ to }0.66 $ 


MINS 
$0.31$ ${}^{+0.10}_{0.07}$ 
^{ 30} 

MINS 
$0.41\text{ to }0.59 $ 
^{ 31} 

SKAM 
$0.39\text{ to }0.61 $ 
^{ 32} 

SKAM 
$0.37\text{ to }0.63 $ 
^{ 33} 

SKAM 
$0.31\text{ to }0.69 $ 


MINS 
$0.05\text{ to }0.95 $ 
^{ 34} 

MINS 
$0.18\text{ to }0.82 $ 
^{ 35} 

K2K 
$0.23\text{ to }0.77 $ 
^{ 36} 

MINS 
$0.18\text{ to }0.82 $ 
^{ 37} 

K2K 
$0.18\text{ to }0.82 $ 
^{ 38} 

SOU2 
$0.36\text{ to }0.64 $ 
^{ 39} 

SKAM 
$0.28\text{ to }0.72 $ 
^{ 40} 

MCRO 
$0.34\text{ to }0.66 $ 
^{ 41} 

SKAM 
$0.08\text{ to }0.92 $ 
^{ 42} 

K2K 
$0.13\text{ to }0.87 $ 
^{ 43} 

MCRO 
$0.26\text{ to }0.74 $ 
^{ 44} 

MCRO 
$0.15\text{ to }0.85 $ 
^{ 45} 

SOU2 
$0.28\text{ to }0.72 $ 
^{ 46} 

MCRO 
$0.29\text{ to }0.71 $ 
^{ 47} 

MCRO 
$0.13\text{ to }0.87 $ 
^{ 48} 

SKAM 
$0.23\text{ to }0.77 $ 
^{ 49} 

SKAM 
$0.08\text{ to }0.92 $ 
^{ 50} 

SKAM 
$0.29\text{ to }0.71 $ 
^{ 51} 

SKAM 
$0.08\text{ to }0.92 $ 
^{ 52} 

KAMI 
$0.24\text{ to }0.76 $ 
^{ 53} 

KAMI 
$0.20\text{ to }0.80 $ 
^{ 54} 

KAMI 
^{1}
ACERO 2019 is based on a sample size of $12.33 \times 10^{20}$ protons on target. The fit combines both antineutrino and neutrino data to extract the oscillation parameters. The results favor the normal mass ordering by 1.9 ${{\mathit \sigma}}$ and $\theta _{23}$ values in octant II by 1.6 ${{\mathit \sigma}}$. Supersedes ACERO 2018 .

^{2}
Errors are from normal mass ordering and ${{\mathit \theta}_{{13}}}$ octant II fits.

^{3}
AARTSEN 2018A uses three years (April 2012 $$ May 2015) of neutrino data from full sky with reconstructed energies between 5.6 and 56 GeV, measured with the lowenergy subdetector DeepCore of the IceCube neutrino telescope. AARTSEN 2018A also reports the best fit result for the inverted mass ordering as $\Delta $m${}^{2}_{32}$ = $2.32 \times 10^{3}$ eV${}^{2}$ and sin$^2({{\mathit \theta}_{{23}}})$ = 0.51. Uncertainties for the inverted mass ordering fits were not provided. Supersedes AARTSEN 2015A.

^{4}
ABE 2018B uses 328 kton$\cdot{}$years of SuperKamiokande IIV atmospheric neutrino data to obtain this result. The fit is performed over the three parameters, $\Delta $m${}^{2}_{32}$, sin$^2({{\mathit \theta}_{{23}}})$, and $\delta $, while the solar parameters and sin$^2({{\mathit \theta}_{{13}}})$ are fixed to $\Delta $m${}^{2}_{21}$= ($7.53$ $\pm0.18$) $ \times 10^{5}$ eV${}^{2}$, sin$^2({{\mathit \theta}_{{12}}})$ = $0.304$ $\pm0.014$, and sin$^2({{\mathit \theta}_{{13}}})$ = $0.0219$ $\pm0.0012$.

