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 $\bf{ -2.529 \pm0.029}$ OUR FIT  Assuming inverted ordering $\bf{ 2.455 \pm0.028}$ OUR FIT  Assuming normal ordering $2.41$ $\pm0.07$ 1 ABBASI 2023 ICCB Normal mass ordering $2.494$ ${}^{+0.041}_{-0.058}$ 2 ABE 2023 F T2K Normal mass ordering, ${{\mathit \theta}_{{{13}}}}$ constrained $-2.54$ ${}^{+0.042}_{-0.056}$ 2, 3 ABE 2023 F T2K Inverted mass ordering, ${{\mathit \theta}_{{{13}}}}$ constrained $2.466$ $\pm0.06$ 4 AN 2023 DAYA Normal mass ordering $-2.571$ $\pm0.06$ 4 AN 2023 DAYA Inverted mass ordering $2.41$ $\pm0.07$ 5 ACERO 2022 NOVA Normal mass ordering, octant II for ${{\mathit \theta}_{{{23}}}}$, ${{\mathit \theta}_{{{13}}}}$ constrained $-2.45$ $\pm0.07$ 5 ACERO 2022 NOVA Inverted mass ordering, octant II for ${{\mathit \theta}_{{{23}}}}$, ${{\mathit \theta}_{{{13}}}}$ constrained $2.40$ ${}^{+0.08}_{-0.09}$ 6 ADAMSON 2020 A MINS Accel., atmospheric, normal mass ordering $-2.45$ ${}^{+0.08}_{-0.07}$ 6 ADAMSON 2020 A MINS Accel., atmospheric, inverted mass ordering $2.50$ ${}^{+0.13}_{-0.20}$ 7 ABE 2018 B SKAM Normal mass ordering, ${{\mathit \theta}_{{{13}}}}$ constrained $-2.58$ ${}^{+0.08}_{-0.37}$ 7 ABE 2018 B SKAM Inverted mass ordering, ${{\mathit \theta}_{{{13}}}}$ constrained $2.63$ $\pm0.14$ 8 BAK 2018 RENO Normal mass ordering $-2.73$ $\pm0.14$ 8 BAK 2018 RENO Inverted mass ordering • • We do not use the following data for averages, fits, limits, etc. • • $2.48$ ${}^{+0.05}_{-0.06}$ 9 ABE 2023 D T2K ${{\mathit \nu}_{{{\mu}}}}$ disappearance $2.53$ ${}^{+0.10}_{-0.11}$ 9 ABE 2023 D T2K ${{\overline{\mathit \nu}}_{{{\mu}}}}$ disappearance $2.47$ ${}^{+0.08}_{-0.09}$ 10 ABE 2021 A T2K ${{\mathit \nu}_{{{\mu}}}}$ disappearance $2.50$ ${}^{+0.18}_{-0.13}$ 10 ABE 2021 A T2K ${{\overline{\mathit \nu}}_{{{\mu}}}}$ disappearance $2.45$ $\pm0.07$ 11 ABE 2020 F T2K Normal mass ordering, ${{\mathit \theta}_{{{13}}}}$ constrained $-2.51$ $\pm0.07$ 11, 12 ABE 2020 F T2K Inverted mass ordering, ${{\mathit \theta}_{{{13}}}}$ constrained $2.517$ ${}^{+0.026}_{-0.028}$ 13 ESTEBAN 2020 A FIT Normal mass ordering, global fit $-2.498$ ${}^{+0.028}_{-0.028}$ 13 ESTEBAN 2020 A FIT Inverted mass ordering, global fit $2.55$ ${}^{+0.12}_{-0.11}$ 14 AARTSEN 2019 C ICCB $2.48$ ${}^{+0.11}_{-0.06}$ 15 ACERO 2019 NOVA Normal mass ordering, octant II for ${{\mathit \theta}_{{{23}}}}$ $-2.54$ ${}^{+0.06}_{-0.11}$ 15 ACERO 2019 NOVA Inverted mass ordering, octant II for ${{\mathit \theta}_{{{23}}}}$ $< 4.1 at 90\% CL$ AGAFONOVA 2019 OPER $2.0$ ${}^{+0.4}_{-0.3}$ 16 ALBERT 2019 ANTR Atmospheric ${{\mathit \nu}}$, deep sea telescope $2.31$ ${}^{+0.11}_{-0.13}$ 17 AARTSEN 2018 A ICCB Normal mass ordering $2.50$ ${}^{+0.13}_{-0.31}$ 18 ABE 2018 B SKAM 3${{\mathit \nu}}$ osc: normal mass ordering, ${{\mathit \theta}_{{{13}}}}$ free $-2.28$ ${}^{+0.33}_{-0.13}$ 18 ABE 2018 B SKAM 3${{\mathit \nu}}$ osc: inverted