$N_{up}(e)/N_{down}(e)$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$0.961^{+0.086}_{-0.079} \pm 0.016$$

1 ASHIE

05

SKAM multi-GeV

1 ASHIE 05 results are based on an exposure of 92 kton yr during the complete Super-Kamiokande I running period. The analyzed data sample consists of fully-contained single-ring e-like events with visible energy > 1.33 GeV. Upward-going events are those with $-1 < \cos(\text{zenith angle}) < -0.2$ and downward-going events are those with $0.2 < \cos(\text{zenith angle}) < 1$. The e-like up-down ratio for the multi-GeV data is consistent with 1 (the expectation for no atmospheric $\nu_e$ oscillations).

$R(\text{up/down}; \mu) = (\text{Measured up/down}; \mu) / (\text{Expected up/down}; \mu)$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$0.62^{+0.05}_{-0.02} \pm 0.02$$

1

ADAMSON

12B

MINS

contained-vertex muons

$$0.62^{+0.19}_{-0.14} \pm 0.02$$

2

ADAMSON

06

MINS

atmospheric $\nu$ with far detector

1 ADAMSON 12b reports the atmospheric neutrino results obtained with MINOS far detector in 2,553 live days (an exposure of 37.9 kton-yr). This result is obtained with a sample of high resolution contained-vertex muons. The expected ratio is calculated with no neutrino oscillation.

2 ADAMSON 06 result is obtained with the MINOS far detector with an exposure of 4.54 kton yr. The expected ratio is calculated with no neutrino oscillation.

$N(\mu^{+})/N(\mu^{-})$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$0.46^{+0.05}_{-0.04} \pm 0.02$$

1,2

ADAMSON

12B

MINS

contained-vertex muons

$$0.63^{+0.09}_{-0.08} \pm 0.02$$

1,3

ADAMSON

12B

MINS

$\nu$-induced rock-muons

1 ADAMSON 12b reports the atmospheric neutrino results obtained with MINOS far detector in 2,553 live days (an exposure of 37.9 kton-yr). The muon charge ratio $N(\mu^{+})/N(\mu^{-})$ represents the $\bar{\nu}_{\mu}/\nu_{\mu}$ ratio.

2 This result is obtained with a charge-separated sample of high resolution contained-vertex muons. The quoted error is statistical only.

3 This result is obtained with a charge-separated sample of high resolution neutrino-induced rock-muons. The quoted error is statistical only.

$R(\mu^{+}/\mu^{-}) = (\text{Measured } N(\mu^{+})/N(\mu^{-})) / (\text{Expected } N(\mu^{+})/N(\mu^{-}))$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$0.93^{+0.09}_{-0.08} \pm 0.09$$

1,2

ADAMSON

12B

MINS

contained-vertex muons

$$1.29^{+0.19}_{-0.17} \pm 0.16$$

1,3

ADAMSON

12B

MINS

$\nu$-induced rock-muons

$$1.03^{+0.08}_{-0.08} \pm 0.08$$

1,4

ADAMSON

12B

MINS

contained

$$1.39^{+0.35}_{-0.46} \pm 0.08$$

5

ADAMSON

07

MINS

Upward and horizontal $\mu$ with far detector

$$0.96^{+0.38}_{-0.27} \pm 0.15$$

6

ADAMSON

06

MINS

atmospheric $\nu$ with far detector

1 ADAMSON 12b reports the atmospheric neutrino results obtained with MINOS far detector in 2,553 live days (an exposure of 37.9 kton-yr). The muon charge ratio $N(\mu^{+})/N(\mu^{-})$ represents the $\bar{\nu}_{\mu}/\nu_{\mu}$ ratio. As far as the same oscillation parameters are used for $\nu_s$ and $\bar{\nu}_s$, the expected $\bar{\nu}_{\mu}/\nu_{\mu}$ ratio is almost entirely independent of any input oscillations.

2 This result is obtained with a charge-separated sample of high resolution contained-vertex muons.

3 This result is obtained with a charge-separated sample of high resolution neutrino-induced rock-muons.

4 The charge-separated samples of high resolution contained-vertex muons and neutrino-induced rock-muons are combined to obtain this result which is consistent with unity.

5 ADAMSON 07 result is obtained with the MINOS far detector in 854.24 live days, based on neutrino-induced upward-going and horizontal muons. This result is consistent with CPT conservation.

6 ADAMSON 06 result is obtained with the MINOS far detector with an exposure of 4.54 kton yr, based on contained events. The expected ratio is calculated by assuming the same oscillation parameters for neutrinos and antineutrinos.

Solar neutrinos

Solar neutrinos are produced by thermonuclear fusion reactions in the Sun. Radiochemical experiments measure particular combinations of fluxes from various neutrino-producing reactions, whereas water-Cherenkov experiments mainly measure a flux of neutrinos from decay of $^8$B. Solar neutrino fluxes are composed of all active neutrino species, $\nu_e$, $\nu_\mu$, and $\nu_\tau$. In addition, some other mechanisms may cause antineutrino components in solar neutrino fluxes. Each measurement method is sensitive to a particular component or a combination of components of solar neutrino fluxes.

$\nu_e$ Capture Rates from Radiochemical Experiments

1 SNU (Solar Neutrino Unit) = $10^{-36}$ captures per atom per second.

<table><thead><tr><th>VALUE (SNU)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$73.4^{+6.1}_{-6.0} \pm 3.7$$

1 KAETHER

10

GALX reanalysis

$$67.6^{+4.0}_{-3.2} \pm 3.2$$

2 KAETHER

10

GNO+GALX reanalysis combined

$$65.4^{+3.1}_{-3.0} \pm 2.6$$

3 ABDURASHI...

09

SAGE 71Ga → 71Ge

$$62.9^{+5.5}_{-5.3} \pm 2.5$$

4 ALTMANN

05

GNO 71Ga → 71Ge

$$69.3^{+4.1}_{-3.6} \pm 3.6$$

5 ALTMANN

05

GNO GNO + GALX combined

$$77.5^{+6.2}_{-4.7} \pm 4.3$$

6 HAMPEL

99

GALX 71Ga → 71Ge

$$2.56^{\pm 0.16}_{\pm 0.16} \pm 0.16$$

7 CLEVELAND

98

HOME 37CI → 37Ar

1 KAETHER 10 reports the reanalysis results of a complete GALLEX data (GALLEX I+II+III+IV, reported in HAMPEL 99) based on the event selection with a new pulse shape analysis, which provides a better background reduction than the rise time analysis adopted in HAMPEL 99.

2 Combined result of GALLEX I+II+III+IV reanalysis and GNO I+II+III (ALTMANN 05).

3 ABDURASHITOV 09 reports a combined analysis of 168 extractions of the SAGE solar neutrino experiment during the period January 1990 through December 2007, and updates the ABDURASHITOV 02 result. The data are consistent with the assumption that the solar neutrino production rate is constant in time. Note that a ~15% systematic uncertainty in the overall normalization may be added to the ABDURASHITOV 09 result, because calibration experiments for gallium solar neutrino measurements using intense $^{51}$Cr (twice by GALLEX and once by SAGE) and $^{37}$Ar (by SAGE) result in an average ratio of 0.87 ± 0.05 of the observed to calculated rates.

4 ALTMANN 05 reports the complete result from the GNO solar neutrino experiment (GNO I+II+III), which is the successor project of GALLEX. Experimental technique of GNO is essentially the same as that of GALLEX. The run data cover the period 20 May 1998 through 9 April 2003.

5 Combined result of GALLEX I+II+III+IV (HAMPEL 99) and GNO I+II+III.

6 HAMPEL 99 report the combined result for GALLEX I+II+III+IV (65 runs in total), which update the HAMPEL 96 result. The GALLEX IV result (12 runs) is 118.4 ± 17.8 ± 6.6 SNU. (HAMPEL 99 discuss the consistency of partial results with the mean.) The GALLEX experimental program has been completed with these runs. The total run data cover the period 14 May 1991 through 23 January 1997. A total of 300 $^{71}$Ge events were observed. Note that a ~15% systematic uncertainty in the overall normalization may be added to the HAMPEL 99 result, because calibration experiments for gallium solar neutrino measurements using intense $^{51}$Cr (twice by GALLEX and once by SAGE) and $^{37}$Ar (by SAGE) result in an average ratio of 0.87 ± 0.05 of the observed to calculated rates.

7 CLEVELAND 98 is a detailed report of the $^{37}$CI experiment at the Homestake Mine. The average solar neutrino-induced $^{37}$Ar production rate from 108 runs between 1970 and 1994 updates the DAVIS 89 result.

$\phi_{ES} (^8\text{B})$

$^8$B solar-neutrino flux measured via $\nu_e$ elastic scattering. This process is sensitive to all active neutrino flavors, but with reduced sensitivity to $\nu_{\mu}$, $\nu_e$ due to the cross-section difference, $\sigma(\nu_{\mu}, \tau e) \sim 0.16\sigma(\nu_e e)$. If the $^8$B solar-neutrino flux involves nonelectron flavor active neutrinos, their contribution to the flux is $\sim 0.16$ times of $\nu_e$.

<table><thead><tr><th>VALUE (10<sup>6</sup> cm<sup>-2</sup>s<sup>-1</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$2.57^{+0.17}_{-0.18} \pm 0.07$$

1 AGOSTINI

20A

BORX average flux

$$2.53^{+0.31}_{-0.28} \pm 0.13$$

2 ANDERSON

19

SNO+ Water phase; average flux

$$2.57^{+0.17}_{-0.18} \pm 0.07$$

3 AGOSTINI

18B

BORX average flux

$$2.345^{\pm 0.014}_{\pm 0.036} \pm 0.036$$

4 ABE

16C

SKAM SK-I+II+III+IV average flux

$$2.308^{\pm 0.020}_{\pm 0.040} \pm 0.040$$

5 ABE

16C

SKAM SK-IV average flux

$$2.250^{+0.030}_{-0.029} \pm 0.038$$

5 ABE

16C

SKAM SK-IV day flux

$$2.364^{\pm 0.029}_{\pm 0.040} \pm 0.040$$

5 ABE

16C

SKAM SK-IV night flux

$$2.404^{\pm 0.039}_{\pm 0.053} \pm 0.053$$

6 ABE

16C

SKAM SK-III average flux

$$2.41^{\pm 0.05}_{\pm 0.15} \pm 0.16$$

7 ABE

11

SKAM SK-II average flux

$$2.38^{\pm 0.02}_{\pm 0.08} \pm 0.08$$

8 ABE

11

SKAM SK-I average flux

$$2.77^{\pm 0.26}_{\pm 0.32} \pm 0.32$$

9 ABE

11B

KLND average flux

$$2.4^{\pm 0.4}_{\pm 0.1} \pm 0.1$$

10 BELLINI

10A

BORX average flux

$$1.77^{+0.24}_{-0.21} \pm 0.09$$

11 AHARMIM

08

SNO Phase III

$$2.38^{\pm 0.05}_{\pm 0.16} \pm 0.16$$

12 CRAVENS

08

SKAM average flux

$$2.35^{\pm 0.02}_{\pm 0.08} \pm 0.08$$

13 HOSAKA

06

SKAM average flux

$$2.35^{\pm 0.22}_{\pm 0.15} \pm 0.15$$

14 AHARMIM

05A

SNO Salty D$_2$O; $^8$B shape not con-

$$2.34^{\pm 0.23}_{-0.24} \pm 0.15$$

15 AHARMIM

05A

SNO average flux

$$2.34^{\pm 0.22}_{\pm 0.15} \pm 0.15$$

16 AHARMIM

01

SNO average flux

$$2.39^{+0.24}_{-0.23} \pm 0.12$$

15 AHARMIM

02

SNO average flux

$$2.39^{+0.34}_{-0.14} \pm 0.16$$

16 AHARMIM

01

SNO average flux
<table><tr><td>2.80 ±0.19 ±0.33</td><td><sup>17</sup>FUKUDA</td><td>96</td><td>KAMI average flux</td></tr><tr><td>2.70 ±0.27</td><td><sup>17</sup>FUKUDA</td><td>96</td><td>KAMI day flux</td></tr><tr><td>2.87 <sup>+0.27</sup><sub>-0.26</sub></td><td><sup>17</sup>FUKUDA</td><td>96</td><td>KAMI night flux</td></tr></table>

1. AGOSTINI 20A obtained this result from the $\nu_e e$ elastic scattering rate over the period between January 2008 and December 2016. Uses the same data as AGOSTINI 18B, but the analysis technique is significantly improved.

2. ANDERSON 19 reports this result from the $\nu_e e$ elastic scattering rate using a 69.2 kton-day (or 114.7 days) of exposure from May through December, 2017 during the SNO+ detector's water commissioning phase. The events over the reconstructed electron kinetic energy range of 5-15 MeV were analyzed.

3. AGOSTINI 18B obtained this result from the $\nu_e e$ elastic scattering rate over the period between January 2008 and December 2016.

4. ABE 16C reports the combined results of the four phases of the Super-Kamiokande average flux measurements. Here the revised Super-Kamiokande-III result is used.

5. ABE 16C reports the Super-Kamiokande-IV results for 1664 live days from September 2008 to February 2014. The analysis threshold is total electron energy of 4.0 MeV.

6. ABE 16C revised the Super-Kamiokande-III average flux value reported in ABE 11. Super-Kamiokande-III results are for 548 live days from August 4, 2006 to August 18, 2008. The analysis threshold is 5.0 MeV, but the event sample in the 5.0-6.5 MeV total electron energy range has a total live time of 298 days.

7. ABE 11 recalculated the Super-Kamiokande-II results using $^8$B spectrum of WINTER 06A.

8. ABE 11 recalculated the Super-Kamiokande-I results using $^8$B spectrum of WINTER 06A.

9. ABE 11B use a 123 kton-day exposure of the KamLAND liquid scintillation detector to measure the $^8$B solar neutrino flux. They utilize $\nu_e$-elastic scattering above a reconstructed-energy threshold of 5.5 MeV, corresponding to 5 MeV electron recoil energy. 299 electron recoil candidate events are reported, of which 157 ± 23.6 are assigned to background.

10. BELLINI 10A reports the Borexino result with 3 MeV energy threshold for scattered electrons. The data correspond to 345.3 live days with a target mass of 100 t, between July 15, 2007 and August 23, 2009.

11. AHARMIM 08 reports the results from SNO Phase III measurement using an array of $^3$He proportional counters to measure the rate of NC interactions in heavy water, over the period between November 27, 2004 and November 28, 2006, corresponding to 385.17 live days. A simultaneous fit was made for the number of NC events detected by the proportional counters and the numbers of NC, CC, and ES events detected by the PMTs, where the spectral distributions of the ES and CC events were not constrained to the $^8$B shape.

12. CRAVENS 08 reports the Super-Kamiokande-II results for 791 live days from December 2002 to October 2005. The photocathode coverage of the detector is 19% (reduced from 40% of that of Super-Kamiokande-I due to an accident in 2001). The analysis threshold for the average flux is 7 MeV.

13. HOSAKA 06 reports the final results for 1496 live days with Super-Kamiokande-I between May 31, 1996 and July 15, 2001, and replace FUKUDA 02 results. The analysis threshold is 5 MeV except for the first 280 live days (6.5 MeV).

14. AHARMIM 05A measurements were made with dissolved NaCl (0.195% by weight) in heavy water over the period between July 26, 2001 and August 28, 2003, corresponding to 391.4 live days, and update AHMED 04A. The CC, ES, and NC events were statistically separated. In one method, the $^8$B energy spectrum was not constrained. In the other method, the constraint of an undistorted $^8$B energy spectrum was added for comparison with AHMAD 02 results.