^{5}
ABE 2018G data prefers normal mass ordering is with a posterior probability of 87$\%$. Supersedes ABE 2017F.

^{6}
ADAMSON 2014 uses a complete set of accelerator and atmospheric data. The analysis combines the ${{\mathit \nu}_{{\mu}}}$ disappearance and ${{\mathit \nu}_{{e}}}$ appearance data using threeneutrino oscillation fit. The fit results are obtained for normal and inverted mass ordering assumptions. The best fit is for first ${{\mathit \theta}_{{23}}}$ octant and inverted mass ordering.

^{7}
AARTSEN 2020 uses the data taken between May 2012 and April 2014 with the lowenergy subdetector DeepCore of the IceCube neutrino telescope. The reconstructed energy range is between 4 (5) and 90 (80) GeV for the main (confirmatory) analysis. Though the observed bestfit is in the lower octant for both mass orderings, a substantial range of sin$^2({{\mathit \theta}_{{23}}})$ $>$ 0.5 is still compatible with the observed data for both mass orderings.

^{8}
AARTSEN 2019C uses three years (April 2012 $$ May 2015) of neutrino data from full sky with reconstructed energies between 5.6 and 56 GeV, measured with the lowenergy subdetector DeepCore of the IceCube neutrino telescope. AARTSEN 2019C adopts looser event selection criteria to prioritize the efficiency of selecting neutrino events, different from tighter event selection criteria which closely follow the criteria used by AARTSEN 2018A to measure the ${{\mathit \nu}_{{\mu}}}$ disappearance.

^{9}
ALBERT 2019 measured the oscillation parameters of atmospheric neutrinos with the ANTARES deep sea neutrino telescope using the data taken from 2007 to 2016 (2830 days of total live time). Supersedes ADRIANMARTINEZ 2012 .

^{10}
ABE 2018B uses 328 kton$\cdot{}$years of SuperKamiokande IIV atmospheric neutrino data to obtain this result. The fit is performed over the four parameters, $\Delta $m${}^{2}_{32}$, sin$^2{{\mathit \theta}_{{23}}}$, sin$^2{{\mathit \theta}_{{13}}}$, and $\delta $, while the solar parameters are fixed to $\Delta $m${}^{2}_{21}$= ($7.53$ $\pm0.18$) $ \times 10^{5}$ eV${}^{2}$ and sin$^2{{\mathit \theta}_{{12}}}$ = $0.304$ $\pm0.014$.

^{11}
ACERO 2018 performs a joint fit to the data for ${{\mathit \nu}_{{\mu}}}$ disappearance and ${{\mathit \nu}_{{e}}}$ appearance. The overall best fit favors normal mass ordering and ${{\mathit \theta}_{{23}}}$ in octant II. No 1$\sigma $ confidence intervals are presented for the inverted mass ordering scenarios. Superseded by ACERO 2019 .

^{12}
Errors are from the projections of the 68$\%$ contour on 2D plot of $\Delta $m${}^{2}$ versus sin$^2({{\mathit \theta}_{{23}}})$. ABE 2017F supersedes ABE 2017A. Superseded by ABE 2018G.

^{13}
Superseded by ACERO 2018 .

^{14}
ABE 2016D reports oscillation results using ${{\overline{\mathit \nu}}_{{\mu}}}$ disappearance in an offaxis beam.

^{15}
ADAMSON 2016A obtains sin$^2({{\mathit \theta}_{{23}}})$ in the 68$\%$ C.L. range [0.38, 0.65] ([0.37, 0.64]), with two statistically degenerate bestfit values of 0.44 and 0.59 (0.44 and 0.59) for normal (inverted) mass ordering. Superseded by ADAMSON 2017A.