mass ordering, ${{\mathit \theta}_{{{13}}}}$ free $2.463$ ${}^{+0.071}_{-0.070}$ 19 ABE 2018 G T2K Normal mass ordering, ${{\mathit \theta}_{{{13}}}}$ constrained $-2.507$ $\pm0.070$ 19, 20 ABE 2018 G T2K Inverted mass ordering, ${{\mathit \theta}_{{{13}}}}$ constrained $2.44$ ${}^{+0.08}_{-0.07}$ 21 ACERO 2018 NOVA Normal mass order, octant II for ${{\mathit \theta}_{{{23}}}}$ $2.45$ ${}^{+0.07}_{-0.08}$ 21, 22 ACERO 2018 NOVA Normal mass order; octant I for ${{\mathit \theta}_{{{23}}}}$ $2.471$ ${}^{+0.068}_{-0.070}$ 23 ADEY 2018 A DAYA Normal mass ordering $-2.575$ ${}^{+0.068}_{-0.070}$ 23 ADEY 2018 A DAYA Inverted mass ordering $2.7$ ${}^{+0.7}_{-0.6}$ 24 AGAFONOVA 2018 OPER OPERA ${{\mathit \nu}_{{{\tau}}}}$ appearance $2.42$ $\pm0.03$ DE-SALAS 2018 FIT Normal mass ordering, global fit $-2.50$ ${}^{+0.03}_{-0.04}$ DE-SALAS 2018 FIT Inverted mass order, global fit $2.57$ ${}^{+0.21}_{-0.23}$ ${}^{+0.12}_{-0.13}$ 25 SEO 2018 RENO Normal mass ordering $-2.67$ ${}^{+0.23}_{-0.21}$ ${}^{+0.13}_{-0.12}$ 25 SEO 2018 RENO Inverted mass ordering $2.53$ ${}^{+0.15}_{-0.13}$ ABE 2017 C T2K Normal mass ordering with neutrinos $2.55$ ${}^{+0.33}_{-0.27}$ ABE 2017 C T2K Normal mass ordering with antineutrinos $2.55$ ${}^{+0.08}_{-0.08}$ ABE 2017 C T2K Normal mass ordering with neutrinos and antineutrinos $-2.63$ ${}^{+0.08}_{-0.08}$ ABE 2017 C T2K Inverted mass ordering with neutrinos and antineutrinos $2.54$ $\pm0.08$ 26 ABE 2017 F T2K Normal mass ordering; ${{\mathit \nu}}+{{\overline{\mathit \nu}}}$ $-2.51$ $\pm0.08$ 26 ABE 2017 F T2K Inverted mass ordering; ${{\mathit \nu}}+{{\overline{\mathit \nu}}}$ $2.67$ $\pm0.11$ 27 ADAMSON 2017 A NOVA 3${{\mathit \nu}}$ osc; normal mass ordering $-2.72$ $\pm0.11$ 27 ADAMSON 2017 A NOVA 3${{\mathit \nu}}$ osc; inverted mass ordering $2.45$ $\pm0.06$ $\pm0.06$ 28 AN 2017 A DAYA Normal mass ordering $-2.56$ $\pm0.06$ $\pm0.06$ 28 AN 2017 A DAYA Inverted mass ordering $2.51$ ${}^{+0.29}_{-0.25}$ 29 ABE 2016 D T2K 3${{\mathit \nu}}$ osc.; normal mass ordering; ${{\overline{\mathit \nu}}}$ beam $2.52$ ${}^{+0.20}_{-0.18}$ 30 ADAMSON 2016 A NOVA 3${{\mathit \nu}}$ osc; normal mass ordering $-2.56$ $\pm0.19$ 30 ADAMSON 2016 A NOVA 3${{\mathit \nu}}$ osc; inverted mass ordering $2.56$ ${}^{+0.21}_{-0.23}$ ${}^{+0.12}_{-0.13}$ 31 CHOI 2016 RENO 3${{\mathit \nu}}$ osc; normal mass ordering $-2.69$ ${}^{+0.23}_{-0.21}$ ${}^{+0.13}_{-0.12}$ 31 CHOI 2016 RENO 3${{\mathit \nu}}$ osc; inverted mass ordering $2.72$ ${}^{+0.19}_{-0.20}$ 32 AARTSEN 2015 A ICCB Normal mass ordering $-2.73$ ${}^{+0.21}_{-0.18}$ 32 AARTSEN 2015 A ICCB Inverted mass ordering $\text{2.0 - 5.0}$ 33 AGAFONOVA 2015 A OPER 90$\%$ CL, 5 events $2.37$ $\pm0.11$ 34 AN 2015 DAYA 3${{\mathit \nu}}$ osc.; normal mass ordering $-2.47$ $\pm0.11$ 34 AN 2015 DAYA 3${{\mathit \nu}}$ osc.; inverted mass ordering $2.51$ $\pm0.10$ 35 ABE 2014 T2K 3${{\mathit \nu}}$ osc.; normal mass ordering $-2.56$ $\pm0.10$ 35 ABE 2014 T2K 3${{\mathit \nu}}$ osc.; inverted mass ordering $2.37$ $\pm0.09$ 36 ADAMSON 2014 MINS Accel., atmospheric, normal mass ordering $-2.41$ ${}^{+0.09}_{-0.12}$ 36 ADAMSON 2014 MINS Accel., atmsopheric, inverted mass ordering $2.54$ ${}^{+0.19}_{-0.20}$ 37 AN 2014 DAYA 3${{\mathit \nu}}$ osc.; normal mass ordering $-2.64$ ${}^{+0.20}_{-0.19}$ 37 AN 2014 DAYA 3${{\mathit \nu}}$ osc.; inverted mass ordering $2.48$ ${}^{+0.05}_{-0.07}$ 38 FORERO 2014 FIT 3${{\mathit \nu}}$; normal mass ordering $-2.38$ ${}^{+0.06}_{-0.05}$ 38 FORERO 2014 FIT 3${{\mathit \nu}}$; inverted mass ordering $2.457$ $\pm0.047$ 39, 40 GONZALEZ-GARC.. 2014 FIT Normal mass ordering; global fit $-2.449$ ${}^{+0.047}_{-0.048}$ 39 GONZALEZ-GARC.. 2014 FIT Inverted mass ordering; global fit $2.3$ ${}^{+0.6}_{-0.5}$ 41 AARTSEN 2013 B ICCB DeepCore, 2${{\mathit \nu}}$ oscillation $2.44$ ${}^{+0.17}_{-0.15}$ 42 ABE 2013 G T2K 3${{\mathit \nu}}$ osc.; normal mass ordering $2.41$ ${}^{+0.09}_{-0.10}$ 43 ADAMSON 2013 B MINS 2${{\mathit \nu}}$ osc.; beam + atmospheric; identical ${{\mathit \nu}}$ $\&$ ${{\overline{\mathit \nu}}}$ $\text{2.2 - 3.1}$ 44 ABE 2012 A T2K off-axis beam $2.62$ ${}^{+0.31}_{-0.28}$ $\pm0.09$ 45 ADAMSON 2012 MINS ${{\overline{\mathit \nu}}}$ beam $\text{1.35 - 2.55}$ 46, 47 ADAMSON 2012 B MINS MINOS atmospheric $\text{1.4 - 5.6}$ 46, 48 ADAMSON 2012 B MINS MINOS pure atmospheric ${{\mathit \nu}}$ $\text{0.9 - 2.5}$ 46, 48 ADAMSON 2012 B MINS MINOS pure atmospheric ${{\overline{\mathit \nu}}}$ $\text{1.8 - 5.0}$ 49 ADRIAN-MARTIN.. 2012 ANTR Atmospheric ${{\mathit \nu}}$ with deep sea telescope $\text{1.3 - 4.0}$ 50 ABE 2011 C SKAM atmospheric ${{\overline{\mathit \nu}}}$ $2.32$ ${}^{+0.12}_{-0.08}$ ADAMSON 2011 MINS 2${{\mathit \nu}}$ oscillation; maximal mixing $3.36$ ${}^{+0.46}_{-0.40}$ 51 ADAMSON 2011 B MINS ${{\overline{\mathit \nu}}}$ beam $\text{< 3.37}$ 52 ADAMSON 2011 C MINS MINOS $\text{1.9 - 2.6}$ 53 WENDELL 2010 SKAM 3${{\mathit \nu}}$ osc.; normal mass ordering $\text{-1.7 - -2.7}$ 53 WENDELL 2010 SKAM 3${{\mathit \nu}}$ osc.; inverted mass ordering $2.43$ $\pm0.13$ ADAMSON 2008 A MINS MINOS $\text{0.07 - 50}$ 54 ADAMSON 2006 MINS atmospheric ${{\mathit \nu}}$ with far detector $\text{1.9 - 4.0}$ 55, 56 AHN 2006 A K2K KEK to Super-K $\text{2.2 - 3.8}$ 57 MICHAEL 2006 MINS MINOS $\text{1.9 - 3.6}$ 55 ALIU 2005 K2K KEK to Super-K $\text{0.3 - 12}$ 58 ALLISON 2005 SOU2 $\text{1.5 - 3.4}$ 59 ASHIE 2005 SKAM atmospheric neutrino $\text{0.6 - 8.0}$ 60 AMBROSIO 2004 MCRO MACRO $1.9\text{ to }3.0 $ 61 ASHIE 2004 SKAM L/E distribution $\text{1.5 - 3.9}$ 62 AHN 2003 K2K KEK to Super-K $\text{0.25 - 9.0}$ 63 AMBROSIO 2003 MCRO MACRO $\text{0.6 - 7.0}$ 64 AMBROSIO 2003 MCRO MACRO $\text{0.15 - 15}$ 65 SANCHEZ 2003 SOU2 Soudan-2 Atmospheric $\text{0.6 - 15}$ 66 AMBROSIO 2001 MCRO upward ${{\mathit \mu}}$ $\text{1.0 - 6.0}$ 67 AMBROSIO 2001 MCRO upward ${{\mathit \mu}}$ $\text{1.0 - 50}$ 68 FUKUDA 1999 C SKAM upward ${{\mathit \mu}}$ $\text{1.5 - 15.0}$ 69 FUKUDA 1999 D SKAM upward ${{\mathit \mu}}$ $\text{0.7 - 18}$ 70 FUKUDA 1999 D SKAM stop ${{\mathit \mu}}$ $/$ through $\text{0.5 - 6.0}$ 71 FUKUDA 1998 C SKAM Super-Kamiokande $\text{0.55 - 50}$ 72 HATAKEYAMA 1998 KAMI Kamiokande $\text{4 - 23}$ 73 HATAKEYAMA 1998 KAMI Kamiokande $\text{5 - 25}$ 74 FUKUDA 1994 KAMI Kamiokande 1  ABBASI 2023 uses atmospheric neutrino data measured between 2011 and 2019 with the low-energy subdetector DeepCore of the IceCube neutrino telescope. Supersedes AARTSEN 2018A. 2  ABE 2023F results are based on data collected between 2010 and 2020 in (anti)neutrino mode and include a neutrino beam exposure of $1.97 \times 10^{21}$ ($1.63 \times 10^{21}$) protons on target. Supersedes ABE 2020F. 3  ABE 2023F reports $\Delta $m${}^{2}_{13}=(2.463$ ${}^{+0.042}_{-0.056}$) $ \times 10^{-3}$ eV${}^{2}$ for inverted mass ordering. We convert to $\Delta $m${}^{2}_{32}$ using PDG 2023 value of $\Delta $m${}^{2}_{21}$ = ($7.53$ $\pm0.18$) $ \times 10^{-5}$ eV${}^{2}$. 4  AN 2023 reports results derived from the complete data set collected by the Daya-Bay experiment, corresponding to 3158 days of operation, resulting in $5.55 \times 10^{6}{{\overline{\mathit \nu}}_{{{e}}}}$ candidate events. Solar oscillation parameters are fixed in the analysis to sin$^2({{\mathit \theta}_{{{12}}}})$ = $0.307$ $\pm0.013$, $\Delta $m${}^{2}_{21}$ = ($7.53$ $\pm0.18$) $ \times 10^{-5}$ eV${}^{2}$ from PDG 2020. Supersedes ADEY 2018A. 5  ACERO 2022 uses data from Jun 29, 2016 to Feb 26, 2019 ($12.5 \times 10^{20}$ POT) and Feb 6, 2014 to Mar 20, 2020 ($13.6 \times 10^{20}$ POT). For normal mass ordering and ${{\mathit \theta}_{{{23}}}}$ octant I (lower octant), best fit is 0.00239 eV${}^{2}$; for inverted mass ordering and octant I, best fit is $-0.00244$ eV${}^{2}$. Supersedes ACERO 2019. 6  ADAMSON 2020A uses the complete dataset from MINOS and MINOS+ experiments. The data were collected using a total exposure of $23.76 \times 10^{20}$ protons on target and 60.75 kton$\cdot{}$yr exposure to atmospheric neutrinos. Supersedes ADAMSON 2014. 7  ABE 2018B uses 328 kton$\cdot{}$years of Super-Kamiokande I-IV 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$^2({{\mathit \theta}_{{{13}}}})$ = $0.0219$ $\pm0.0012$. 8  BAK 2018 reports results of the RENO experiment using about 2200 live-days of data taken with detectors placed at 410.6 and 1445.7 m from reactors of the Hanbit Nuclear Power Plant. We convert the results to $\Delta $m${}^{2}_{32}$ using the PDG 2018 values of sin$^2{{\mathit \theta}_{{{12}}}}$ = $0.307$ ${}^{+0.013}_{-0.012}$ and $\Delta $m${}^{2}_{21}$ = ($7.53$ $\pm0.18$) $ \times 10^{-5}$ eV${}^{2}$. Supersedes SEO 2018. 