15. AHMAD 02 reports the $^8$B solar-neutrino flux measured via $\nu_e$ elastic scattering above the kinetic energy threshold of 5 MeV. The data correspond to 306.4 live days with SNO between November 2, 1999 and May 28, 2001, and updates AHMAD 01 results.

16. AHMAD 01 reports the $^8$B solar-neutrino flux measured via $\nu_e$ elastic scattering above the kinetic energy threshold of 6.75 MeV. The data correspond to 241 live days with SNO between November 2, 1999 and January 15, 2001.

17. FUKUDA 96 results are for a total of 2079 live days with Kamiokande II and III from January 1987 through February 1995, covering the entire solar cycle 22, with threshold $E_e > 9.3$ MeV (first 449 days), > 7.5 MeV (middle 794 days), and > 7.0 MeV (last 836 days). These results update the HIRATA 90 result for the average $^8$B solar-neutrino flux and HIRATA 91 result for the day-night variation in the $^8$B solar-neutrino flux. The total data sample was also analyzed for short-term variations: within experimental errors, no strong correlation of the solar-neutrino flux with the sunspot numbers was found.

## $\phi_{CC}$ ($^8$B)

$^8$B solar-neutrino flux measured with charged-current reaction which is sensitive exclusively to $\nu_e$.

<table><tr><td>VALUE (10<sup>6</sup> cm<sup>-2</sup>s<sup>-1</sup>)</td><td>DOCUMENT ID</td><td>TECN</td><td>COMMENT</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>1.67<sup>+0.05</sup><sub>-0.04</sub> ±0.07</td><td>1 AHARMIM</td><td>08</td><td>SNO</td><td>Phase III</td></tr><tr><td>1.68<sup>+0.06</sup><sub>-0.09</sub></td><td>2 AHARMIM</td><td>05A</td><td>SNO</td><td>Salty D<sub>2</sub>O; <sup>8</sup>B shape not const.</td></tr><tr><td>1.72<sup>+0.05</sup><sub>-0.11</sub></td><td>2 AHARMIM</td><td>05A</td><td>SNO</td><td>Salty D<sub>2</sub>O; <sup>8</sup>B shape constrained</td></tr><tr><td>1.76<sup>+0.06</sup><sub>-0.05</sub></td><td>3 AHMAD</td><td>02</td><td>SNO</td><td>average flux</td></tr><tr><td>1.75<sup>+0.07</sup><sub>-0.11</sub></td><td>4 AHMAD</td><td>01</td><td>SNO</td><td>average flux</td></tr></table>

1. AHARMIM 08 reports the results from SNO Phase III measurement using an array of $^3$He proportional counters to measure the rate of NC interactions in heavy water, over the period between November 27, 2004 and November 28, 2006, corresponding to 385.17 live days. A simultaneous fit was made for the number of NC events detected by the proportional counters and the numbers of NC, CC, and ES events detected by the PMTs, where the spectral distributions of the ES and CC events were not constrained to the $^8$B shape.

where the spectral distributions of the ES and CC events were not constrained to the $^8$B shape.

2. AHARMIM 05A measurements were made with dissolved NaCl (0.195% by weight) in heavy water over the period between July 26, 2001 and August 28, 2003, corresponding to 391.4 live days, and update AHMED 04A. The CC, ES, and NC events were statistically separated. In one method, the $^8$B energy spectrum was not constrained. In the other method, the constraint of an undistorted $^8$B energy spectrum was added for comparison with AHMAD 02 results.

3. AHMAD 02 reports the SNO result of the $^8$B solar-neutrino flux measured with charged-current reaction on deuterium, $\nu_e d \rightarrow ppe^{-}$, above the kinetic energy threshold of 5 MeV. The data correspond to 306.4 live days with SNO between November 2, 1999 and May 28, 2001, and updates AHMAD 01 results. The complete description of the SNO Phase I data set is given in AHARMIM 07.

4. AHMAD 01 reports the first SNO result of the $^8$B solar-neutrino flux measured with the charged-current reaction on deuterium, $\nu_e d \rightarrow ppe^{-}$, above the kinetic energy threshold of 6.75 MeV. The data correspond to 241 live days with SNO between November 2, 1999 and January 15, 2001.

## $\phi_{NC}$ ($^8$B)

$^8$B solar neutrino flux measured with neutral-current reaction, which is equally sensitive to $\nu_e$, $\nu_\mu$, and $\nu_\tau$.

<table><tr><td>VALUE (10<sup>6</sup> cm<sup>-2</sup>s<sup>-1</sup>)</td><td>CL%</td><td>DOCUMENT ID</td><td>TECN</td><td>COMMENT</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>&lt;9.0</td><td>90</td><td>1 MA</td><td>23A</td><td>PNDX</td><td>CE/NS, liquid Xe detector</td></tr><tr><td>5.25 ±0.16</td><td>+0.11</td><td>2 AHARMIM</td><td>13</td><td>SNO</td><td>All three phases combined</td></tr><tr><td>5.140<sup>+0.160</sup><sub>-0.158</sub></td><td>+0.132</td><td>3 AHARMIM</td><td>10</td><td>SNO</td><td>Phase I+II, low threshold</td></tr><tr><td>5.54<sup>+0.33</sup><sub>-0.31</sub></td><td>+0.36</td><td>4 AHARMIM</td><td>08</td><td>SNO</td><td>Phase III, prop. counter + PMT</td></tr><tr><td>4.94 ±0.21</td><td>+0.38</td><td>5 AHARMIM</td><td>05A</td><td>SNO</td><td>Salty D<sub>2</sub>O; <sup>8</sup>B shape not const.</td></tr><tr><td>4.81 ±0.19</td><td>+0.28</td><td>5 AHARMIM</td><td>05A</td><td>SNO</td><td>Salty D<sub>2</sub>O; <sup>8</sup>B shape constrained</td></tr><tr><td>5.09<sup>+0.44</sup><sub>-0.43</sub></td><td>+0.46</td><td>6 AHMAD</td><td>02</td><td>SNO</td><td>average flux; <sup>8</sup>B shape const.</td></tr><tr><td>6.42 ±1.57</td><td>+0.55</td><td>6 AHMAD</td><td>02</td><td>SNO</td><td>average flux; <sup>8</sup>B shape not const.</td></tr></table>

1. MA 23A searched for $^8$B solar neutrinos elastically scattered off xenon nuclei in the commissioning phase of the PANDAX-4T experiment with an effective exposure of 0.48 ton-yr. This experiment is dedicated to dark matter direct search using a dual-phase xenon TPC with a sensitive volume of 3.7 tons of liquid Xe.

2. AHARMIM 13 obtained this result from a combined analysis of the data from all three phases, SNO-I, II, and III. The measurement of the $^8$B flux mostly comes from the NC signal, however, CC contribution is included in the fit.

3. AHARMIM 10 reports this result from a joint analysis of SNO Phase I+II data with the "effective electron kinetic energy" threshold of 3.5 MeV. This result is obtained with a "binned-histogram unconstrained fit" where binned probability distribution functions of the neutrino signal observables were used without any model constraints on the shape of the neutrino spectrum.

4. AHARMIM 08 reports the results from SNO Phase III measurement using an array of $^3$He proportional counters to measure the rate of NC interactions in heavy water, over the period between November 27, 2004 and November 28, 2006, corresponding to 385.17 live days. A simultaneous fit was made for the number of NC events detected by the proportional counters and the numbers of NC, CC, and ES events detected by the PMTs, where the spectral distributions of the ES and CC events were not constrained to the $^8$B shape.

5. AHARMIM 05A measurements were made with dissolved NaCl (0.195% by weight) in heavy water over the period between July 26, 2001 and August 28, 2003, corresponding to 391.4 live days, and update AHMED 04A. The CC, ES, and NC events were statistically separated. In one method, the $^8$B energy spectrum was not constrained. In the other method, the constraint of an undistorted $^8$B energy spectrum was added for comparison with AHMAD 02 results.

6. AHMAD 02 reports the first SNO result of the $^8$B solar-neutrino flux measured with the neutral-current reaction on deuterium, $\nu_e d \rightarrow n\nu_e\nu_e$, above the neutral-current reaction threshold of 2.2 MeV. The data correspond to 306.4 live days with SNO between November 2, 1999 and May 28, 2001. The complete description of the SNO Phase I data set is given in AHARMIM 07.

## $\phi_{\nu_\mu+\nu_\tau}$ ($^8$B)

Nonelectron-flavor active neutrino component ($\nu_\mu$ and $\nu_\tau$) in the $^8$B solar-neutrino flux.

<table><tr><td>VALUE (10<sup>6</sup> cm<sup>-2</sup>s<sup>-1</sup>)</td><td>DOCUMENT ID</td><td>TECN</td><td>COMMENT</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>3.26<sup>+0.25</sup><sub>-0.35</sub></td><td>1 AHARMIM</td><td>05A</td><td>SNO</td><td>From $\phi_{NC}$, $\phi_{CC}$, and $\phi_{ES}$; <sup>8</sup>B shape not const.</td></tr><tr><td>3.09<sup>+0.22</sup><sub>-0.27</sub></td><td>1 AHARMIM</td><td>05A</td><td>SNO</td><td>From $\phi_{NC}$, $\phi_{CC}$, and $\phi_{ES}$; <sup>8</sup>B shape constrained</td></tr><tr><td>3.41<sup>+0.45</sup><sub>-0.48</sub></td><td>2 AHMAD</td><td>02</td><td>SNO</td><td>From $\phi_{NC}$, $\phi_{CC}$, and $\phi_{ES}$</td></tr><tr><td>3.69<sup>+1.13</sup></td><td>3 AHMAD</td><td>01</td><td></td><td>Derived from SNO+SuperKam, water Cherenkov</td></tr></table>

1. AHARMIM 05A measurements were made with dissolved NaCl (0.195% by weight) in heavy water over the period between July 26, 2001 and August 28, 2003, corresponding
to 391.4 live days, and update AHMED 04A. The CC, ES, and NC events were statistically separated. In one method, the $^8$B energy spectrum was not constrained. In the other method, the constraint of an undistorted $^8$B energy spectrum was added for comparison with AHMAD 02 results.

2 AHMAD 02 deduced the nonelectron-flavor active neutrino component ($\nu_\mu$ and $\nu_\tau$) in the $^8$B solar-neutrino flux, by combining the charged-current result, the $\nu e$ elastic-scattering result and the neutral-current result. The complete description of the SNO Phase I data set is given in AHARMIM 07.

3 AHMAD 01 deduced the nonelectron-flavor active neutrino component ($\nu_\mu$ and $\nu_\tau$) in the $^8$B solar-neutrino flux, by combining the SNO charged-current result (AHMAD 01) and the Super-Kamiokande $\nu e$ elastic-scattering result (FUKUDA 01).

## Total Flux of Active pp Solar Neutrinos

Total flux of active neutrinos ($\nu_e, \nu_\mu, \nu_\tau$).

<table><thead><tr><th>VALUE (10<sup>10</sup> cm<sup>-2</sup>s<sup>-1</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$6.1 \pm 0.5 \frac{+0.3}{-0.5}$$

1 AGOSTINI

18B BORX $\nu_e e$ scattering rate

1 AGOSTINI 18B obtained this result from the measured $\nu_e e$ elastic scattering rate over the period between December 2011 and May 2016, assuming the MSW-LMA oscillation parameters derived by ESTEBAN 17. Assuming a high-metallicity standard solar model, the electron neutrino survival probability for the pp solar neutrino is calculated to be 0.57 ± 0.09.

## Total Flux of Active $^7$Be Solar Neutrinos

Total flux of active neutrinos ($\nu_e, \nu_\mu, \nu_\tau$).

<table><thead><tr><th>VALUE (10<sup>9</sup> cm<sup>-2</sup>s<sup>-1</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$4.99 \pm 0.11 \frac{+0.06}{-0.08}$$

1 AGOSTINI

18B BORX $\nu_e e$ scattering rate

1 AGOSTINI 18B obtained this result from the measured $\nu_e e$ elastic scattering rate over the period between December 2011 and May 2016, assuming the MSW-LMA oscillation parameters derived by ESTEBAN 17. Assuming a high-metallicity standard solar model, the electron neutrino survival probability for the $^7$Be solar neutrino is calculated to be 0.53 ± 0.05.

## Total Flux of Active pep Solar Neutrinos

Total flux of active neutrinos ($\nu_e, \nu_\mu, \nu_\tau$).

<table><thead><tr><th>VALUE (10<sup>8</sup> cm<sup>-2</sup>s<sup>-1</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$1.27 \pm 0.19 \frac{+0.08}{-0.12}$$

1 AGOSTINI

18B BORX $\nu_e e$ scattering rate

1 AGOSTINI 18B obtained this result from the measured $\nu_e e$ elastic scattering rate over the period between December 2011 and May 2016, assuming the MSW-LMA oscillation parameters derived by ESTEBAN 17 and a high-metallicity standard solar model. The electron neutrino survival probability for the pep solar neutrino is calculated to be 0.43 ± 0.11.

## Total Flux of Active $^8$B Solar Neutrinos

Total flux of active neutrinos ($\nu_e, \nu_\mu$ and $\nu_\tau$).

<table><thead><tr><th>VALUE (10<sup>6</sup> cm<sup>-2</sup>s<sup>-1</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$5.95 \pm 0.75 \frac{+0.28}{-0.71 \pm 0.30}$$

1 ANDERSON

19 SNO+ Water phase; $\nu_e e$ scattering rate

$$5.68 \pm 0.39 \frac{+0.03}{-0.41 \pm 0.03}$$

2 AGOSTINI

18B BORX From $\nu_e e$ scattering rate

$$5.25 \pm 0.16 \frac{+0.11}{-0.13}$$

3 AHARMIM

13 SNO All three phases combined

$$5.046 \pm 0.159 \frac{+0.107}{-0.152 \pm 0.123}$$

4 AHARMIM

10 SNO From $\phi_{NC'}$ in Phase I+II, low threshold

$$5.54 \pm 0.33 \frac{+0.36}{-0.31 \pm 0.34}$$

5 AHARMIM

08 SNO $\phi_{NC'}$ in Phase III

$$4.94 \pm 0.21 \frac{+0.38}{-0.34}$$

6 AHARMIM

05A SNO From $\phi_{NC'}$ $^8$B shape not const.

$$4.81 \pm 0.19 \frac{+0.28}{-0.27}$$

6 AHARMIM

05A SNO From $\phi_{NC'}$ $^8$B shape constrained

$$5.09 \pm 0.44 \frac{+0.46}{-0.43 \pm 0.43}$$

7 AHMAD

02 SNO Direct measurement from $\phi_{NC}$

$$5.44 \pm 0.99$$

8 AHMAD

01 Derived from SNO+SuperKam, water Cherenkov

1 ANDERSON 19 reports this result from the measured $\nu_e e$ elastic scattering rate using a 69.2 kton-day (or 114.7 days) of exposure from May through December, 2017 during the SNO+ detector's water commissioning phase, assuming the neutrino mixing parameters given in PDG 16 and a standard solar model given in BAHCALL 05.

2 AGOSTINI 18B obtained this result from the measured $\nu_e e$ elastic scattering rate over the period between January 2008 and December 2016, assuming the MSW-LMA oscillation parameters derived by ESTEBAN 17. Assuming a high-metallicity standard solar model, the electron neutrino survival probability for the $^8$B solar neutrino is calculated to be 0.37 ± 0.08.

