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 $\bf{ -2.536 \pm0.034}$ OUR FIT  Assuming inverted ordering $\bf{ 2.453 \pm0.033}$ OUR FIT  Assuming normal ordering $2.45$ $\pm0.07$ 1 ABE 2020 F T2K Normal mass ordering, ${{\mathit \theta}_{{13}}}$ constrained $-2.51$ $\pm0.07$ 1, 2 ABE 2020 F T2K Inverted mass ordering, ${{\mathit \theta}_{{13}}}$ constrained $2.40$ ${}^{+0.08}_{-0.09}$ 3 ADAMSON 2020 A MINS Accel., atmospheric, normal mass ordering $-2.45$ ${}^{+0.08}_{-0.07}$ 3 ADAMSON 2020 A MINS Accel., atmospheric, inverted mass ordering $2.48$ ${}^{+0.11}_{-0.06}$ 4 ACERO 2019 NOVA Normal mass ordering, octant II for ${{\mathit \theta}_{{23}}}$ $-2.54$ ${}^{+0.06}_{-0.11}$ 4 ACERO 2019 NOVA Inverted mass ordering, octant II for ${{\mathit \theta}_{{23}}}$ $2.31$ ${}^{+0.11}_{-0.13}$ 5 AARTSEN 2018 A ICCB Normal mass ordering $2.50$ ${}^{+0.13}_{-0.20}$ 6 ABE 2018 B SKAM Normal mass ordering, ${{\mathit \theta}_{{13}}}$ constrained $-2.58$ ${}^{+0.08}_{-0.37}$ 6 ABE 2018 B SKAM Inverted mass ordering, ${{\mathit \theta}_{{13}}}$ constrained $2.471$ ${}^{+0.068}_{-0.070}$ 7 ADEY 2018 A DAYA Normal mass ordering $-2.575$ ${}^{+0.068}_{-0.070}$ 7 ADEY 2018 A DAYA Inverted mass ordering $2.63$ $\pm0.14$ 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. • • $2.47$ ${}^{+0.08}_{-0.09}$ 9 ABE 2021 A T2K ${{\mathit \nu}_{{\mu}}}$ disappearance $2.50$ ${}^{+0.18}_{-0.13}$ 9 ABE 2021 A T2K ${{\overline{\mathit \nu}}_{{\mu}}}$ disappearance $2.517$ ${}^{+0.026}_{-0.028}$ 10 ESTEBAN 2020 A FIT Normal mass ordering, global fit $-2.498$ ${}^{+0.028}_{-0.028}$ 10 ESTEBAN 2020 A FIT Inverted mass ordering, global fit $2.55$ ${}^{+0.12}_{-0.11}$ 11 AARTSEN 2019 C ICCB $< 4.1 at 90\% CL$ AGAFONOVA 2019 OPER $2.0$ ${}^{+0.4}_{-0.3}$ 12 ALBERT 2019 ANTR Atmospheric ${{\mathit \nu}}$ , deep sea telescope $2.50$ ${}^{+0.13}_{-0.31}$ 13 ABE 2018 B SKAM 3${{\mathit \nu}}$ osc: normal mass ordering, ${{\mathit \theta}_{{13}}}$ free $-2.28$ ${}^{+0.33}_{-0.13}$ 13 ABE 2018 B SKAM 3${{\mathit \nu}}$ osc: inverted mass ordering, ${{\mathit \theta}_{{13}}}$ free $2.463$ ${}^{+0.071}_{-0.070}$ 14 ABE 2018 G T2K Normal mass ordering, ${{\mathit \theta}_{{13}}}$ constrained $-2.507$ $\pm0.070$ 14, 15 ABE 2018 G T2K Inverted mass ordering, ${{\mathit \theta}_{{13}}}$ constrained $2.44$ ${}^{+0.08}_{-0.07}$ 16 ACERO 2018 NOVA Normal mass order, octant II for ${{\mathit \theta}_{{23}}}$ $2.45$ ${}^{+0.07}_{-0.08}$ 16, 17 ACERO 2018 NOVA Normal mass order; octant I for ${{\mathit \theta}_{{23}}}$ $2.7$ ${}^{+0.7}_{-0.6}$ 18 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 $2.57$ ${}^{+0.21}_{-0.23}$ ${}^{+0.12}_{-0.13}$ 19 SEO 2018 RENO Normal mass ordering $-2.67$ ${}^{+0.23}_{-0.21}$ ${}^{+0.13}_{-0.12}$ 19 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 $2.54$ $\pm0.08$ 20 ABE 2017 F T2K Normal mass ordering; ${{\mathit \nu}}$ +${{\overline{\mathit \nu}}}$ $-2.51$ $\pm0.08$ 20 ABE 2017 F T2K Inverted mass ordering; ${{\mathit \nu}}$ +${{\overline{\mathit \nu}}}$ $2.67$ $\pm0.11$ 21 ADAMSON 2017 A NOVA 3${{\mathit \nu}}$ osc; normal mass ordering $-2.72$ $\pm0.11$ 21 ADAMSON 2017 A NOVA 3${{\mathit \nu}}$ osc; inverted mass ordering $2.45$ $\pm0.06$ $\pm0.06$ 22 AN 2017 A DAYA Normal mass ordering $-2.56$ $\pm0.06$ $\pm0.06$ 22 AN 2017 A DAYA Inverted mass ordering $2.51$ ${}^{+0.29}_{-0.25}$ 23 ABE 2016 D T2K 3${{\mathit \nu}}$ osc.; normal mass ordering; ${{\overline{\mathit \nu}}}$ beam $2.52$ ${}^{+0.20}_{-0.18}$ 24 ADAMSON 