9  ABE 2023D uses the same dataset as ABE 2023F. The measurement of $\Delta $m${}^{2}_{32}$ is performed independently for ${{\mathit \nu}_{{{\mu}}}}$ and ${{\overline{\mathit \nu}}_{{{\mu}}}}$. 10  ABE 2021A results are based on $1.49 \times 10^{21}$ POT in neutrino mode and $1.64 \times 10^{21}$ POT in antineutrino mode. 11  ABE 2020F results are based on data collected between 2009 and 2018 in (anti)neutrino mode and include a neutrino beam exposure of $1.49 \times 10^{21}$ ($1.64 \times 10^{21}$) protons on target. Supersedes ABE 2018G. 12  ABE 2020F reports $\Delta $m${}^{2}_{13}=(2.43$ $\pm0.07$) $ \times 10^{-3}$ eV${}^{2}$ for inverted mass ordering. We convert to $\Delta $m${}^{2}_{32}$ using PDG 2020 value of $\Delta $m${}^{2}_{21}$ = ($7.53$ $\pm0.18$) $ \times 10^{-5}$ eV${}^{2}$. 13  ESTEBAN 2020A reports results of a global fit to neutrino oscillation data available at the time of the Neutrino2020 conference. 14  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 low-energy 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. 15  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 ${{\mathit \sigma}}$. Superseded by ACERO 2022. 16  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 ADRIAN-MARTINEZ 2012. 17  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 low-energy subdetector DeepCore of the IceCube neutrino telescope. AARTSEN 2018A also reports the best fit values 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. 18  ABE 2018B uses 328 kton$\cdot{}$years of Super-Kamiokande I-IV 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$^2{{\mathit \theta}_{{{12}}}}$ = $0.304$ $\pm0.014$. 19  ABE 2018G data prefers normal ordering with a posterior probability of 87$\%$. Supersedes ABE 2017F. 20  ABE 2018G reports $\Delta $m${}^{2}_{13}=(2.432$ $\pm0.070$) $ \times 10^{-3}$ eV${}^{2}$ for inverted mass ordering. We convert to $\Delta $m${}^{2}_{32}$ using PDG 2018 value of $\Delta $m${}^{2}_{21}=(7.53$ $\pm0.18$) $ \times 10^{-5}$ eV${}^{2}$. 21  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. 22  The error for octant I is taken from the result for octant II. 23  ADEY 2018A reports results from analysis of 1958 days of data taking with the Daya-Bay experiment, with $3.9 \times 10^{6}$ ${{\overline{\mathit \nu}}_{{{e}}}}$ candidates. The fit to the data gives $\Delta $m${}^{2}_{ee}$ = ($2.522$ ${}^{+0.068}_{-0.070}$) $ \times 10^{-3}$ eV${}^{2}$. Solar oscillation parameters are fixed in the analysis using the global averages, sin$^2({{\mathit \theta}_{{{12}}}})$ = $0.307$ ${}^{+0.013}_{-0.012}$, $\Delta $m${}^{2}_{21}$ = ($7.53$ $\pm0.18$) $ \times 10^{-5}$ eV${}^{2}$, from PDG 2018. Supersedes AN 2017A. 24  AGAFONOVA 2018 assumes maximal ${{\mathit \theta}_{{{23}}}}$ mixing. 