3 AHARMIM 13 obtained this result from a combined analysis of the data from all three phases, SNO-I, II, and III. The measurement of the $^8$B flux mostly comes from the NC signal, however, CC contribution is included in the fit.

4 AHARMIM 10 reports this result from a joint analysis of SNO Phase I+II data with the "effective electron kinetic energy" threshold of 3.5 MeV. This result is obtained with the assumption of unitarity, which relates the NC, CC, and ES rates. The data were fit with the free parameters directly describing the total $^8$B neutrino flux and the energy-dependent $\nu_e$ survival probability.

5 AHARMIM 08 reports the results from SNO Phase III measurement using an array of 3 He proportional counters to measure the rate of NC interactions in heavy water, over the period between November 27, 2004 and November 28, 2006, corresponding to 385.17 live days. A simultaneous fit was made for the number of NC events detected by the proportional counters and the numbers of NC, CC, and ES events detected by the PMTs, where the spectral distributions of the ES and CC events were not constrained to the $^8$B shape.

6 AHARMIM 05A measurements were made with dissolved NaCl (0.195% by weight) in heavy water over the period between July 26, 2001 and August 28, 2003, corresponding to 391.4 live days, and update AHMED 04A. The CC, ES, and NC events were statistically separated. In one method, the $^8$B energy spectrum was not constrained. In the other method, the constraint of an undistorted $^8$B energy spectrum was added for comparison with AHMAD 02 results.

7 AHMAD 02 determined the total flux of active $^8$B solar neutrinos by directly measuring the neutral-current reaction, $\nu_\ell d \to n p \nu_\ell$, which is equally sensitive to $\nu_e, \nu_\mu$, and $\nu_\tau$. The complete description of the SNO Phase I data set is given in AHARMIM 07.

8 AHMAD 01 deduced the total flux of active $^8$B solar neutrinos by combining the SNO charged-current result (AHMAD 01) and the Super-Kamiokande $\nu e$ elastic-scattering result (FUKUDA 01).

## Total Flux of Active CNO Solar Neutrinos

Total flux of active neutrinos ($\nu_e, \nu_\mu, \nu_\tau$).

<table><thead><tr><th>VALUE (10<sup>8</sup> cm<sup>-2</sup>s<sup>-1</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$6.7 \pm 1.2 \frac{+0.8}{-0.8}$$

1 BASILICO

23 BORX $\nu_e e$ directional + spectral information

$$6.6 \pm 2.0 \frac{+0.9}{-0.9}$$

2 APPEL

22 BORX $\nu_e e$ scattering rate

$$7.0 \pm 3.0 \frac{+0.9}{-0.9}$$

3 AGOSTINI

20D BORX $\nu_e e$ scattering rate

<7.9

95

4 AGOSTINI

18B BORX $\nu_e e$ scattering rate

1 BASILICO 23 obtained this result by combining the newly developed Correlated Integrated Directionality (CID)-based CNO result obtained by using the complete Borexino data-taking period from 2007 to 2021, with a spectral fit of the Phase-III dataset (from July 2016 to October 2021, characterized by a thermally stable detector). Note that the directional information is independent from the spectral information on which the previous CNO solar neutrino measurements by Borexino were based. Neutrino flavor conversion was taken into account.

2 APPEL 22 obtained this result from the measured $\nu_e e$ elastic scattering rate over the period between January 2017 and October 2021, assuming the MSW-LMA oscillation parameters derived by ESTEBAN 20A. The exposure corresponding to this data is 1431.6 days × 71.3 tons.

3 AGOSTINI 20D obtained this result from the measured $\nu_e e$ elastic scattering rate over the period between July 2016 to February 2020, assuming the MSW-LMA oscillation parameters derived by CAPOZZI 18.

4 AGOSTINI 18B obtained this result from an upper limit of the $\nu_e e$ elastic scattering rate for the CNO neutrinos over the period between December 2011 and May 2016, assuming the MSW-LMA oscillation parameters derived by ESTEBAN 17.

## Total Flux of Active hep Solar Neutrinos

Total flux of active neutrinos ($\nu_e, \nu_\mu, \nu_\tau$).

<table><thead><tr><th>VALUE (10<sup>6</sup> cm<sup>-2</sup>s<sup>-1</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<1.8

90

1 AGOSTINI

20A BORX $\nu_e e$ scattering and $^{12}\text{C}(\nu, \nu')^{12}\text{C}$

<0.3

90

2 AHARMIM

20 SNO CC, NC, $\nu_e e$ scattering

<2.2

90

3 AGOSTINI

18B BORX $\nu_e e$ scattering rate

1 AGOSTINI 20A obtained this result from an upper limit of the $\nu_e e$ elastic scattering rate and NC-mediated inelastic scattering on carbon nuclei with 15.1 MeV deexcitation γ-ray for the hep neutrino. The dataset corresponds to an effective exposure of 0.745 kt·yr from November 2009 to October 2017. A FADC DAQ system, optimized for the acquisition of high-energy events was used for data collection. The MSW-LMA oscillation parameters derived by ESTEBAN 17 were assumed.

2 AHARMIM 20 uses the entire SNO dataset, corresponding to 2.47 kton·yrs of exposure after fiducialization. With the D$_2$O target, SNO was sensitive to charged current, neutral current, and elastic scattering channels.

3 AGOSTINI 18B obtained this result from an upper limit of the $\nu_e e$ elastic scattering rate for the hep neutrino using the dataset corresponding to an exposure of 0.8 kt·yr and assuming the MSW-LMA oscillation parameters derived by ESTEBAN 17.

## Day-Night Asymmetry ($^8$B)

$A = (\phi_{\text{night}} - \phi_{\text{day}}) / \phi_{\text{average}}$

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.033 ± 0.010 ± 0.005</td><td>1 ABE</td><td>16C</td><td>SKAM SK combined; Based on $\phi_{ES}$</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

$$0.036 \pm 0.016 \pm 0.006$$

2 ABE

16C SKAM SK-IV; Based on $\phi_{ES}$

$$0.032 \pm 0.011 \pm 0.005$$

3 RENSHAW

14 SKAM Based on $\phi_{ES}$

$$0.063 \pm 0.042 \pm 0.037$$

4 CRAVENS

08 SKAM Based on $\phi_{ES}$
<table><tr><td>0.021 ± 0.020<sup>+0.012</sup><sub>-0.013</sub></td><td>5 HOSAKA</td><td>06 SKAM</td><td>Based on φ<sub>ES</sub></td></tr><tr><td>0.017 ± 0.016<sup>+0.012</sup><sub>-0.013</sub></td><td>6 HOSAKA</td><td>06 SKAM</td><td>Fitted in the LMA region</td></tr><tr><td>-0.056 ± 0.074 ± 0.053</td><td>7 AHARMIM</td><td>05A SNO</td><td>From salty SNO φ<sub>CC</sub></td></tr><tr><td>-0.037 ± 0.063 ± 0.032</td><td>7 AHARMIM</td><td>05A SNO</td><td>From salty SNO φ<sub>CC</sub>; const. of no φ<sub>NC</sub> asymmetry</td></tr><tr><td>0.14 ± 0.063<sup>+0.015</sup><sub>-0.014</sub></td><td>8 AHMAD</td><td>02B SNO</td><td>Derived from SNO φ<sub>CC</sub></td></tr><tr><td>0.07 ± 0.049<sup>+0.013</sup><sub>-0.012</sub></td><td>9 AHMAD</td><td>02B SNO</td><td>Const. of no φ<sub>NC</sub> asymmetry</td></tr></table>

1 ABE 16c reports the combined day-night flux asymmetry results of the four phases of the Super-Kamiokande measurements. Amplitude fit method is used. See footnote to RENSHAW 14.

2 ABE 16c reports the Super-Kamiokande-IV results for 1664 live days from September 2008 to February 2014. The analysis threshold for day-night flux asymmetry is recoil electron energy of 4.49 MeV (total electron energy of 5.0 MeV). Amplitude fit method is used. See footnote to RENSHAW 14.

3 RENSHAW 14 obtains this result by using the "amplitude fit" introduced in SMY 04. The data from the Super-Kamiokande(SK)-1, -II, -III, and 1306 live days of the SK-IV measurements are used. The analysis threshold is recoil-electron kinetic energy of 4.5 MeV for SK-III, and SK-IV except for 250 live days in SK-III (6.0 MeV). The analysis threshold for SK-I and SK-II is the same as in the previous reports. (Note that in the previous SK solar-neutrino results, the analysis threshold is quoted as recoil-electron total energy.) This day-night asymmetry result is consistent with neutrino oscillations for $4 \times 10^{-5}$ eV$^2 < \Delta m^2_{21} < 7 \times 10^{-5}$ eV$^2$ and large mixing values of $\theta_{12}$ at the 68% CL.

4 CRAVENS 08 reports the Super-Kamiokande-II results for 791 live days from December 2002 to October 2005. The photocathode coverage of the detector is 19% (reduced from 40% of that of Super-Kamiokande-I due to an accident in 2001). The analysis threshold for the day and night fluxes is 7.5 MeV except for the first 159 live days (8.0 MeV).

5 HOSAKA 06 reports the final results for 1496 live days with Super-Kamiokande-I between May 31, 1996 and July 15, 2001, and replace FUKUDA 02 results. The analysis threshold is 5 MeV except for the first 280 live days (6.5 MeV).

6 This result with reduced statistical uncertainty is obtained by assuming two-neutrino oscillations within the LMA (large mixing angle) region and by fitting the time variation of the solar neutrino flux measured via $\nu_e$ elastic scattering to the variations expected from neutrino oscillations. For details, see SMY 04. There is an additional small systematic error of $\pm 0.0004$ coming from uncertainty of oscillation parameters.

7 AHARMIM 05A measurements were made with dissolved NaCl (0.195% by weight) in heavy water over the period between July 26, 2001 and August 28, 2003, with 176.5 days of the live time recorded during the day and 214.9 days during the night. This result is obtained with the spectral distribution of the CC events not constrained to the $^8$B shape.

8 AHMAD 02B results are based on the charged-current interactions recorded between November 2, 1999 and May 28, 2001, with the day and night live times of 128.5 and 177.9 days, respectively. The complete description of the SNO Phase I data set is given in AHARMIM 07.

9 AHMAD 02B results are derived from the charged-current interactions, neutral-current interactions, and $\nu_e$ elastic scattering, with the total flux of active neutrinos constrained to have no asymmetry. The data were recorded between November 2, 1999 and May 28, 2001, with the day and night live times of 128.5 and 177.9 days, respectively. The complete description of the SNO Phase I data set is given in AHARMIM 07.

### $\phi_{ES}$ ($^7$Be)

$^7$Be solar-neutrino flux measured via $\nu_e$ elastic scattering. This process is sensitive to all active neutrino flavors, but with reduced sensitivity to $\nu_{\mu,\tau}$ due to the cross-section difference, $\sigma(\nu_{\mu,\tau} e) \sim 0.2 \sigma(\nu_e e)$. If the $^7$Be solar-neutrino flux involves nonelectron flavor active neutrinos, their contribution to the flux is $\sim 0.2$ times that of $\nu_e$.

<table><tr><td>VALUE (10<sup>9</sup> cm<sup>-2</sup> s<sup>-1</sup>)</td><td>DOCUMENT ID</td><td>TECN</td><td>COMMENT</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>3.26 ± 0.52</td><td>1 GANDO</td><td>15 KLND</td><td>average flux</td></tr><tr><td>3.10 ± 0.15</td><td>2 BELLINI</td><td>11A BORX</td><td>average flux</td></tr></table>

1 GANDO 15 uses 165.4 kton-day exposure of the KamLAND liquid scintillator detector to measure the 862 keV $^7$Be solar neutrino flux via $\nu - e$ elastic scattering

2 BELLINI 11A reports the $^7$Be solar neutrino flux measured via $\nu - e$ elastic scattering. The data correspond to 740.7 live days between May 16, 2007 and May 8, 2010, and also correspond to 153.6 ton-year fiducial exposure. BELLINI 11A measured the 862 keV $^7$Be solar neutrino flux, which is an 89.6% branch of the $^7$Be solar neutrino flux, to be ($2.78 \pm 0.13) \times 10^9$ cm$^{-2}$ s$^{-1}$. Supercedes ARPESELLA 08A.

### $\phi_{ES}$ (pep)

pep solar-neutrino flux measured via $\nu_e$ elastic scattering. This process is sensitive to all active neutrino flavors, but with reduced sensitivity to $\nu_{\mu,\tau}$ due to the cross-section difference, $\sigma(\nu_{\mu,\tau} e) \sim 0.2 \sigma(\nu_e e)$. If the pep solar-neutrino flux involves non-electron flavor active neutrinos, their contribution to the flux is $\sim 0.2$ times that of $\nu_e$.

<table><tr><td>VALUE (10<sup>8</sup> cm<sup>-2</sup> s<sup>-1</sup>)</td><td>DOCUMENT ID</td><td>TECN</td><td>COMMENT</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>1.0 ± 0.2</td><td>1 BELLINI</td><td>12A BORX</td><td>average flux</td></tr></table>

1 BELLINI 12A reports 1.44 MeV pep solar-neutrino flux measured via $\nu_e$ elastic scattering. The data were collected between January 13, 2008 and May 9, 2010, corresponding to 20,4009 ton-day fiducial exposure. The listed flux value is calculated from the observed rate of pep solar neutrino interactions in Borexino (3.1 ± 0.6 ± 0.3 counts/(day-100

ton)) and the corresponding rate expected for no neutrino flavor oscillations (4.47 ± 0.05 counts/(day-100 ton)), using the SSM prediction for the pep solar neutrino flux of (1.441 ± 0.012) × 10$^8$ cm$^{-2}$ s$^{-1}$.

### $\phi_{ES}$ (CNO)

CNO solar-neutrino flux measured via $\nu_e$ elastic scattering. This process is sensitive to all active neutrino flavors, but with reduced sensitivity to $\nu_{\mu,\tau}$ due to the cross section difference, $\sigma(\nu_{\mu,\tau} e) \sim 0.2 \sigma(\nu_e e)$. If the CNO solar-neutrino flux involves non-electron flavor active neutrinos, their contribution to the flux is $\sim 0.2$ times that of $\nu_e$.

<table><tr><td>VALUE (10<sup>8</sup> cm<sup>-2</sup> s<sup>-1</sup>)</td><td>CL%</td><td>DOCUMENT ID</td><td>TECN</td><td>COMMENT</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>&lt;7.7</td><td>90</td><td>1 BELLINI</td><td>12A BORX</td><td>MSW-LMA solution assumed</td></tr></table>

1 BELLINI 12A reports an upper limit of the CNO solar neutrino flux measured via $\nu_e$ elastic scattering. The data were collected between January 13, 2008 and May 9, 2010, corresponding to 20,409 ton-day fiducial exposure.

### $\phi_{ES}$ (pp)

pp solar-neutrino flux measured via $\nu e$ elastic scattering. This process is sensitive to all active neutrino flavors, but with reduced sensitivity to $\nu_{\mu,\tau}$ due to the cross-section difference, $\sigma(\nu_{\mu,\tau} e) \sim 0.3 \sigma(\nu_e e)$. If the pp solar-neutrino flux involves nonelectron flavor active neutrinos, their contribution to the flux is $\sim 0.3$ times of $\nu_e$.