2016 A NOVA 3${{\mathit \nu}}$ osc; normal mass ordering $-2.56$ $\pm0.19$ 24 ADAMSON 2016 A NOVA 3${{\mathit \nu}}$ osc; inverted mass ordering $2.56$ ${}^{+0.21}_{-0.23}$ ${}^{+0.12}_{-0.13}$ 25 CHOI 2016 RENO 3${{\mathit \nu}}$ osc; normal mass ordering $-2.69$ ${}^{+0.23}_{-0.21}$ ${}^{+0.13}_{-0.12}$ 25 CHOI 2016 RENO 3${{\mathit \nu}}$ osc; inverted mass ordering $2.72$ ${}^{+0.19}_{-0.20}$ 26 AARTSEN 2015 A ICCB Normal mass ordering $-2.73$ ${}^{+0.21}_{-0.18}$ 26 AARTSEN 2015 A ICCB Inverted mass ordering $\text{2.0 - 5.0}$ 27 AGAFONOVA 2015 A OPER 90$\%$ CL, 5 events $2.37$ $\pm0.11$ 28 AN 2015 DAYA 3${{\mathit \nu}}$ osc.; normal mass ordering $-2.47$ $\pm0.11$ 28 AN 2015 DAYA 3${{\mathit \nu}}$ osc.; inverted mass ordering $2.51$ $\pm0.10$ 29 ABE 2014 T2K 3${{\mathit \nu}}$ osc.; normal mass ordering $-2.56$ $\pm0.10$ 29 ABE 2014 T2K 3${{\mathit \nu}}$ osc.; inverted mass ordering $2.37$ $\pm0.09$ 30 ADAMSON 2014 MINS Accel., atmospheric, normal mass ordering $-2.41$ ${}^{+0.09}_{-0.12}$ 30 ADAMSON 2014 MINS Accel., atmsopheric, inverted mass ordering $2.54$ ${}^{+0.19}_{-0.20}$ 31 AN 2014 DAYA 3${{\mathit \nu}}$ osc.; normal mass ordering $-2.64$ ${}^{+0.20}_{-0.19}$ 31 AN 2014 DAYA 3${{\mathit \nu}}$ osc.; inverted mass ordering $2.48$ ${}^{+0.05}_{-0.07}$ 32 FORERO 2014 FIT 3${{\mathit \nu}}$ ; normal mass ordering $-2.38$ ${}^{+0.06}_{-0.05}$ 32 FORERO 2014 FIT 3${{\mathit \nu}}$ ; inverted mass ordering $2.457$ $\pm0.047$ 33, 34 GONZALEZ-GARC.. 2014 FIT Normal mass ordering; global fit $-2.449$ ${}^{+0.047}_{-0.048}$ 33 GONZALEZ-GARC.. 2014 FIT Inverted mass ordering; global fit $2.3$ ${}^{+0.6}_{-0.5}$ 35 AARTSEN 2013 B ICCB DeepCore, 2${{\mathit \nu}}$ oscillation $2.44$ ${}^{+0.17}_{-0.15}$ 36 ABE 2013 G T2K 3${{\mathit \nu}}$ osc.; normal mass ordering $2.41$ ${}^{+0.09}_{-0.10}$ 37 ADAMSON 2013 B MINS 2${{\mathit \nu}}$ osc.; beam + atmospheric; identical ${{\mathit \nu}}$ $\&$ ${{\overline{\mathit \nu}}}$ $\text{2.2 - 3.1}$ 38 ABE 2012 A T2K off-axis beam $2.62$ ${}^{+0.31}_{-0.28}$ $\pm0.09$ 39 ADAMSON 2012 MINS ${{\overline{\mathit \nu}}}$ beam $\text{1.35 - 2.55}$ 40, 41 ADAMSON 2012 B MINS MINOS atmospheric $\text{1.4 - 5.6}$ 40, 42 ADAMSON 2012 B MINS MINOS pure atmospheric ${{\mathit \nu}}$ $\text{0.9 - 2.5}$ 40, 42 ADAMSON 2012 B MINS MINOS pure atmospheric ${{\overline{\mathit \nu}}}$ $\text{1.8 - 5.0}$ 43 ADRIAN-MARTIN.. 2012 ANTR Atmospheric ${{\mathit \nu}}$ with deep sea telescope $\text{1.3 - 4.0}$ 44 ABE 2011 C SKAM atmospheric ${{\overline{\mathit \nu}}}$ $2.32$ ${}^{+0.12}_{-0.08}$ ADAMSON 2011 MINS 2${{\mathit \nu}}$ oscillation; maximal mixing $3.36$ ${}^{+0.46}_{-0.40}$ 45 ADAMSON 2011 B MINS ${{\overline{\mathit \nu}}}$ beam $\text{< 3.37}$ 46 ADAMSON 2011 C MINS MINOS $\text{1.9 - 2.6}$ 47 WENDELL 2010 SKAM 3${{\mathit \nu}}$ osc.; normal mass ordering $\text{-1.7 - -2.7}$ 47 WENDELL 2010 SKAM 3${{\mathit \nu}}$ osc.; inverted mass ordering $2.43$ $\pm0.13$ ADAMSON 2008 A MINS MINOS $\text{0.07 - 50}$ 48 ADAMSON 2006 MINS atmospheric ${{\mathit \nu}}$ with far detector $\text{1.9 - 4.0}$ 49, 50 AHN 2006 A K2K KEK to Super-K $\text{2.2 - 3.8}$ 51 MICHAEL 2006 MINS MINOS $\text{1.9 - 3.6}$ 49 ALIU 2005 K2K KEK to Super-K $\text{0.3 - 12}$ 52 ALLISON 2005 SOU2 $\text{1.5 - 3.4}$ 53 ASHIE 2005 SKAM atmospheric neutrino $\text{0.6 - 8.0}$ 54 AMBROSIO 2004 MCRO MACRO $1.9\text{ to }3.0 $ 55 ASHIE 2004 SKAM L/E distribution $\text{1.5 - 3.9}$ 56 AHN 2003 K2K KEK to Super-K $\text{0.25 - 9.0}$ 57 AMBROSIO 2003 MCRO MACRO $\text{0.6 - 7.0}$ 58 AMBROSIO 2003 MCRO MACRO $\text{0.15 - 15}$ 59 SANCHEZ 2003 SOU2 Soudan-2 Atmospheric $\text{0.6 - 15}$ 60 AMBROSIO 2001 MCRO upward ${{\mathit \mu}}$ $\text{1.0 - 6.0}$ 61 AMBROSIO 2001 MCRO upward ${{\mathit \mu}}$ $\text{1.0 - 50}$ 62 FUKUDA 1999 C SKAM upward ${{\mathit \mu}}$ $\text{1.5 - 15.0}$ 63 FUKUDA 1999 D SKAM upward ${{\mathit \mu}}$ $\text{0.7 - 18}$ 64 FUKUDA 1999 D SKAM stop ${{\mathit \mu}}$ $/$ through $\text{0.5 - 6.0}$ 65 FUKUDA 1998 C SKAM Super-Kamiokande $\text{0.55 - 50}$ 66 HATAKEYAMA 1998 KAMI Kamiokande $\text{4 - 23}$ 67 HATAKEYAMA 1998 KAMI Kamiokande $\text{5 - 25}$ 68 FUKUDA 1994 KAMI Kamiokande 1  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. 2  ABE 2020F reports $\Delta $m${}^{2}_{13}=0.00243$ $\pm0.00007$ 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${}^{2}$. 3  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 . 4  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 . 5  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. 6  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$^2({{\mathit \theta}_{{13}}} )$ = $0.0219$ $\pm0.0012$. 7  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}$ = $0.002522$ ${}^{+0.000068}_{-0.000070}$ 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. 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 2021A results are based on $1.49 \times 10^{21}$ POT in neutrino mode and $1.64 \times 10^{21}$ POT in antineutrino mode. 10  ESTEBAN 2020A reports results of a global fit to neutrino oscillation data available at the time of the Neutrino2020 conference. 11  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. 12  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 . 13  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}}} $ = $0.304$ $\pm0.014$. 14  ABE 2018G data prefers normal ordering with a posterior probability of 87$\%$. Supersedes ABE 2017F. 15  ABE 2018G reports $\Delta $m${}^{2}_{13}=0.002432$ $\pm0.000070$ 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${}^{2}$. 16  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 . 17  The error for octant I is taken from the result for octant II. 18  AGAFONOVA 2018 assumes maximal ${{\mathit \theta}_{{23}}}$ mixing. 19  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}$ = $0.00262$ ${}^{+0.00021}_{-0.00023}{}^{+0.00012}_{-0.00013}$ 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 20  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. 21  Superseded by ACERO 2018 . 22  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. Superseded by ADEY 2018A. 23  ABE 2016D reports oscillation results using ${{\overline{\mathit \nu}}_{{\mu}}}$ disappearance in an off-axis beam. 24  Superseded by ADAMSON 2017A. 25  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}$ = $0.00262$ ${}^{+0.00021}_{-0.00023}{}^{+0.00012}_{-0.00013}$ 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}$. 26  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. 27  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${}^{2}$. 28  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. 29  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. 30  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. 31  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}$ = $0.00259$ ${}^{+0.00019}_{-0.00020}$ eV${}^{2}$. Assuming the normal (inverted) ordering, the fitted $\Delta $m${}^{2}_{32}$ = $0.00254$ ${}^{+0.00019}_{-0.00020}$ ($0.00264$ ${}^{+0.00019}_{-0.00020}$) eV${}^{2}$. Superseded by AN 2015 . 