^{16}
AARTSEN 2015A obtains this result by a threeneutrino oscillation analysis using $10  100$ GeV muon neutrino sample from a total of 953 days of measurement with the lowenergy subdetector DeepCore of the IceCube neutrino telescope. Superseded by AARTSEN 2018A.

^{17}
ABE 2014 results are based on ${{\mathit \nu}_{{\mu}}}$ disappearance using threeneutrino oscillation fit. The confidence intervals are derived from one dimensional profiled likelihoods. Superseded by ABE 2017A.

^{18}
FORERO 2014 performs a global fit to neutrino oscillations using solar, reactor, longbaseline accelerator, and atmospheric neutrino data.

^{19}
GONZALEZGARCIA 2014 result comes from a frequentist global fit. The corresponding Bayesian global fit to the same data results are reported in BERGSTROM 2015 as 68$\%$ CL intervals of $0.433  0.496$ or $0.530  0.594$ for normal and $0.514  0.612$ for inverted mass ordering.

^{20}
AARTSEN 2013B obtained this result by a twoneutrino oscillation analysis using $20  100$ GeV muon neutrino sample from a total of 318.9 days of livetime measurement with the lowenergy subdetector DeepCore of the IceCube neutrino telescope.

^{21}
The best fit value is sin${}^{2}({{\mathit \theta}_{{23}}}$) = $0.514$ $\pm0.082$. Superseded by ABE 2014 .

^{22}
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 (37.88ktonyears) data from MINOS The fit assumed twoflavor neutrino hypothesis and identical ${{\mathit \nu}_{{\mu}}}$ and ${{\overline{\mathit \nu}}_{{\mu}}}$ oscillation parameters. Superseded by ADAMSON 2014 .

^{23}
ABE 2012A obtained this result by a twoneutrino oscillation analysis. The bestfit point is sin${}^{2}(2{{\mathit \theta}_{{23}}}$) = 0.98.

^{24}
ADAMSON 2012 is a twoneutrino oscillation analysis using antineutrinos. The best fit value is sin${}^{2}(2{{\mathit \theta}_{{23}}}$) = $0.95$ ${}^{+0.10}_{0.11}$ $\pm0.01$.

^{25}
ADAMSON 2012B obtained this result by a twoneutrino oscillation analysis of the L/E distribution using 37.9 kton$\cdot{}$yr atmospheric neutrino data with the MINOS far detector.

^{26}
The best fit point is $\Delta $m${}^{2}$ = 0.0019 eV${}^{2}$ and sin$^22\theta $ = 0.99. The 90$\%$ singleparameter confidence interval at the best fit point is sin$^22\theta $ $>$ 0.86.

^{27}
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 loglikelihood function with respect to the other oscillation parameters.

^{28}
ADRIANMARTINEZ 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). Superseded by ALBERT 2019 .

^{29}
ABE 2011C obtained this result by a twoneutrino oscillation analysis using the SuperKamiokandeI+II+III atmospheric neutrino data. ABE 2011C also reported results under a twoneutrino disappearance model with separate mixing parameters between ${{\mathit \nu}}$ and ${{\overline{\mathit \nu}}}$, and obtained sin$^22{{\mathit \theta}}>$ 0.93 for ${{\mathit \nu}}$ and sin$^22{{\mathit \theta}}>$ 0.83 for ${{\overline{\mathit \nu}}}$ at 90$\%$ C.L.

^{30}
ADAMSON 2011B obtained this result by a twoneutrino 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.

^{31}
WENDELL 2010 obtained this result (sin$^2\theta _{23}$ = $0.407  0.583$) by a threeneutrino oscillation analysis using the SuperKamiokandeI+II+III atmospheric neutrino data, assuming $\theta _{13}$ = 0 but including the solar oscillation parameters $\Delta $m${}^{2}_{21}$ and sin$^2\theta _{12}$ in the fit.