<table><tr><td>VALUE (10<sup>10</sup> cm<sup>-2</sup> s<sup>-1</sup>)</td><td>DOCUMENT ID</td><td>TECN</td><td>COMMENT</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>4.4 ± 0.5</td><td>1 BELLINI</td><td>14A BORX</td><td>average flux</td></tr></table>

1 BELLINI 14A reports pp solar-neutrino flux measured via $\nu e$ elastic scattering. The data were collected between January 2012 and May 2013, corresponding to 408 days of data. The pp neutrino interaction rate in Borexino is measured to be 144 ± 13 ± 10 counts/(day-100 ton) by fitting the measured energy spectrum of events in the 165-590 keV recoil electron kinetic energy window with the expected signal + background spectrum. The listed flux value $\phi_{ES}(pp)$ is calculated from the observed rate and the number of (3.307 ± 0.003) × 10$^{31}$ electrons for 100 tons of the Borexino scintillator, and the $\nu_e e$ integrated cross section over the pp neutrino spectrum, $\sigma(\nu_e e) = 11.38 \times 10^{-46}$ cm$^2$.

### $\phi_{CC}$ (pp)

pp solar-neutrino flux measured with charged-current reaction which is sensitive exclusively to $\nu_e$.

<table><tr><td>VALUE (10<sup>10</sup> cm<sup>-2</sup> s<sup>-1</sup>)</td><td>DOCUMENT ID</td><td>TECN</td><td>COMMENT</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>3.38 ± 0.47</td><td>1 ABDURASHI... 09</td><td>FIT</td><td>Fit existing solar-$\nu$ data</td></tr></table>

1 ABDURASHITOV 09 reports the pp solar-neutrino flux derived from the Ga solar neutrino capture rate by subtracting contributions from $^8$B, $^7$Be, pep and CNO solar neutrino fluxes determined by other solar neutrino experiments as well as neutrino oscillation parameters determined from available world neutrino oscillation data.

### $\phi_{ES}$ (hep)

hep solar-neutrino flux measured via $\nu e$ elastic scattering. This process is sensitive to all active neutrino flavors, but with reduced sensitivity to $\nu_{\mu,\tau}$ due to the cross-section difference, $\sigma(\nu_{\mu,\tau} e) \sim 0.16\sigma(\nu_e e)$. If the hep solar-neutrino flux involves nonelectron flavor active neutrinos, their contribution to the flux is $\sim 0.16$ times of $\nu_e$.

<table><tr><td>VALUE (10<sup>3</sup> cm<sup>-2</sup> s<sup>-1</sup>)</td><td>CL%</td><td>DOCUMENT ID</td><td>TECN</td><td>COMMENT</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>&lt;73</td><td>90</td><td>1 HOSAKA</td><td>06 SKAM</td></tr></table>

1 HOSAKA 06 result is obtained from the recoil electron energy window of 18-21 MeV, and updates FUKUDA 01 result.

### $\phi_{\tau_e}$ ($^8$B)

Searches are made for electron antineutrino flux from the Sun. Flux limits listed here are derived relative to the BS05(OP) Standard Solar Model $^8$B solar neutrino flux (5.69 × 10$^6$ cm$^{-2}$ s$^{-1}$), with an assumption that solar $\tau_e$s follow an unoscillated $^8$B neutrino spectrum.

<table><tr><td>VALUE (%)</td><td>CL%</td><td>DOCUMENT ID</td><td>TECN</td><td>COMMENT</td></tr></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tr><td>&lt;0.0072</td><td>90</td><td>1 AGOSTINI</td><td>21 BORX</td><td>E<sub>\tau_e</sub> > 1.8 MeV</td></tr><tr><td>&lt;0.013</td><td>90</td><td>2 BELLINI</td><td>11 BORX</td><td>E<sub>\tau_e</sub> > 1.8 MeV</td></tr><tr><td>&lt;1.9</td><td>90</td><td>3 BALATA</td><td>06 CNTR</td><td>1.8 &lt; E<sub>\tau_e</sub> &lt; 20.0 MeV</td></tr><tr><td>&lt;0.72</td><td>90</td><td>AHARMIM</td><td>04 SNO</td><td>4.0 &lt; E<sub>\tau_e</sub> &lt; 14.8 MeV</td></tr><tr><td>&lt;0.022</td><td>90</td><td>EGUCHI</td><td>04 KLND</td><td>8.3 &lt; E<sub>\tau_e</sub> &lt; 14.8 MeV</td></tr><tr><td>&lt;0.7</td><td>90</td><td>GANDO</td><td>03 SKAM</td><td>8.0 &lt; E<sub>\tau_e</sub> &lt; 20.0 MeV</td></tr><tr><td>&lt;1.7</td><td>90</td><td>AGLIETTA</td><td>96 LSD</td><td>7 &lt; E<sub>\tau_e</sub> &lt; 17 MeV</td></tr></table>

1 AGOSTINI 21 derived this result relative to the Standard Solar Model $^8$B solar neutrino flux, under an assumption of high solar metallicity, of 5.46 (1 ± 0.12) × 10$^6$ cm$^{-2}$ s$^{-1}$ (see VINYOLES 17).

2 Superseded by AGOSTINI 21.
³BALATA 06 obtained this result from the search for $\bar{\nu}_e$ interactions with Counting Test Facility (the prototype of the Borexino detector).

(B) Three-neutrino mixing parameters

$\sin^2(\theta_{12})$

If an experiment reports $\sin^2(2\theta_{12})$ we convert the value to $\sin^2(\theta_{12})$.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN.</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.307 +0.013 -0.012</td><td>1 ABE</td><td>16c</td><td>KamLAND+global solar; 3ν</td></tr><tr><td>0.318 ±0.016</td><td>2 SALAS</td><td>21</td><td>global fit</td></tr><tr><td>0.304 ±0.012</td><td>3 ESTEBAN</td><td>20A</td><td>Global fit</td></tr><tr><td>0.320 +0.020 -0.016</td><td>DE-SALAS</td><td>18</td><td>Global fit</td></tr><tr><td>0.310 ±0.014</td><td>4 ABE</td><td>16c</td><td>SKAM+SNO; 3ν</td></tr><tr><td>0.334 +0.027 -0.023</td><td>5 ABE</td><td>16c</td><td>SK-I+II+III+IV; 3ν</td></tr><tr><td>0.327 +0.026 -0.031</td><td>6 ABE</td><td>16c</td><td>SK-IV; 3ν</td></tr><tr><td>0.323 ±0.016</td><td>7 FORERO</td><td>14</td><td>3ν</td></tr><tr><td>0.304 +0.013 -0.012</td><td>8 GONZALEZ...</td><td>14</td><td>Either mass ordering; global fit</td></tr><tr><td>0.299 +0.014 -0.014</td><td>9,10 AHARMIM</td><td>13</td><td>global solar: 2ν</td></tr><tr><td>0.307 +0.016 -0.013</td><td>10,11 AHARMIM</td><td>13</td><td>global solar: 3ν</td></tr><tr><td>0.304 +0.022 -0.018</td><td>10,12 AHARMIM</td><td>13</td><td>KamLAND + global solar: 3ν</td></tr><tr><td>0.304 +0.014 -0.013</td><td>13 GANDO</td><td>13</td><td>KamLAND + global solar + SBL + accelerator: 3ν</td></tr><tr><td>0.304 +0.014 -0.013</td><td>14 GANDO</td><td>13</td><td>KamLAND + global solar: 3ν</td></tr><tr><td>0.325 +0.039 -0.039</td><td>15 GANDO</td><td>13</td><td>KamLAND: 3ν</td></tr><tr><td>0.30 +0.02 -0.01</td><td>16 ABE</td><td>11</td><td>KamLAND + global solar: 2ν</td></tr><tr><td>0.30 +0.02 -0.01</td><td>17 ABE</td><td>11</td><td>global solar: 2ν</td></tr><tr><td>0.31 +0.03 -0.02</td><td>18 ABE</td><td>11</td><td>KamLAND + global solar: 3ν</td></tr><tr><td>0.31 +0.03 -0.03</td><td>19 ABE</td><td>11</td><td>global solar: 3ν</td></tr><tr><td>0.314 +0.015 -0.012</td><td>20 BELLINI</td><td>11A</td><td>KamLAND + global solar: 2ν</td></tr><tr><td>0.319 +0.017 -0.015</td><td>21 BELLINI</td><td>11A</td><td>global solar: 2ν</td></tr><tr><td>0.311 +0.016 -0.016</td><td>22 GANDO</td><td>11</td><td>KamLAND + solar: 3ν</td></tr><tr><td>0.304 +0.046 -0.042</td><td>23 GANDO</td><td>11</td><td>KamLAND: 3ν</td></tr><tr><td>0.314 +0.018 -0.014</td><td>24,25 AHARMIM</td><td>10</td><td>FIT KamLAND + global solar: 2ν</td></tr><tr><td>0.314 +0.017 -0.020</td><td>24,26 AHARMIM</td><td>10</td><td>FIT global solar: 2ν</td></tr><tr><td>0.319 +0.019 -0.016</td><td>24,27 AHARMIM</td><td>10</td><td>FIT KamLAND + global solar: 3ν</td></tr><tr><td>0.319 +0.023 -0.024</td><td>24,28 AHARMIM</td><td>10</td><td>FIT global solar: 3ν</td></tr><tr><td>0.36 +0.05 -0.04</td><td>29 ABE</td><td>08A</td><td>KamLAND</td></tr><tr><td>0.32 ±0.03</td><td>30 ABE</td><td>08A</td><td>KamLAND + global fit</td></tr><tr><td>0.32 ±0.02</td><td>31 AHARMIM</td><td>08</td><td>KamLAND + global solar</td></tr><tr><td>0.31 +0.04 -0.04</td><td>32 HOSAKA</td><td>06</td><td>KamLAND + global solar</td></tr><tr><td>0.31 +0.04 -0.03</td><td>33 HOSAKA</td><td>06</td><td>SKAM+SNO+KamLAND</td></tr><tr><td>0.31 +0.03 -0.04</td><td>34 HOSAKA</td><td>06</td><td>SKAM+SNO</td></tr><tr><td>0.31 +0.02 -0.03</td><td>35 AHARMIM</td><td>05A</td><td>KamLAND + global solar</td></tr><tr><td>0.25-0.39</td><td>36 AHARMIM</td><td>05A</td><td>global solar</td></tr><tr><td>0.29 ±0.03</td><td>37 ARAKI</td><td>05</td><td>KamLAND + global solar</td></tr><tr><td>0.29 +0.03 -0.02</td><td>38 AHMED</td><td>04A</td><td>KamLAND + global solar</td></tr><tr><td>0.23-0.37</td><td>39 AHMED</td><td>04A</td><td>global solar</td></tr><tr><td>0.31 +0.04 -0.04</td><td>40 SMY</td><td>04</td><td>KamLAND + global solar</td></tr><tr><td>0.29 +0.04 -0.04</td><td>41 SMY</td><td>04</td><td>global solar</td></tr><tr><td>0.32 +0.06 -0.05</td><td>42 SMY</td><td>04</td><td>SKAM + SNO</td></tr><tr><td>0.19-0.33</td><td>43 AHMAD</td><td>02B</td><td>global solar</td></tr><tr><td>0.19-0.39</td><td>44 FUKUDA</td><td>02</td><td>global solar</td></tr></tbody></table>

<footnote n="1">¹ ABE 16c obtained this result by a three-neutrino oscillation analysis, with a constraint of $\sin^2(\theta_{13}) = 0.0219 \pm 0.0014$ coming from reactor neutrino experiments, using all solar data and KamLAND data. CPT invariance is assumed.</footnote>

<footnote n="2">² SALAS 21 reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference.</footnote>

<footnote n="3">³ ESTEBAN 20A reports results of a global fit to neutrino oscillation data available at the time of the Neutrino2020 conference.</footnote>

<footnote n="4">⁴ ABE 16c obtained this result by a three-neutrino oscillation analysis, with a constraint of $\sin^2(\theta_{13}) = 0.0219 \pm 0.0014$ coming from reactor neutrino experiments, using Super-Kamiokande (I+II+III+IV) and SNO data.</footnote>

<footnote n="5">⁵ ABE 16c obtained this result by a three-neutrino oscillation analysis, with a constraint of $\sin^2(\theta_{13}) = 0.0219 \pm 0.0014$ coming from reactor neutrino experiments, by combining the four phases of the Super-Kamiokande solar data.</footnote>

<footnote n="6">⁶ ABE 16c obtained this result by a three-neutrino oscillation analysis, with a constraint of $\sin^2(\theta_{13}) = 0.0219 \pm 0.0014$ coming from reactor neutrino experiments, using the Super-Kamiokande-IV data.</footnote>

<footnote n="7">⁷ FORERO 14 performs a global fit to neutrino oscillations using solar, reactor, long-baseline accelerator, and atmospheric neutrino data.</footnote>

<footnote n="8">⁸ GONZALEZ-GARCIA 14 result comes from a frequentist global fit. The corresponding Bayesian global fit to the same data results are reported in BERGSTROM 15 as $0.304^{+0.013}_{-0.012}$ for normal and $0.305^{+0.012}_{-0.013}$ for inverted mass ordering.</footnote>

<footnote n="9">⁹ AHARMIM 13 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data.</footnote>

<footnote n="10">¹⁰ AHARMIM 13 global solar neutrino data include SNO's all-phases-combined analysis results on the total active ⁸B neutrino flux and energy-dependent $\nu_e$ survival probability parameters, measurements of CI (CLEVELAND 98), Ga (ABDURASHITOV 09 which contains combined analysis with GNO (ALTMANN 05 and Ph.D. thesis of F. Kaether)), and ⁷Be (BELLINI 11A) rates, and ⁸B solar-neutrino recoil electron measurements of SK-I (HOSAKA 06) zenith, SK-II (CRAVENS 08) and SK-III (ABE 11) day/night spectra, and Borexino (BELLINI 10A) spectra.</footnote>

<footnote n="11">¹¹ AHARMIM 13 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m_{32}^2$ fixed to $2.45 \times 10^{-3} \text{ eV}^2$, using global solar neutrino data.</footnote>

<footnote n="12">¹² AHARMIM 13 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m_{32}^2$ fixed to $2.45 \times 10^{-3} \text{ eV}^2$, using global solar neutrino and KamLAND (GANDO 11) data. CPT invariance is assumed.</footnote>

<footnote n="13">¹³ GANDO 13 obtained this result by a three-neutrino oscillation analysis using KamLAND, global solar neutrino, short-baseline (SBL) reactor, and accelerator data, assuming CPT invariance. Supersedes GANDO 11.</footnote>

<footnote n="14">¹⁴ GANDO 13 obtained this result by a three-neutrino oscillation analysis using KamLAND and global solar neutrino data, assuming CPT invariance. Supersedes GANDO 11.</footnote>

<footnote n="15">¹⁵ GANDO 13 obtained this result by a three-neutrino oscillation analysis using KamLAND data. Supersedes GANDO 11.</footnote>

<footnote n="16">¹⁶ ABE 11 obtained this result by a two-neutrino oscillation analysis using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake, GALLEX/GNO, SAGE, and KamLAND data. CPT invariance is assumed.</footnote>

<footnote n="17">¹⁷ ABE 11 obtained this result by a two-neutrino oscillation analysis using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake, GALLEX/GNO, and SAGE data.</footnote>

<footnote n="18">¹⁸ ABE 11 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m_{32}^2$ fixed to $2.4 \times 10^{-3} \text{ eV}^2$, using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake, GALLEX/GNO, SAGE, and KamLAND data. The normal neutrino mass ordering and CPT invariance are assumed.</footnote>

<footnote n="19">¹⁹ ABE 11 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m_{32}^2$ fixed to $2.4 \times 10^{-3} \text{ eV}^2$, using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake, and GALLEX/GNO data. The normal neutrino mass ordering is assumed.</footnote>