32  FORERO 2014 performs a global fit to $\Delta $m${}^{2}_{31}$ using solar, reactor, long-baseline accelerator, and atmospheric neutrino data. 33  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 $0.002445$ ${}^{+0.000047}_{-0.000045}$ eV${}^{2}$ for inverted mass ordering. 34  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 $\Delta {{\mathit m}^{2}}_{\mathrm {12}}$. 35  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. 36  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 . 37  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. 38  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${}^{2}$. 39  ADAMSON 2012 is a two-neutrino oscillation analysis using antineutrinos. 40  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. 41  The 90$\%$ single-parameter confidence interval at the best fit point is $\Delta $m${}^{2}$ = $0.0019$ $\pm0.0004$ eV${}^{2}$. 42  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 $) plane obtained by minimizing the four parameter log-likelihood function with respect to the other oscillation parameters. 43  ADRIAN-MARTINEZ 2012 measured the oscillation parameters of atmospheric neutrinos with the ANTARES deep sea neutrino telescope using the data taken from 2007 to 2010 (863 days of total live time). Superseded by ALBERT 2019 44  ABE 2011C obtained this result by a two-neutrino oscillation analysis with separate mixing parameters between neutrinos and antineutrinos, using the Super-Kamiokande-I+II+III atmospheric neutrino data. The corresponding 90$\%$ CL neutrino oscillation parameter range obtained from this analysis is $\Delta {{\mathit m}^{2}}_{\mathrm {}}$ = $1.7 - 3.0 \times 10^{-3}$ eV${}^{2}$. 45  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. 46  ADAMSON 2011C obtains this result based on a study of antineutrinos in a neutrino beam and assumes maximal mixing in the two-flavor approximation. 47  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. 48  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. 49  The best fit in the physical region is for $\Delta \mathit m{}^{2}$ = $2.8 \times 10^{-3}$ eV${}^{2}$. 50  Supercedes ALIU 2005 . 51  MICHAEL 2006 best fit is $2.74 \times 10^{-3}$ eV${}^{2}$. See also ADAMSON 2008 . 52  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. 53  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${}^{2}$. 54  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${}^{2}$. 55  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${}^{2}$. 56  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${}^{2}$. 57  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${}^{2}$. 58  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${}^{2}$. 59  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${}^{2}$. 60  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. 61  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. 62  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${}^{2}$. 63  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${}^{2}$. 64  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${}^{2}$. 65  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${}^{2}$. 66  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${}^{2}$. 67  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${}^{2}$. 