^{32}
WENDELL 2010 obtained this result (sin$^2\theta _{23}$ = $0.43  0.61$) by a threeneutrino oscillation analysis with one mass scale dominance ($\Delta $m${}^{2}_{21}$ = 0) using the SuperKamiokandeI+II+III atmospheric neutrino data, and updates the HOSAKA 2006A result.

^{33}
WENDELL 2010 obtained this result (sin$^2\theta _{23}$ = $0.44  0.63$) by a threeneutrino oscillation analysis with one mass scale dominance ($\Delta $m${}^{2}_{21}$ = 0) using the SuperKamiokandeI+II+III atmospheric neutrino data, and updates the HOSAKA 2006A result.

^{34}
ADAMSON 2006 obtained this result by a twoneutrino oscillation analysis of the L/E distribution using 4.54 kton yr atmospheric neutrino data with the MINOS far detector.

^{35}
Supercedes ALIU 2005 .

^{36}
MICHAEL 2006 best fit is for maximal mixing. See also ADAMSON 2008 .

^{37}
The best fit is for maximal mixing.

^{38}
ALLISON 2005 result is based upon atmospheric neutrino interactions including upwardstopping muons, with an exposure of 5.9 kton yr. From a twoflavor oscillation analysis the bestfit point is $\Delta \mathit m{}^{2}$ = 0.0017 eV${}^{2}$ and sin$^2(2\theta )$ = 0.97.

^{39}
ASHIE 2005 obtained this result by a twoneutrino oscillation analysis using 92 kton yr atmospheric neutrino data from the complete SuperKamiokande I running period.

^{40}
AMBROSIO 2004 obtained this result, without using the absolute normalization of the neutrino flux, by combining the angular distribution of upward throughgoing 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 upwardgoing tracks starting inside the detector due to neutrino interactions, while UpStop represents entering upwardgoing tracks which stop in the detector. The best fit is for maximal mixing.

^{41}
ASHIE 2004 obtained this result from the L(flight length)/E(estimated neutrino energy) distribution of ${{\mathit \nu}_{{\mu}}}$ disappearance probability, using the SuperKamiokandeI 1489 liveday atmospheric neutrino data.

^{42}
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 maximal mixing.

^{43}
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 throughgoing 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.

^{44}
AMBROSIO 2003 obtained this result by using the ratio R and the angular distribution of the upward throughgoing 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 to maximal mixing.

^{45}
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 sin$^2(2{{\mathit \theta}})$ = 0.97.

^{46}
AMBROSIO 2001 result is based on the angular distribution of upward throughgoing 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. The best fit is for maximal mixing.

^{47}
AMBROSIO 2001 result is based on the angular distribution and normalization of upward throughgoing muon tracks with ${{\mathit E}_{{\mu}}}$ $>$ 1 GeV. See the previous footnote.

^{48}
FUKUDA 1999C obtained this result from a total of 537 live days of upward throughgoing muon data in SuperKamiokande 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 sin$^2(2{{\mathit \theta}})$ = 0.95.

^{49}
FUKUDA 1999D obtained this result from a simultaneous fitting to zenith angle distributions of upwardstopping and throughgoing muons. The flux of upwardstopping 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 to maximal mixing.

^{50}
FUKUDA 1999D obtained this result from the zenith dependence of the upwardstopping/throughgoing flux ratio. The best fit is to maximal mixing.

^{51}
FUKUDA 1998C obtained this result by an analysis of 33.0 kton yr atmospheric neutrino data. The best fit is for maximal mixing.

^{52}
HATAKEYAMA 1998 obtained this result from a total of 2456 live days of upwardgoing 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 throughgoing 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 maximal mixing.

^{53}
HATAKEYAMA 1998 obtained this result from a combined analysis of Kamiokande contained events (FUKUDA 1994 ) and upward going muon events. The best fit is sin$^2(2{{\mathit \theta}})$ = 0.95.

^{54}
FUKUDA 1994 obtained the result by a combined analysis of sub and multiGeV atmospheric neutrino events in Kamiokande. The best fit is for maximal mixing.