<footnote n="20">²⁰ BELLINI 11A obtained this result by a two-neutrino oscillation analysis using KamLAND, Homestake, SAGE, Gallex, GNO, Kamiokande, Super-Kamiokande, SNO, and Borexino (BELLINI 11A) data and the SSM flux prediction in SERENELLI 11 (Astrophysical Journal 743 24 (2011)) with the exception that the ⁸B flux was left free. CPT invariance is assumed.</footnote>

<footnote n="21">²¹ BELLINI 11A obtained this result by a two-neutrino oscillation analysis using Homestake, SAGE, Gallex, GNO, Kamiokande, Super-Kamiokande, SNO, and Borexino (BELLINI 11A) data and the SSM flux prediction in SERENELLI 11 (Astrophysical Journal 743 24 (2011)) with the exception that the ⁸B flux was left free.</footnote>

<footnote n="22">²² GANDO 11 obtained this result with three-neutrino fit using the KamLAND + solar data. Supersedes GANDO 13.</footnote>

<footnote n="23">²³ GANDO 11 obtained this result with three-neutrino fit using the KamLAND data only. Supersedes GANDO 13.</footnote>

<footnote n="24">²⁴ AHARMIM 10 global solar neutrino data include SNO's low-energy-threshold analysis survival probability day/night curves, SNO Phase III integral rates (AHARMIM 08), CI (CLEVELAND 98), SAGE (ABDURASHITOV 09), Gallex/GNO (HAMPEL 99, ALT-MANN 05), Borexino (ARPESELLA 08A), SK-I zenith (HOSAKA 06), and SK-II day/night spectra (CRAVENS 08).</footnote>

<footnote n="25">²⁵ AHARMIM 10 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data and KamLAND data (ABE 08A). CPT invariance is assumed.</footnote>

<footnote n="26">²⁶ AHARMIM 10 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data.</footnote>

<footnote n="27">²⁷ AHARMIM 10 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m_{31}^2$ fixed to $2.3 \times 10^{-3} \text{ eV}^2$, using global solar neutrino data and KamLAND data (ABE 08A). CPT invariance is assumed.</footnote>

<footnote n="28">²⁸ AHARMIM 10 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m_{31}^2$ fixed to $2.3 \times 10^{-3} \text{ eV}^2$, using global solar neutrino data.</footnote>

<footnote n="29">²⁹ ABE 08A obtained this result by a rate + shape + time combined geoneutrino and reactor two-neutrino fit for $\Delta m_{31}^2$ and $\tan^2\theta_{12}$, using KamLAND data only. Supersedes by GANDO 11.</footnote>

<footnote n="30">³⁰ ABE 08A obtained this result by means of a two-neutrino fit using KamLAND, Homestake, SAGE, GALLEX, GNO, SK (zenith angle and E-spectrum), the SNO $\chi^2$-map, and solar flux data. CPT invariance is assumed. Supersedes by GANDO 11.</footnote>
31 The result given by AHARMIM 08 is $\theta = (34.4^{+1.3}_{-1.2})^{\circ}$. This result is obtained by a two-neutrino oscillation analysis using solar neutrino data including those of Borexino (ARPESELLA 08A) and Super-Kamiokande-I (HOSAKA 06), and KamLAND data (ABE 08A). CPT invariance is assumed.

32 HOSAKA 06 obtained this result by a two-neutrino oscillation analysis using SK $\nu_e$ data, CC data from other solar neutrino experiments, and KamLAND data (ARAKI 05). CPT invariance is assumed.

33 HOSAKA 06 obtained this result by a two-neutrino oscillation analysis using the data from Super-Kamiokande, SNO (AHMAD 02 and AHMAD 02b), and KamLAND (ARAKI 05) experiments. CPT invariance is assumed.

34 HOSAKA 06 obtained this result by a two-neutrino oscillation analysis using the Super-Kamiokande and SNO (AHMAD 02 and AHMAD 02b) solar neutrino data.

35 The result given by AHARMIM 05A is $\theta = (33.9 \pm 1.6)^{\circ}$. This result is obtained by a two-neutrino oscillation analysis using SNO pure deuteron and salt phase data, SK $\nu_e$ data, Cl and Ga CC data, and KamLAND data (ARAKI 05). CPT invariance is assumed. AHARMIM 05A also quotes $\theta = (33.9^{+2.4}_{-2.2})^{\circ}$ as the error enveloping the 68% CL two-dimensional region. This translates into $\sin^2\theta = 0.86^{+0.05}_{-0.06}$.

36 AHARMIM 05A obtained this result by a two-neutrino oscillation analysis using the data from all solar neutrino experiments. The listed range of the parameter envelops the 95% CL two-dimensional region shown in figure 35a of AHARMIM 05A. AHARMIM 05A also quotes $\tan^2\theta = 0.45^{+0.09}_{-0.08}$ as the error enveloping the 68% CL two-dimensional region. This translates into $\sin^2\theta = 0.86^{+0.05}_{-0.07}$.

37 ARAKI 05 obtained this result by a two-neutrino oscillation analysis using KamLAND and solar neutrino data. CPT invariance is assumed. The $1\sigma$ error shown here is extrapolated from the number provided by the KamLAND collaboration, $\tan^2\theta = 0.40^{+0.05}_{-0.05}$. The corresponding number quoted in ARAKI 05 is $\tan^2\theta = 0.40^{+0.10}_{-0.07}$ ($\sin^2\theta = 0.82 \pm 0.07$), which envelops the 68% CL two-dimensional region.

38 The result given by AHMED 04A is $\theta = (32.5^{+1.7}_{-1.6})^{\circ}$. This result is obtained by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (EGUCHI 03). CPT invariance is assumed. AHMED 04A also quotes $\theta = (32.5^{+2.4}_{-2.3})^{\circ}$ as the error enveloping the 68% CL two-dimensional region. This translates into $\sin^2\theta = 0.82 \pm 0.06$.

39 AHMED 04A obtained this result by a two-neutrino oscillation analysis using the data from all solar neutrino experiments. The listed range of the parameter envelops the 95% CL two-dimensional region shown in Fig. 5(a) of AHMED 04A. The best-fit point is $\Delta(m^2) = 6.5 \times 10^{-5} \text{ eV}^2$, $\tan^2\theta = 0.40$ ($\sin^2\theta = 0.82$).

40 The result given by SMY 04 is $\tan^2\theta = 0.44 \pm 0.08$. This result is obtained by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (IANNI 03). CPT invariance is assumed.

41 SMY 04 obtained this result by a two-neutrino oscillation analysis using the data from all solar neutrino experiments. The $1\sigma$ errors are read from Fig. 6(a) of SMY 04.

42 SMY 04 obtained this result by a two-neutrino oscillation analysis using the Super-Kamiokande and SNO (AHMAD 02 and AHMAD 02b) solar neutrino data. The $1\sigma$ errors are read from Fig. 6(a) of SMY 04.

43 AHMAD 02b obtained this result by a two-neutrino oscillation analysis using the data from all solar neutrino experiments. The listed range of the parameter envelops the 95% CL two-dimensional region shown in Fig. 4(b) of AHMAD 02b. The best fit point is $\Delta(m^2) = 5.0 \times 10^{-5} \text{ eV}^2$ and $\tan\theta = 0.34$ ($\sin^2\theta = 0.76$).

44 FUKUDA 02 obtained this result by a two-neutrino oscillation analysis using the data from all solar neutrino experiments. The listed range of the parameter envelops the 95% CL two-dimensional region shown in Fig. 4 of FUKUDA 02. The best fit point is $\Delta(m^2) = 6.9 \times 10^{-5} \text{ eV}^2$ and $\tan^2\theta = 0.38$ ($\sin^2\theta = 0.80$).

$\Delta m^2_{21}$

<table><thead><tr><th>VALUE (10<sup>-5</sup> eV<sup>2</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>7.53&plusmn;0.18</td><td>1 GANDO</td><td>13</td><td>FIT KamLAND + global solar + SBL + accelerator: 3&nu;</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>7.50<sup>+0.22</sup><sub>-0.20</sub></td><td>2 SALAS</td><td>21</td><td>FIT global fit</td></tr><tr><td>7.42<sup>+0.21</sup><sub>-0.20</sub></td><td>3 ESTEBAN</td><td>20A</td><td>FIT Global fit</td></tr><tr><td>7.55<sup>+0.20</sup><sub>-0.16</sub></td><td>DE-SALAS</td><td>18</td><td>FIT Global fit</td></tr><tr><td>7.49<sup>+0.19</sup><sub>-0.18</sub></td><td>4 ABE</td><td>16C</td><td>FIT KamLAND+global solar; 3&nu;</td></tr><tr><td>4.8<sup>+1.3</sup><sub>-0.6</sub></td><td>5 ABE</td><td>16C</td><td>FIT SKAM+SNO; 3&nu;</td></tr><tr><td>4.8<sup>+1.5</sup><sub>-0.8</sub></td><td>6 ABE</td><td>16C</td><td>FIT SK-I+II+III+IV; 3&nu;</td></tr><tr><td>3.2<sup>+2.8</sup><sub>-0.2</sub></td><td>7 ABE</td><td>16C</td><td>FIT SK-IV; 3&nu;</td></tr><tr><td>7.6<sup>+0.19</sup><sub>-0.18</sub></td><td>8 FORERO</td><td>14</td><td>FIT 3&nu;</td></tr><tr><td>7.50<sup>+0.19</sup><sub>-0.17</sub></td><td>9 GONZALEZ...</td><td>14</td><td>FIT Either mass ordering; global fit</td></tr><tr><td>5.13<sup>+1.29</sup><sub>-0.96</sub></td><td>10,11 AHARMIM</td><td>13</td><td>FIT global solar: 2&nu;</td></tr><tr><td>5.13<sup>+1.49</sup><sub>-0.98</sub></td><td>11,12 AHARMIM</td><td>13</td><td>FIT global solar: 3&nu;</td></tr><tr><td>7.46<sup>+0.20</sup><sub>-0.19</sub></td><td>11,13 AHARMIM</td><td>13</td><td>FIT KamLAND + global solar: 3&nu;</td></tr><tr><td>7.53<sup>+0.19</sup><sub>-0.18</sub></td><td>14 GANDO</td><td>13</td><td>FIT KamLAND + global solar: 3&nu;</td></tr><tr><td>7.54<sup>+0.19</sup><sub>-0.18</sub></td><td>15 GANDO</td><td>13</td><td>FIT KamLAND: 3&nu;</td></tr><tr><td>7.6<sup>+0.2</sup></td><td>16 ABE</td><td>11</td><td>FIT KamLAND + global solar: 2&nu;</td></tr></tbody></table>

<table><tbody><tr><td>6.2<sup>+1.1</sup><sub>-1.9</sub></td><td>17 ABE</td><td>11</td><td>FIT global solar: 2&nu;</td></tr><tr><td>7.7<sup>+0.3</sup><sub>-0.9</sub></td><td>18 ABE</td><td>11</td><td>FIT KamLAND + global solar: 3&nu;</td></tr><tr><td>6.0<sup>+2.2</sup><sub>-2.5</sub></td><td>19 ABE</td><td>11</td><td>FIT global solar: 3&nu;</td></tr><tr><td>7.50<sup>+0.16</sup><sub>-0.24</sub></td><td>20 BELLINI</td><td>11A</td><td>FIT KamLAND + global solar: 2&nu;</td></tr><tr><td>5.2<sup>+1.5</sup><sub>-0.9</sub></td><td>21 BELLINI</td><td>11A</td><td>FIT global solar: 2&nu;</td></tr><tr><td>7.50<sup>+0.19</sup><sub>-0.20</sub></td><td>22 GANDO</td><td>11</td><td>FIT KamLAND + solar: 3&nu;</td></tr><tr><td>7.49<sup>+0.20</sup></td><td>23 GANDO</td><td>11</td><td>FIT KamLAND: 3&nu;</td></tr><tr><td>7.59<sup>+0.20</sup><sub>-0.21</sub></td><td>24,25 AHARMIM</td><td>10</td><td>FIT KamLAND + global solar: 2&nu;</td></tr><tr><td>5.89<sup>+2.13</sup><sub>-2.16</sub></td><td>24,26 AHARMIM</td><td>10</td><td>FIT global solar: 2&nu;</td></tr><tr><td>7.59<sup>+0.21</sup></td><td>24,27 AHARMIM</td><td>10</td><td>FIT KamLAND + global solar: 3&nu;</td></tr><tr><td>6.31<sup>+2.49</sup><sub>-2.58</sub></td><td>24,28 AHARMIM</td><td>10</td><td>FIT global solar: 3&nu;</td></tr><tr><td>7.58<sup>+0.14</sup><sub>-0.13</sub></td><td>29 ABE</td><td>08A</td><td>FIT KamLAND</td></tr><tr><td>7.59<sup>+0.21</sup></td><td>30 ABE</td><td>08A</td><td>FIT KamLAND + global solar</td></tr><tr><td>7.59<sup>+0.19</sup><sub>-0.21</sub></td><td>31 AHARMIM</td><td>08</td><td>FIT KamLAND + global solar</td></tr><tr><td>8.0<sup>+0.3</sup></td><td>32 HOSAKA</td><td>06</td><td>FIT KamLAND + global solar</td></tr><tr><td>8.0<sup>+0.3</sup></td><td>33 HOSAKA</td><td>06</td><td>FIT SKAM+SNO+KamLAND</td></tr><tr><td>6.3<sup>+3.7</sup><sub>-1.5</sub></td><td>34 HOSAKA</td><td>06</td><td>FIT SKAM+SNO</td></tr><tr><td>5-12</td><td>35 HOSAKA</td><td>06</td><td>FIT SKAM day/night in the LMA region</td></tr><tr><td>8.0<sup>+0.4</sup><sub>-0.3</sub></td><td>36 AHARMIM</td><td>05A</td><td>FIT KamLAND + global solar LMA</td></tr><tr><td>3.3-14.4</td><td>37 AHARMIM</td><td>05A</td><td>FIT global solar</td></tr><tr><td>7.9<sup>+0.4</sup><sub>-0.3</sub></td><td>38 ARAKI</td><td>05</td><td>FIT KamLAND + global solar</td></tr><tr><td>7.1<sup>+1.0</sup><sub>-0.3</sub></td><td>39 AHMED</td><td>04A</td><td>FIT KamLAND + global solar</td></tr><tr><td>3.2-13.7</td><td>40 AHMED</td><td>04A</td><td>FIT global solar</td></tr><tr><td>7.1<sup>+0.6</sup><sub>-0.5</sub></td><td>41 SMY</td><td>04</td><td>FIT KamLAND + global solar</td></tr><tr><td>6.0<sup>+1.7</sup><sub>-1.6</sub></td><td>42 SMY</td><td>04</td><td>FIT global solar</td></tr><tr><td>6.0<sup>+2.5</sup><sub>-1.6</sub></td><td>43 SMY</td><td>04</td><td>FIT SKAM + SNO</td></tr><tr><td>2.8-12.0</td><td>44 AHMAD</td><td>02B</td><td>FIT global solar</td></tr><tr><td>3.2-19.1</td><td>45 FUKUDA</td><td>02</td><td>FIT global solar</td></tr></tbody></table>

1 GANDO 13 obtained this result by a three-neutrino oscillation analysis using KamLAND, global solar neutrino, short-baseline (SBL) reactor, and accelerator data, assuming CPT invariance. Supersedes GANDO 11.

2 SALAS 21 reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference.

3 ESTEBAN 20A reports results of a global fit to neutrino oscillation data available at the time of the Neutrino2020 conference.