68  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 2021A PR D103 L011101 T2K measurements of muon neutrino and antineutrino disappearance using $3.13\times 10^{21}$ protons on target ABE 2020F NAT 580 339 Constraint on the matter?antimatter symmetry-violating phase in neutrino oscillations Also PR D103 112008 Improved constraints on neutrino mixing from the T2K experiment with $\mathbf{3.13\times10^{21}}$ protons on target ADAMSON 2020A PRL 125 131802 Precision Constraints for Three-Flavor Neutrino Oscillations from the Full MINOS+ and MINOS Dataset ESTEBAN 2020A JHEP 2009 178 The fate of hints: updated global analysis of three-flavor neutrino oscillations AARTSEN 2019C PR D99 032007 Measurement of Atmospheric Tau Neutrino Appearance with IceCube DeepCore ACERO 2019 PRL 123 151803 First Measurement of Neutrino Oscillation Parameters using Neutrinos and Antineutrinos by NOvA AGAFONOVA 2019 PR D100 051301 Final results on neutrino oscillation parameters from the OPERA experiment in the CNGS beam ALBERT 2019 JHEP 1906 113 Measuring the atmospheric neutrino oscillation parameters and constraining the 3+1 neutrino model with ten years of ANTARES data AARTSEN 2018A PRL 120 071801 Measurement of Atmospheric Neutrino Oscillations at 6?56 GeV with IceCube DeepCore ABE 2018B PR D97 072001 Atmospheric neutrino oscillation analysis with external constraints in Super-Kamiokande I-IV ABE 2018G PRL 121 171802 Search for CP Violation in Neutrino and Antineutrino Oscillations by the T2K Experiment with $2.2\times10^{21}$ Protons on Target ACERO 2018 PR D98 032012 New constraints on oscillation parameters from $\nu_e$ appearance and $\nu_\mu$ disappearance in the NOvA experiment ADEY 2018A PRL 121 241805 Measurement of electron antineutrino oscillation with 1958 days of operation at Daya Bay AGAFONOVA 2018 PRL 120 211801 Final Results of the OPERA Experiment on ?? Appearance in the CNGS Neutrino Beam BAK 2018 PRL 121 201801 Measurement of Reactor Antineutrino Oscillation Amplitude and Frequency at RENO DE-SALAS 2018 PL B782 633 Status of neutrino oscillations 2018: 3$\sigma$ hint for normal mass ordering and improved CP sensitivity SEO 2018 PR D98 012002 Spectral Measurement of the Electron Antineutrino Oscillation Amplitude and Frequency using 500 Live Days of RENO Data 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 Also PR D98 019902 (errat.) Measurement of neutrino and antineutrino oscillations by the T2K experiment including a new additional sample of $\nu_e$ 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 Also PR D91 072010 Measurements of Neutrino Oscillation in Appearance and Disappearance Channels by the T2K Experiment with $6.6 \times 10^{20}$ Protons on Target 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 2012B PR D86 052007 Measurements of Atmospheric Neutrinos and Antineutrinos in the MINOS Far Detector ADAMSON 2012 PRL 108 191801 Improved Measurement of Muon Antineutrino Disappearance in MINOS 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 2011 PRL 106 181801 Measurement of the Neutrino Mass Splitting and Flavor Mixing by MINOS ADAMSON 2011C PR D84 071103 Search for the Disappearance of Muon Antineutrinos in the NuMI Neutrino Beam ADAMSON 2011B PRL 107 021801 First Direct Observation of Muon Antineutrino Disappearance 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 1999D PL B467 185 Neutrino Induced Upward Stopping Muons in Super-Kamiokande FUKUDA 1999C PRL 82 2644 Measurement of the Flux and Zenith Angle Distribution of Upward Through Going Muons by 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