25  SEO 2018 reports result of the RENO experiment from a rate and shape analysis of 500 days of data. A simultaneous fit to ${{\mathit \theta}_{{{13}}}}$ and $\Delta $m${}^{2}_{ee}$ yields $\Delta $m${}^{2}_{ee}$ = ($2.62$ ${}^{+0.21}_{-0.23}{}^{+0.12}_{-0.13}$) $ \times 10^{-3}$ eV${}^{2}$. We convert the results to $\Delta $m${}^{2}_{32}$ using the PDG 2018 values of sin$^2{{\mathit \theta}_{{{12}}}}$ and $\Delta $m${}^{2}_{21}$. SEO 2018 is a detailed description of the results published in CHOI 2016, which it supersedes. Superseded by BAK 2018 26  ABE 2017F confidence intervals are obtained using a frequentist analysis including ${{\mathit \theta}_{{{13}}}}$ constraint from reactor experiments. Bayesian intervals based on Markov Chain Monte Carlo method are also provided by the authors. Superseded by ABE 2018G. 27  Superseded by ACERO 2018. 28  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 $\Delta {}^{2}_{ee}=(2.50$ $\pm0.06$ $\pm0.06$) $ \times 10^{-3}$ eV. Superseded by ADEY 2018A. 29  ABE 2016D reports oscillation results using ${{\overline{\mathit \nu}}_{{{\mu}}}}$ disappearance in an off-axis beam. 30  Superseded by ADAMSON 2017A. 31  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}$ = ($2.62$ ${}^{+0.21}_{-0.23}{}^{+0.12}_{-0.13}$) $ \times 10^{-3}$ eV. We convert the results to $\Delta $m${}^{2}_{32}$ using PDG 2018 values of sin$^2({{\mathit \theta}_{{{12}}}})$ and $\Delta $m${}^{2}_{21}$. 32  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. Superseded by AARTSEN 2018A. 33  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${}^{2}$. 34  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}$ = ($2.42$ $\pm0.11$) $ \times 10^{-3}$ eV${}^{2}$. Assuming the normal (inverted) ordering, the fitted $\Delta $m${}^{2}_{32}$ = ($2.37$ $\pm0.11$) $ \times 10^{-3}$ (($2.47$ $\pm0.11$) $ \times 10^{-3}$) eV${}^{2}$. Superseded by AN 2017A. 35  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}$ = ($2.48$ $\pm0.10$) $ \times 10^{-3}$ 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. 36  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. 37  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}$ = ($2.59$ ${}^{+0.19}_{-0.20}$) $ \times 10^{-3}$ eV${}^{2}$. Assuming the normal (inverted) ordering, the fitted $\Delta $m${}^{2}_{32}$ = ($2.54$ ${}^{+0.19}_{-0.20}$) $ \times 10^{-3}$ (($2.64$ ${}^{+0.19}_{-0.20}$) $ \times 10^{-3}$) eV${}^{2}$. Superseded by AN 2015. 38  FORERO 2014 performs a global fit to $\Delta $m${}^{2}_{31}$ using solar, reactor, long-baseline accelerator, and atmospheric neutrino data. 39  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 ($2.460$ $\pm0.046$) $ \times 10^{-3}$ eV${}^{2}$ for normal and ($2.445$ ${}^{+0.047}_{-0.045}$) $ \times 10^{-3}$ eV${}^{2}$ for inverted mass ordering. 40  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 $\Delta {{\mathit m}^{2}}_{\mathrm {12}}$. 41  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. 42  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. 43  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. 