4 ABE 16C obtained this result by a three-neutrino oscillation analysis, with a constraint of $\sin^2(\theta_{13}) = 0.0219 \pm 0.0014$ coming from reactor neutrino experiments, using all solar data and KamLAND data. CPT invariance is assumed.

5 ABE 16C obtained this result by a three-neutrino oscillation analysis, with a constraint of $\sin^2(\theta_{13}) = 0.0219 \pm 0.0014$ coming from reactor neutrino experiments, using Super-Kamiokande (I+II+III+IV) and SNO data.

6 ABE 16C obtained this result by a three-neutrino oscillation analysis, with a constraint of $\sin^2(\theta_{13}) = 0.0219 \pm 0.0014$ coming from reactor neutrino experiments, by combining the four phases of the Super-Kamiokande solar data.

7 ABE 16C obtained this result by a three-neutrino oscillation analysis, with a constraint of $\sin^2(\theta_{13}) = 0.0219 \pm 0.0014$ coming from reactor neutrino experiments, using the Super-Kamiokande-IV data.

8 FORERO 14 performs a global fit to $\Delta m^2_{21}$ using solar, reactor, long-baseline accelerator, and atmospheric neutrino data.

9 GONZALEZ-GARCIA 14 result comes from a frequentist global fit. The corresponding Bayesian global fit to the same data results are reported in BERGSTROM 15 as $(7.50^{+0.19}_{-0.17}) \times 10^{-5} \text{ eV}^2$ for normal and $(7.50^{+0.18}_{-0.17}) \times 10^{-5} \text{ eV}^2$ for inverted mass ordering.

10 AHARMIM 13 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data.

11 AHARMIM 13 global solar neutrino data include SNO's all-phases-combined analysis results on the total active $^8$B neutrino flux and energy-dependent $\nu_e$ survival probability parameters, measurements of Cl (CLEVELAND 98), Ga (ABDURASHITOV 09) which contains combined analysis with GNO (ALTMANN 05 and Ph.D. thesis of F. Kaether)), and $^7$Be (BELLINI 11A) rates, and $^8$B solar-neutrino recoil electron measurements of SK-I (HOSAKA 06) zenith, SK-II (CRAVENS 08), and SK-III (ABE 11) day/night spectra, and Borexino (BELLINI 10A) spectra.

12 AHARMIM 13 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m^2_{31}$ fixed to $2.45 \times 10^{-3} \text{ eV}^2$, using global solar neutrino data.

13 AHARMIM 13 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m^2_{21}$ fixed to $2.45 \times 10^{-3} \text{ eV}^2$, using global solar neutrino and KamLAND data (GANDO 11). CPT invariance is assumed.

14 GANDO 13 obtained this result by a three-neutrino oscillation analysis using KamLAND and global solar neutrino data, assuming CPT invariance. Supersedes GANDO 11.

15 GANDO 13 obtained this result by a three-neutrino oscillation analysis using KamLAND data. Supersedes GANDO 11.
16 ABE 11 obtained this result by a two-neutrino oscillation analysis using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake, GALLEX/GNO, SAGE, and KamLAND data. CPT invariance is assumed.

17 ABE 11 obtained this result by a two-neutrino oscillation analysis using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake, GALLEX/GNO, and SAGE data.

18 ABE 11 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m_{32}^2$ fixed to $2.4 \times 10^{-3}$ eV$^2$, using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake, GALLEX/GNO, SAGE, and KamLAND data. The normal neutrino mass ordering and CPT invariance are assumed.

19 ABE 11 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m_{32}^2$ fixed to $2.4 \times 10^{-3}$ eV$^2$, using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake, and GALLEX/GNO data. The normal neutrino mass ordering is assumed.

20 BELLINI 11A obtained this result by a two-neutrino oscillation analysis using KamLAND, Homestake, SAGE, Gallex, GNO, Kamiokande, Super-Kamiokande, SNO, and Borexino (BELLINI 11A) data and the SSM flux prediction in SERENELLI 11 (Astrophysical Journal 743 24 (2011)) with the exception that the $^8$B flux was left free. CPT invariance is assumed.

21 BELLINI 11A obtained this result by a two-neutrino oscillation analysis using Homestake, SAGE, Gallex, GNO, Kamiokande, Super-Kamiokande, SNO, and Borexino (BELLINI 11A) data and the SSM flux prediction in SERENELLI 11 (Astrophysical Journal 743 24 (2011)) with the exception that the $^8$B flux was left free.

22 GANDO 11 obtain this result with three-neutrino fit using the KamLAND + solar data. Superseded by GANDO 13.

23 GANDO 11 obtain this result with three-neutrino fit using the KamLAND data only. Supersedes ABE 08A.

24 AHARMIM 10 global solar neutrino data include SNO's low-energy-threshold analysis survival probability day/night curves, SNO Phase III integral rates (AHARMIM 08), Cl (CLEVELAND 98), SAGE (ABDURASHITOV 09), Gallex/GNO (HAMPEL 99, ALT-MANN 05), Borexino (ARPESELLA 08A), SK-I zenith (HOSAKA 06), and SK-II day/night spectra (CRAVENS 08).

25 AHARMIM 10 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data and KamLAND data (ABE 08A). CPT invariance is assumed.

26 AHARMIM 10 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data.

27 AHARMIM 10 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m_{31}^2$ fixed to $2.3 \times 10^{-3}$ eV$^2$, using global solar neutrino data and KamLAND data (ABE 08A). CPT invariance is assumed.

28 AHARMIM 10 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m_{31}^2$ fixed to $2.3 \times 10^{-3}$ eV$^2$, using global solar neutrino data.

29 ABE 08A obtained this result by a rate + shape + time combined geoneutrino and reactor two-neutrino fit for $\Delta m_{21}^2$ and $\tan^2\theta_{12}$, using KamLAND data only. Superseded by GANDO 11.

30 ABE 08A obtained this result by means of a two-neutrino fit using KamLAND, Homestake, SAGE, GALLEX, GNO, SK (zenith angle and E-spectrum), the SNO $\chi^2$-map, and solar flux data. CPT invariance is assumed. Supersedes by GANDO 11.

31 AHARMIM 08 obtained this result by a two-neutrino oscillation analysis using all solar neutrino data including those of Borexino (ARPESELLA 08A) and Super-Kamiokande-I (HOSAKA 06), and KamLAND data (ABE 08A). CPT invariance is assumed.

32 HOSAKA 06 obtained this result by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (ARAKI 05). CPT invariance is assumed.

33 HOSAKA 06 obtained this result by a two-neutrino oscillation analysis using the data from Super-Kamiokande, SNO (AHMAD 02 and AHMAD 02B), and KamLAND (ARAKI 05) experiments. CPT invariance is assumed.

34 HOSAKA 06 obtained this result by a two-neutrino oscillation analysis using the Super-Kamiokande and SNO (AHMAD 02 and AHMAD 02B) solar neutrino data.

35 HOSAKA 06 obtained this result from the consistency between the observed and expected day-night flux asymmetry amplitude. The listed 68% CL range is derived from the $1\sigma$ boundary of the amplitude fit to the data. Oscillation parameters are constrained to be in the LMA region. The mixing angle is fixed at $\tan^2\theta = 0.44$ because the fit depends only very weekly on it.

36 AHARMIM 05A obtained this result by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (ARAKI 05). CPT invariance is assumed. AHARMIM 05A also quotes $\Delta(m^2) = (8.0^{+0.6}_{-0.4}) \times 10^{-5}$ eV$^2$ as the error enveloping the 68% CL two-dimensional region.

37 AHARMIM 05A obtained this result by a two-neutrino oscillation analysis using the data from all solar neutrino experiments. The listed range of the parameter envelops the 95% CL two-dimensional region shown in figure 35a of AHARMIM 05A. AHARMIM 05A also quotes $\Delta(m^2) = (6.5^{+4.4}_{-2.3}) \times 10^{-5}$ eV$^2$ as the error enveloping the 68% CL two-dimensional region.

38 ARAKI 05 obtained this result by a two-neutrino oscillation analysis using KamLAND and solar neutrino data. CPT invariance is assumed. The $1\sigma$ error shown here is provided by the KamLAND collaboration. The error quoted in ARAKI 05, $\Delta(m^2) = (7.9^{+0.6}_{-0.5}) \times 10^{-5}$, envelops the 68% CL two-dimensional region.

39 AHMED 04A obtained this result by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (EGUCHI 03). CPT invariance is assumed. AHMED 04A also quotes $\Delta(m^2) = (7.1^{+1.2}_{-0.6}) \times 10^{-5}$ eV$^2$ as the error enveloping the 68% CL two-dimensional region.

40 AHMED 04A obtained this result by a two-neutrino oscillation analysis using the data from all solar neutrino experiments. The listed range of the parameter envelops the 95% CL two-dimensional region shown in Fig. 5(a) of AHMED 04A. The best-fit point is $\Delta(m^2) = 6.5 \times 10^{-5}$ eV$^2$, $\tan^2\theta = 0.40$ ($\sin^2 2\theta = 0.82$).

41 SMY 04 obtained this result by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (IANNI 03). CPT invariance is assumed.

42 SMY 04 obtained this result by a two-neutrino oscillation analysis using the data from all solar neutrino experiments. The $1\sigma$ errors are read from Fig. 6(a) of SMY 04.

43 SMY 04 obtained this result by a two-neutrino oscillation analysis using the Super-Kamiokande and SNO (AHMAD 02 and AHMAD 02B) solar neutrino data. The $1\sigma$ errors are read from Fig. 6(a) of SMY 04.

44 AHMAD 02B obtained this result by a two-neutrino oscillation analysis using the data from all solar neutrino experiments. The listed range of the parameter envelops the 95% CL two-dimensional region shown in Fig. 4(b) of AHMAD 02B. The best fit point is $\Delta(m^2) = 5.0 \times 10^{-5}$ eV$^2$ and $\tan\theta = 0.34$ ($\sin^2 2\theta = 0.76$).

45 FUKUDA 02 obtained this result by a two-neutrino oscillation analysis using the data from all solar neutrino experiments. The listed range of the parameter envelops the 95% CL two-dimensional region shown in Fig. 4 of FUKUDA 02. The best fit point is $\Delta(m^2) = 6.9 \times 10^{-5}$ eV$^2$ and $\tan^2\theta = 0.38$ ($\sin^2 2\theta = 0.80$).

### $\sin^2(\theta_{23})$

The reported limits below correspond to the projection onto the $\sin^2(\theta_{23})$ axis of the 90% CL contours in the $\sin^2(\theta_{23}) - \Delta m_{32}^2$ plane presented by the authors. Unless otherwise specified, the limits are 90% CL and the reported uncertainties are 68% CL.

If an experiment reports $\sin^2(2\theta_{23})$ we convert the value to $\sin^2(\theta_{23})$.

<table><thead><tr><th>VALUE</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>0.553</strong><sup>+0.016</sup><sub>-0.024</sub></td><td><strong>OUR FIT</strong></td><td></td><td>Error includes scale factor of 1.1. Assuming inverted mass ordering</td></tr><tr><td><strong>0.558</strong><sup>+0.015</sup><sub>-0.021</sub></td><td><strong>OUR FIT</strong></td><td></td><td>Assuming normal mass ordering</td></tr><tr><td>0.51 ±0.05</td><td>1 ABBASI</td><td>23</td><td>ICCB Normal mass ordering</td></tr><tr><td>0.561 ±0.021</td><td>2 ABE</td><td>23F</td><td>T2K Normal mass ordering</td></tr><tr><td>0.563 ±0.017</td><td>2 ABE</td><td>23F</td><td>T2K Inverted mass ordering</td></tr><tr><td>0.57 ±0.03</td><td>3 ACERO</td><td>22</td><td>NOVA Normal mass ordering; octant II for $\theta_{23}$</td></tr><tr><td>0.56 ±0.04</td><td>3 ACERO</td><td>22</td><td>NOVA Inverted mass ordering; octant II for $\theta_{23}$</td></tr><tr><td>0.43 ±0.20</td><td>4 ADAMSON</td><td>20A</td><td>MINS Normal mass ordering</td></tr><tr><td>0.42 ±0.07</td><td>4 ADAMSON</td><td>20A</td><td>MINS Inverted mass ordering</td></tr><tr><td>0.588 ±0.031</td><td>5 ABE</td><td>18B</td><td>SKAM Normal mass ordering, $\theta_{13}$ constrained</td></tr><tr><td>0.575 ±0.036</td><td>5 ABE</td><td>18B</td><td>SKAM Inverted mass ordering, $\theta_{13}$ constrained</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>0.47 ±0.11</td><td>6 ABE</td><td>23D</td><td>T2K $\nu_\mu$ disappearance</td></tr><tr><td>0.45 ±0.16</td><td>6 ABE</td><td>23D</td><td>T2K $\bar{\nu}_\mu$ disappearance</td></tr><tr><td>0.51 ±0.06</td><td>7 ABE</td><td>21A</td><td>T2K $\nu_\mu$ disappearance</td></tr><tr><td>0.43 ±0.21</td><td>7 ABE</td><td>21A</td><td>T2K $\bar{\nu}_\mu$ disappearance</td></tr><tr><td>0.574 ±0.014</td><td>8 SALAS</td><td>21</td><td>FIT Normal mass ordering, global fit</td></tr><tr><td>0.578 ±0.100</td><td>8 SALAS</td><td>21</td><td>FIT Inverted mass ordering, global fit</td></tr><tr><td>0.455</td><td>9 AARTSEN</td><td>20</td><td>ICCB For both mass orderings</td></tr><tr><td>0.53 ±0.03</td><td>10 ABE</td><td>20F</td><td>T2K Both mass orderings</td></tr><tr><td>0.573 ±0.016</td><td>11 ESTEBAN</td><td>20A</td><td>FIT Normal mass ordering, global fit</td></tr><tr><td>0.575 ±0.016</td><td>11 ESTEBAN</td><td>20A</td><td>FIT Inverted mass ordering, global fit</td></tr><tr><td>0.58 ±0.04</td><td>12 AARTSEN</td><td>19C</td><td>ICCB</td></tr><tr><td>0.56 ±0.04</td><td>13 ACERO</td><td>19</td><td>NOVA Normal mass order; octant II for $\theta_{23}$</td></tr><tr><td>0.48 ±0.04</td><td>13.14 ACERO</td><td>19</td><td>NOVA Normal mass order; octant I for $\theta_{23}$</td></tr><tr><td>0.56 ±0.04</td><td>13.14 ACERO</td><td>19</td><td>NOVA Inverted mass order; octant II for $\theta_{23}$</td></tr><tr><td>0.47 ±0.04</td><td>13.14 ACERO</td><td>19</td><td>NOVA Inverted mass order; octant I for $\theta_{23}$</td></tr><tr><td>0.49 ±0.30</td><td>AGAFONOVA</td><td>19</td><td>OPER</td></tr><tr><td>0.50 ±0.20</td><td>15 ALBERT</td><td>19</td><td>ANTR Atmospheric $\nu$, deep sea telescope</td></tr><tr><td>0.51 ±0.07</td><td>16 AARTSEN</td><td>18A</td><td>ICCB Normal mass ordering</td></tr><tr><td>0.587 ±0.036</td><td>17 ABE</td><td>18B</td><td>SKAM $3\nu$ osc: normal mass ordering, $\theta_{13}$ free</td></tr><tr><td>0.551 ±0.044</td><td>17 ABE</td><td>18B</td><td>SKAM $3\nu$ osc: inverted mass ordering, $\theta_{13}$ free</td></tr><tr><td>0.526 ±0.032</td><td>18 ABE</td><td>18G</td><td>T2K Normal mass ordering, $\theta_{13}$ constrained</td></tr><tr><td>0.530 ±0.030</td><td>18 ABE</td><td>18G</td><td>T2K Inverted mass ordering, $\theta_{13}$ constrained</td></tr><tr><td>0.56 ±0.04</td><td>19 ACERO</td><td>18</td><td>NOVA Normal mass order; octant II for $\theta_{23}$</td></tr><tr><td>0.47 ±0.04</td><td>19 ACERO</td><td>18</td><td>NOVA Normal mass order; octant I for $\theta_{23}$</td></tr><tr><td>0.547 ±0.020</td><td>DE-SALAS</td><td>18</td><td>FIT Normal mass ordering, global fit</td></tr></tbody></table>
<table>
  <tbody>
    <tr>
      <td>0.551<sup>+0.018</sup><sub>-0.030</sub></td>
      <td>DE-SALAS</td>
      <td>18</td>
      <td>FIT</td>
      <td>Inverted mass order, global fit</td>
    </tr>
    <tr>
      <td>0.532<sup>+0.061</sup><sub>-0.087</sub></td>
      <td>20 ABE</td>
      <td>17A</td>
      <td>T2K</td>
      <td>Normal mass ordering</td>
    </tr>
    <tr>
      <td>0.534<sup>+0.061</sup><sub>-0.087</sub></td>
      <td>20 ABE</td>
      <td>17A</td>
      <td>T2K</td>
      <td>Inverted mass ordering</td>
    </tr>
    <tr>
      <td>0.51<sup>+0.08</sup><sub>-0.07</sub></td>
      <td>ABE</td>
      <td>17C</td>
      <td>T2K</td>
      <td>Normal mass ordering with neutrinos</td>
    </tr>
    <tr>
      <td>0.42<sup>+0.25</sup><sub>-0.07</sub></td>
      <td>ABE</td>
      <td>17C</td>
      <td>T2K</td>
      <td>Normal mass ordering with antineutrinos</td>
    </tr>
    <tr>
      <td>0.52<sup>+0.075</sup><sub>-0.09</sub></td>
      <td>ABE</td>
      <td>17C</td>
      <td>T2K</td>
      <td>normal mass ordering with neutrinos<br>and antineutrinos</td>
    </tr>
    <tr>
      <td>0.55<sup>+0.05</sup><sub>-0.09</sub></td>
      <td>20 ABE</td>
      <td>17F</td>
      <td>T2K</td>
      <td>Normal mass ordering</td>
    </tr>
    <tr>
      <td>0.55<sup>+0.05</sup><sub>-0.08</sub></td>
      <td>20 ABE</td>
      <td>17F</td>
      <td>T2K</td>
      <td>Inverted mass ordering</td>
    </tr>
    <tr>
      <td>0.404<sup>+0.022</sup><sub>-0.030</sub></td>
      <td>21 ADAMSON</td>
      <td>17A</td>
      <td>NOVA</td>
      <td>Normal mass ordering; octant I for θ<sub>23</sub></td>
    </tr>
    <tr>
      <td>0.624<sup>+0.022</sup><sub>-0.030</sub></td>
      <td>21 ADAMSON</td>
      <td>17A</td>
      <td>NOVA</td>
      <td>Normal mass ordering; octant II for θ<sub>23</sub></td>
    </tr>
    <tr>
      <td>0.398<sup>+0.030</sup><sub>-0.022</sub></td>
      <td>21 ADAMSON</td>
      <td>17A</td>
      <td>NOVA</td>
      <td>Inverted mass ordering; octant I for θ<sub>23</sub></td>
    </tr>
    <tr>
      <td>0.618<sup>+0.022</sup><sub>-0.030</sub></td>
      <td>21 ADAMSON</td>
      <td>17A</td>
      <td>NOVA</td>
      <td>Inverted mass ordering; octant II for θ<sub>23</sub></td>
    </tr>
    <tr>
      <td>0.45<sup>+0.19</sup><sub>-0.07</sub></td>
      <td>22 ABE</td>
      <td>16D</td>
      <td>T2K</td>
      <td>3ν osc; normal mass ordering; π beam</td>
    </tr>
    <tr>
      <td>0.38 to 0.65</td>
      <td>23 ADAMSON</td>
      <td>16A</td>
      <td>NOVA</td>
      <td>normal mass ordering</td>
    </tr>
    <tr>
      <td>0.37 to 0.64</td>
      <td>23 ADAMSON</td>
      <td>16A</td>
      <td>NOVA</td>
      <td>Inverted mass ordering</td>
    </tr>
    <tr>
      <td>0.53<sup>+0.09</sup><sub>-0.12</sub></td>
      <td>24 AARTSEN</td>
      <td>15A</td>
      <td>ICCB</td>
      <td>Normal mass ordering</td>
    </tr>
    <tr>
      <td>0.51<sup>+0.09</sup><sub>-0.11</sub></td>
      <td>24 AARTSEN</td>
      <td>15A</td>
      <td>ICCB</td>
      <td>Inverted mass ordering</td>
    </tr>
    <tr>
      <td>0.514<sup>+0.055</sup><sub>-0.056</sub></td>
      <td>25 ABE</td>
      <td>14</td>
      <td>T2K</td>
      <td>3ν osc.; normal mass ordering</td>
    </tr>
    <tr>
      <td>0.511<sup>+0.055</sup></td>
      <td>25 ABE</td>
      <td>14</td>
      <td>T2K</td>
      <td>3ν osc.; inverted mass ordering</td>
    </tr>
    <tr>
      <td>0.41<sup>+0.23</sup><sub>-0.06</sub></td>
      <td>26 ADAMSON</td>
      <td>14</td>
      <td>MINS</td>
      <td>Normal mass ordering</td>
    </tr>
    <tr>
      <td>0.41<sup>+0.26</sup><sub>-0.07</sub></td>
      <td>26 ADAMSON</td>
      <td>14</td>
      <td>MINS</td>
      <td>Inverted mass ordering</td>
    </tr>
    <tr>
      <td>0.567<sup>+0.032</sup><sub>-0.128</sub></td>
      <td>27 FORERO</td>
      <td>14</td>
      <td>FIT</td>
      <td>Normal mass ordering</td>
    </tr>
    <tr>
      <td>0.573<sup>+0.025</sup><sub>-0.043</sub></td>
      <td>27 FORERO</td>
      <td>14</td>
      <td>FIT</td>
      <td>Inverted mass ordering</td>
    </tr>
    <tr>
      <td>0.452<sup>+0.052</sup><sub>-0.028</sub></td>
      <td>28 GONZALEZ...</td>
      <td>14</td>
      <td>FIT</td>
      <td>Normal mass ordering; global fit</td>
    </tr>
    <tr>
      <td>0.579<sup>+0.025</sup><sub>-0.037</sub></td>
      <td>28 GONZALEZ...</td>
      <td>14</td>
      <td>FIT</td>
      <td>Inverted mass ordering; global fit</td>
    </tr>
    <tr>
      <td>0.24 to 0.76</td>
      <td>29 AARTSEN</td>
      <td>13B</td>
      <td>ICCB</td>
      <td>DeepCore, 2ν oscillation</td>
    </tr>
    <tr>
      <td>0.514<sup>+0.082</sup></td>
      <td>30 ABE</td>
      <td>13G</td>
      <td>T2K</td>
      <td>3ν osc.; normal mass ordering</td>
    </tr>
    <tr>
      <td>0.388<sup>+0.051</sup><sub>-0.053</sub></td>
      <td>31 ADAMSON</td>
      <td>13B</td>
      <td>MINS</td>
      <td>Beam + Atmospheric; identical ν &amp; π</td>
    </tr>
    <tr>
      <td>0.3 to 0.7</td>
      <td>32 ABE</td>
      <td>12A</td>
      <td>T2K</td>
      <td>Off-axis beam</td>
    </tr>
    <tr>
      <td>0.28 to 0.72</td>
      <td>33 ADAMSON</td>
      <td>12</td>
      <td>MINS</td>
      <td>π beam</td>
    </tr>
    <tr>
      <td>0.25 to 0.75</td>
      <td>34,35 ADAMSON</td>
      <td>12B</td>
      <td>MINS</td>
      <td>MINOS atmospheric</td>
    </tr>
    <tr>
      <td>0.27 to 0.73</td>
      <td>34,36 ADAMSON</td>
      <td>12B</td>
      <td>MINS</td>
      <td>MINOS pure atmospheric ν</td>
    </tr>
    <tr>
      <td>0.21 to 0.79</td>
      <td>34,36 ADAMSON</td>
      <td>12B</td>
      <td>MINS</td>
      <td>MINOS pure atmospheric π</td>
    </tr>
    <tr>
      <td>0.15 to 0.85</td>
      <td>37 ADRIAN-MAR.12</td>
      <td>ANTR</td>
      <td></td>
      <td>Atmospheric ν with deep see telescope</td>
    </tr>
    <tr>
      <td>0.39 to 0.61</td>
      <td>38 ABE</td>
      <td>11C</td>
      <td>SKAM</td>
      <td>Super-Kamiokande</td>
    </tr>
    <tr>
      <td>0.34 to 0.66</td>
      <td>ADAMSON</td>
      <td>11</td>
      <td>MINS</td>
      <td>2ν osc.; maximal mixing</td>
    </tr>
    <tr>
      <td>0.31<sup>+0.10</sup><sub>-0.07</sub></td>
      <td>39 ADAMSON</td>
      <td>11B</td>
      <td>MINS</td>
      <td>π beam</td>
    </tr>
    <tr>
      <td>0.41 to 0.59</td>
      <td>40 WENDELL</td>
      <td>10</td>
      <td>SKAM</td>
      <td>3ν osc. with solar terms; θ<sub>13</sub>=0</td>
    </tr>
    <tr>
      <td>0.39 to 0.61</td>
      <td>41 WENDELL</td>
      <td>10</td>
      <td>SKAM</td>
      <td>3ν osc.; normal mass ordering</td>
    </tr>
    <tr>
      <td>0.37 to 0.63</td>
      <td>42 WENDELL</td>
      <td>10</td>
      <td>SKAM</td>
      <td>3ν osc.; inverted mass ordering</td>
    </tr>
    <tr>
      <td>0.31 to 0.69</td>
      <td>ADAMSON</td>
      <td>08A</td>
      <td>MINS</td>
      <td>MINOS</td>
    </tr>
    <tr>
      <td>0.05 to 0.95</td>
      <td>43 ADAMSON</td>
      <td>06</td>
      <td>MINS</td>
      <td>Atmospheric ν with far detector</td>
    </tr>
    <tr>
      <td>0.18 to 0.82</td>
      <td>44 AHN</td>
      <td>06A</td>
      <td>K2K</td>
      <td>KEK to Super-K</td>
    </tr>
    <tr>
      <td>0.23 to 0.77</td>
      <td>45 MICHAEL</td>
      <td>06</td>
      <td>MINS</td>
      <td>MINOS</td>
    </tr>
    <tr>
      <td>0.18 to 0.82</td>
      <td>46 ALIU</td>
      <td>05</td>
      <td>K2K</td>
      <td>KEK to Super-K</td>
    </tr>
    <tr>
      <td>0.18 to 0.82</td>
      <td>47 ALLISON</td>
      <td>05</td>
      <td>SOU2</td>
      <td></td>
    </tr>
    <tr>
      <td>0.36 to 0.64</td>
      <td>48 ASHIE</td>
      <td>05</td>
      <td>SKAM</td>
      <td>Super-Kamiokande</td>
    </tr>
    <tr>
      <td>0.28 to 0.72</td>
      <td>49 AMBROSIO</td>
      <td>04</td>
      <td>MCRO</td>
      <td>MACRO</td>
    </tr>
    <tr>
      <td>0.34 to 0.66</td>
      <td>50 ASHIE</td>
      <td>04</td>
      <td>SKAM</td>
      <td>L/E distribution</td>
    </tr>
    <tr>
      <td>0.08 to 0.92</td>
      <td>51 AHN</td>
      <td>03</td>
      <td>K2K</td>
      <td>KEK to Super-K</td>
    </tr>
    <tr>
      <td>0.13 to 0.87</td>
      <td>52 AMBROSIO</td>
      <td>03</td>
      <td>MCRO</td>
      <td>MACRO</td>
    </tr>
    <tr>
      <td>0.26 to 0.74</td>
      <td>53 AMBROSIO</td>
      <td>03</td>
      <td>MCRO</td>
      <td>MACRO</td>
    </tr>
    <tr>
      <td>0.15 to 0.85</td>
      <td>54 SANCHEZ</td>
      <td>03</td>
      <td>SOU2</td>
      <td>Soudan-2 Atmospheric</td>
    </tr>
    <tr>
      <td>0.28 to 0.72</td>
      <td>55 AMBROSIO</td>
      <td>01</td>
      <td>MCRO</td>
      <td>Upward μ</td>
    </tr>
    <tr>
      <td>0.29 to 0.71</td>
      <td>56 AMBROSIO</td>
      <td>01</td>
      <td>MCRO</td>
      <td>Upward μ</td>
    </tr>
    <tr>
      <td>0.13 to 0.87</td>
      <td>57 FUKUDA</td>
      <td>99C</td>
      <td>SKAM</td>
      <td>Upward μ</td>
    </tr>
    <tr>
      <td>0.23 to 0.77</td>
      <td>58 FUKUDA</td>
      <td>99D</td>
      <td>SKAM</td>
      <td>Upward μ</td>
    </tr>
    <tr>
      <td>0.08 to 0.92</td>
      <td>59 FUKUDA</td>
      <td>99D</td>
      <td>SKAM</td>
      <td>Stop μ / through</td>
    </tr>
    <tr>
      <td>0.29 to 0.71</td>
      <td>60 FUKUDA</td>
      <td>98C</td>
      <td>SKAM</td>
      <td>Super-Kamiokande</td>
    </tr>
    <tr>
      <td>0.08 to 0.92</td>
      <td>61 HATAKEYAMA98</td>
      <td>KAMI</td>
      <td></td>
      <td>Kamiokande</td>
    </tr>
    <tr>
      <td>0.24 to 0.76</td>
      <td>62 HATAKEYAMA98</td>
      <td>KAMI</td>
      <td></td>
      <td>Kamiokande</td>
    </tr>
    <tr>
      <td>0.20 to 0.80</td>
      <td>63 FUKUDA</td>
      <td>94</td>
      <td>KAMI</td>
      <td>Kamiokande</td>
    </tr>
  </tbody>
</table>

<footnote n="1">1 ABBASI 23 uses atmospheric neutrino data measured between 2011 and 2019 with the low-energy subdetector DeepCore of the IceCube neutrino telescope. Supersedes AARTSEN 18A.</footnote>

<footnote n="2">2 ABE 23f results are based on data collected between 2010 and 2020 in (anti)neutrino mode and include a neutrino beam exposure of 1.97 × 10<sup>21</sup> (1.63 × 10<sup>21</sup>) protons on target. Supersedes ABE 20F.</footnote>

<footnote n="3">3 ACERO 22 uses data from Jun 29, 2016 to Feb 26, 2019 (12.5 × 10<sup>20</sup> POT) and Feb 6, 2014 to Mar 20, 2020 (13.6 × 10<sup>20</sup> POT). Best fit for octant I (lower octant) is 0.46 for both normal and inverted mass orderings. Supersedes ACERO 19.</footnote>