44  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${}^{2}$. 45  ADAMSON 2012 is a two-neutrino oscillation analysis using antineutrinos. 46  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. 47  The 90$\%$ single-parameter confidence interval at the best fit point is $\Delta $m${}^{2}$ = $0.0019$ $\pm0.0004$ eV${}^{2}$. 48  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 $) plane obtained by minimizing the four parameter log-likelihood function with respect to the other oscillation parameters. 49  ADRIAN-MARTINEZ 2012 measured the oscillation parameters of atmospheric neutrinos with the ANTARES deep sea neutrino telescope using the data taken from 2007 to 2010 (863 days of total live time). Superseded by ALBERT 2019 50  ABE 2011C obtained this result by a two-neutrino oscillation analysis with separate mixing parameters between neutrinos and antineutrinos, using the Super-Kamiokande-I+II+III atmospheric neutrino data. The corresponding 90$\%$ CL neutrino oscillation parameter range obtained from this analysis is $\Delta {{\mathit m}^{2}}_{\mathrm {}}$ = $1.7 - 3.0 \times 10^{-3}$ eV${}^{2}$. 51  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. 52  ADAMSON 2011C obtains this result based on a study of antineutrinos in a neutrino beam and assumes maximal mixing in the two-flavor approximation. 53  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. 54  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. 55  The best fit in the physical region is for $\Delta \mathit m{}^{2}$ = $2.8 \times 10^{-3}$ eV${}^{2}$. 56  Supercedes ALIU 2005. 57  MICHAEL 2006 best fit is $2.74 \times 10^{-3}$ eV${}^{2}$. See also ADAMSON 2008. 58  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. 59  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 $\Delta {{\mathit m}^{2}}_{}$ = $2.1 \times 10^{-3}$ eV${}^{2}$. 60  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${}^{2}$. 61  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${}^{2}$. 62  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${}^{2}$. 63  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${}^{2}$. 64  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${}^{2}$. 65  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${}^{2}$. 66  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. 67  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. 68  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${}^{2}$. 69  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${}^{2}$. 70  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${}^{2}$. 71  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${}^{2}$. 72  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${}^{2}$. 73  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${}^{2}$. 74  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${}^{2}$.

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References