<footnote n="4">4 ADAMSON 20A uses the complete dataset from MINOS and MINOS+ experiments. The data were collected using a total exposure of 23.76 × 10<sup>20</sup> protons on target and 60.75 kton-yr exposure to atmospheric neutrinos. Supersedes ADAMSON 14.</footnote>

<footnote n="5">5 ABE 18B uses 328 kton-years of Super-Kamiokande I-IV atmospheric neutrino data to obtain this result. The fit is performed over the three parameters, Δm<sup>2</sup><sub>32</sub>, sin<sup>2</sup>(θ<sub>23</sub>), and δ, while the solar parameters and sin<sup>2</sup>(θ<sub>13</sub>) are fixed to Δm<sup>2</sup><sub>21</sub> = (7.53 ± 0.18) × 10<sup>-5</sup> eV<sup>2</sup>, sin<sup>2</sup>(θ<sub>12</sub>) = 0.304 ± 0.014, and sin<sup>2</sup>(θ<sub>13</sub>) = 0.0219 ± 0.0012.</footnote>

<footnote n="6">6 ABE 23D uses the same dataset as ABE 23F. The measurement of sin<sup>2</sup>(θ<sub>23</sub>) is performed independently for ν<sub>μ</sub> and π<sub>μ</sub>.</footnote>

<footnote n="7">7 ABE 21A results are based on 1.49 × 10<sup>21</sup> POT in neutrino mode and 1.64 × 10<sup>21</sup> POT in antineutrino mode.</footnote>

<footnote n="8">8 SALAS 21 reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference.</footnote>

<footnote n="9">9 AARTSEN 20 uses the data taken between May 2012 and April 2014 with the low-energy 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 best-fit is in the lower octant for both mass orderings, a substantial range of sin<sup>2</sup>(θ<sub>23</sub>) > 0.5 is still compatible with the observed data for both mass orderings.</footnote>

<footnote n="10">10 ABE 20F results are based on data collected between 2009 and 2018 in (anti)neutrino mode and include a neutrino beam exposure of 1.49 × 10<sup>21</sup> (1.64 × 10<sup>21</sup>) protons on target. Supersedes ABE 18G.</footnote>

<footnote n="11">11 ESTEBAN 20a reports results of a global fit to neutrino oscillation data available at the time of the Neutrino2020 conference.</footnote>

<footnote n="12">12 AARTSEN 19c 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 sub-detector DeepCore of the IceCube neutrino telescope. AARTSEN 19c 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 18A to measure the ν<sub>μ</sub> disappearance.</footnote>

<footnote n="13">13 ACERO 19 is based on a sample size of 12.33 × 10<sup>20</sup> 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 σ and θ<sub>23</sub> values in octant II by 1.6 σ. Supersedes ACERO 18.</footnote>

<footnote n="14">14 Errors are from normal mass ordering and θ<sub>13</sub> octant II fits.</footnote>

<footnote n="15">15 ALBERT 19 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 12.</footnote>

<footnote n="16">16 AARTSEN 18A 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 sub-detector DeepCore of the IceCube neutrino telescope. AARTSEN 18A also reports the best fit result for the inverted mass ordering as Δm<sup>2</sup><sub>32</sub> = -2.32 × 10<sup>-3</sup> eV<sup>2</sup> and sin<sup>2</sup>(θ<sub>23</sub>) = 0.51. Uncertainties for the inverted mass ordering fits were not provided. Supersedes AARTSEN 15A.</footnote>

<footnote n="17">17 ABE 18B uses 328 kton-years of Super-Kamiokande I-IV atmospheric neutrino data to obtain this result. The fit is performed over the four parameters, Δm<sup>2</sup><sub>32</sub>, sin<sup>2</sup>(θ<sub>23</sub>), sin<sup>2</sup>(θ<sub>13</sub>), and δ, while the solar parameters are fixed to Δm<sup>2</sup><sub>21</sub> = (7.53 ± 0.18) × 10<sup>-5</sup> eV<sup>2</sup> and sin<sup>2</sup>(θ<sub>12</sub>) = 0.304 ± 0.014.</footnote>

<footnote n="18">18 ABE 18G data prefers normal mass ordering is with a posterior probability of 87%. Supersedes ABE 17F.</footnote>

<footnote n="19">19 ACERO 18 performs a joint fit to the data for ν<sub>μ</sub> disappearance and ν<sub>e</sub> appearance. The overall best fit favors normal mass ordering and θ<sub>23</sub> in octant II. No 1σ confidence intervals are presented for the inverted mass ordering scenarios. Supersedes by ACERO 19.</footnote>

<footnote n="20">20 Errors are from the projections of the 68% contour on 2D plot of Δm<sup>2</sup> versus sin<sup>2</sup>(θ<sub>23</sub>). ABE 17F supersedes ABE 17A. Supersedes by ABE 18G.</footnote>

<footnote n="21">21 Supersedes by ABE 18.</footnote>

<footnote n="22">22 ABE 16D reports oscillation results using π̄<sub>μ</sub> disappearance in an off-axis beam.</footnote>

<footnote n="23">23 ADAMSON 16A obtains sin<sup>2</sup>(θ<sub>23</sub>) in the 68% C.L. range [0.38, 0.65] ([0.37, 0.64]), with two statistically degenerate best-fit values of 0.44 and 0.59 (0.44 and 0.59) for normal (inverted) mass ordering. Supersedes by ADAMSON 17A.</footnote>

<footnote n="24">24 AARTSEN 15A obtains this result by a three-neutrino oscillation analysis using 10–100 GeV muon neutrino sample from a total of 953 days of measurement with the low-energy subdetector DeepCore of the IceCube neutrino telescope. Supersedes by AARTSEN 18A.</footnote>

<footnote n="25">25 ABE 14 results are based on ν<sub>μ</sub> disappearance using three-neutrino oscillation fit. The confidence intervals are derived from one dimensional profiled likelihoods. Supersedes by ABE 17A.</footnote>

<footnote n="26">26 ADAMSON 14 uses a complete set of accelerator and atmospheric data. The analysis combines the ν<sub>μ</sub> disappearance and ν<sub>e</sub> appearance data using three-neutrino oscillation fit. The fit results are obtained for normal and inverted mass ordering assumptions. The best fit is for first θ<sub>23</sub> octant and inverted mass ordering.</footnote>

<footnote n="27">27 FORERO 14 performs a global fit to neutrino oscillations using solar, reactor, long-baseline accelerator, and atmospheric neutrino data.</footnote>

<footnote n="28">28 GONZALEZ-GARCIA 14 result comes from a frequentist global fit. The corresponding Bayesian global fit to the same data results are reported in BERGSTROM 15 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.</footnote>

<footnote n="29">29 AARTSEN 13B 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.</footnote>

<footnote n="30">30 The best fit value is sin<sup>2</sup>(θ<sub>23</sub>) = 0.514 ± 0.082. Supersedes by ABE 14.</footnote>

<footnote n="31">31 ADAMSON 13B obtained this result from ν<sub>μ</sub> and π<sub>μ</sub> disappearance using ν<sub>μ</sub> (10.71 × 10<sup>20</sup> POT) and π<sub>μ</sub> (3.36 × 10<sup>20</sup> POT) beams, and atmospheric (37.88kton-years) data</footnote>
from MINOS. The fit assumed two-flavor neutrino hypothesis and identical $\nu_{\mu}$ and $\bar{\nu}_{\mu}$ oscillation parameters. Superseded by ADAMSON 14.

32 ABE 12a obtained this result by a two-neutrino oscillation analysis. The best-fit point is $\sin^2(2\theta_{23}) = 0.98$.

33 ADAMSON 12 is a two-neutrino oscillation analysis using antineutrinos. The best fit value is $\sin^2(2\theta_{23}) = 0.95^{+0.10}_{-0.11} \pm 0.01$.

34 ADAMSON 12b obtained this result by a two-neutrino oscillation analysis of the L/E distribution using 37.9 kton-yr atmospheric neutrino data with the MINOS far detector.

35 The best fit point is $\Delta m^2 = 0.0019 \text{ eV}^2$ and $\sin^2 2\theta = 0.99$. The 90% single-parameter confidence interval at the best fit point is $\sin^2 2\theta > 0.86$.

36 The data are separated into pure samples of $\nu_s$ and $\tau_s$, and separate oscillation parameters for $\nu_s$ and $\tau_s$ are fit to the data. The best fit point is $(\Delta m^2, \sin^2 2\theta) = (0.0022 \text{ eV}^2, 0.99)$ and $(\Delta \bar{m}^2, \sin^2 2\bar{\theta}) = (0.0016 \text{ eV}^2, 1.00)$. The quoted result is taken from the 90% C.L. contour in the $(\Delta m^2, \sin^2 2\theta)$ plane obtained by minimizing the four parameter log-likelihood function with respect to the other oscillation parameters.

37 ADRIAN-MARTINEZ 12 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 19.

38 ABE 11c obtained this result by a two-neutrino oscillation analysis using the Super-Kamiokande-I-II+III atmospheric neutrino data. ABE 11c also reported results under a two-neutrino disappearance model with separate mixing parameters between $\nu$ and $\tau$, and obtained $\sin^2 2\theta > 0.93$ for $\nu$ and $\sin^2 2\theta > 0.83$ for $\tau$ at 90% C.L.

39 ADAMSON 11b 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 11 at 2% C.L.

40 WENDELL 10 obtained this result ($\sin^2 2\theta_{23} = 0.407-0.583$) by a three-neutrino oscillation analysis using the Super-Kamiokande-I-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.

41 WENDELL 10 obtained this result ($\sin^2 2\theta_{23} = 0.43-0.61$) 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 06A result.

42 WENDELL 10 obtained this result ($\sin^2 2\theta_{23} = 0.44-0.63$) 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 06A result.

43 ADAMSON 06 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.

44 Supersedes ALIU 05.

45 MICHAEL 06 best fit is for maximal mixing. See also ADAMSON 08.

46 The best fit is for maximal mixing.

47 ALLISON 05 result is based upon atmospheric neutrino interactions including upward-stopping muons, with an exposure of 5.9 kton yr. From a two-flavor oscillation analysis the best-fit point is $\Delta m^2 = 0.0017 \text{ eV}^2$ and $\sin^2(2\theta) = 0.97$.

48 ASHIE 05 obtained this result by a two-neutrino oscillation analysis using 92 kton yr atmospheric neutrino data from the complete Super-Kamiokande I running period.

49 AMBROSIO 04 obtained this result, without using the absolute normalization of the neutrino flux, by combining the angular distribution of upward through-going muon tracks with $E_{\mu} > 1$ 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 maximal mixing.

50 ASHIE 04 obtained this result from the L(flight length)/E(estimated neutrino energy) distribution of $\nu_{\mu}$ disappearance probability, using the Super-Kamiokande-I 1489 live-day atmospheric neutrino data.

51 There are several islands of allowed region from this K2K analysis, extending to high values of $\Delta m^2$. We only include the one that overlaps atmospheric neutrino analyses. The best fit is for maximal mixing.

52 AMBROSIO 03 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 98 is used to obtain the limits.

53 AMBROSIO 03 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 01. The method of FELDMAN 98 is used to obtain the limits. The best fit is to maximal mixing.

54 SANCHEZ 03 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 $\mu$ flavor sample while the e-flavor sample provides flux normalization. The method of FELDMAN 98 is used to obtain the allowed region. The best fit is $\sin^2(2\theta) = 0.97$.

55 AMBROSIO 01 result is based on the angular distribution of upward through-going muon tracks with $E_{\mu} > 1$ 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 98 is used to obtain the limits. The best fit is for maximal mixing.

56 AMBROSIO 01 result is based on the angular distribution and normalization of upward through-going muon tracks with $E_{\mu} > 1$ GeV. See the previous footnote.

57 FUKUDA 99c 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 $E_{\mu} > 1.6$ GeV, the observed flux is $(1.74 \pm 0.07 \pm 0.02) \times 10^{-13} \text{ cm}^{-2} \text{s}^{-1} \text{ sr}^{-1}$. The best fit is $\sin^2(2\theta) = 0.95$.

58 FUKUDA 99d 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 $(0.39 \pm 0.04 \pm 0.02) \times 10^{-13} \text{ cm}^{-2} \text{s}^{-1} \text{ sr}^{-1}$. This is compared to the expected flux of $(0.73 \pm 0.16)$ (theoretical error)) $\times 10^{-13} \text{ cm}^{-2} \text{s}^{-1} \text{ sr}^{-1}$. The best fit is to maximal mixing.

59 FUKUDA 99d obtained this result from the zenith dependence of the upward-stopping/through-going flux ratio. The best fit is to maximal mixing.

60 FUKUDA 98c obtained this result by an analysis of 33.0 kton yr atmospheric neutrino data. The best fit is for maximal mixing.

61 HATAKEYAMA 98 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 $E_{\mu} > 1.6$ GeV, the observed flux of upward through-going muons is $(1.94 \pm 0.10^{+0.07}_{-0.06}) \times 10^{-13} \text{ cm}^{-2} \text{s}^{-1} \text{ sr}^{-1}$. This is compared to the expected flux of $(2.46 \pm 0.54)$ (theoretical error)) $\times 10^{-13} \text{ cm}^{-2} \text{s}^{-1} \text{ sr}^{-1}$. The best fit is for maximal mixing.

62 HATAKEYAMA 98 obtained this result from a combined analysis of Kamiokande contained events (FUKUDA 94) and upward going muon events. The best fit is $\sin^2(2\theta) = 0.95$.

63 FUKUDA 94 obtained the result by a combined analysis of sub- and multi-GeV atmospheric neutrino events in Kamiokande. The best fit is for maximal mixing.

$\Delta m^2_{32}$

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.

<table><thead><tr><th>VALUE (10<sup>-3</sup> eV<sup>2</sup>)</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>-2.529 &pm; 0.029</strong> OUR FIT</td><td></td><td>Assuming inverted ordering</td><td></td></tr><tr><td><strong>2.455 &pm; 0.028</strong> OUR FIT</td><td></td><td>Assuming normal ordering</td><td></td></tr><tr><td>2.41 &pm; 0.07</td><td>1 ABBASI</td><td>23 ICCB</td><td>Normal mass ordering</td></tr><tr><td>2.494 <sup>+0.041</sup><sub>-0.058</sub></td><td>2 ABE</td><td>23F T2K</td><td>Normal mass ordering, &theta;<sub>13</sub> constrained</td></tr><tr><td>-2.54 <sup>+0.042</sup><sub>-0.056</sub></td><td>2,3 ABE</td><td>23F T2K</td><td>Inverted mass ordering, &theta;<sub>13</sub> constrained</td></tr><tr><td>2.47 &pm; 0.06</td><td>4 AN</td><td>23 DAYA</td><td>Normal mass ordering</td></tr><tr><td>-2.57 &pm; 0.06</td><td>4 AN</td><td>23 DAYA</td><td>Inverted mass ordering</td></tr><tr><td>2.41 &pm; 0.07</td><td>5 ACERO</td><td>22 NOVA</td><td>Normal mass ordering, octant II for &theta;<sub>23</sub>, &theta;<sub>13</sub> constrained</td></tr><tr><td>-2.45 &pm; 0.07</td><td>5 ACERO</td><td>22 NOVA</td><td>Inverted mass ordering, octant II for &theta;<sub>23</sub>, &theta;<sub>13</sub> constrained</td></tr><tr><td>2.40 <sup>+0.08</sup><sub>-0.09</sub></td><td>6 ADAMSON</td><td>20A MINS</td><td>Accel., atmospheric, normal mass ordering</td></tr><tr><td>-2.45 <sup>+0.08</sup><sub>-0.07</sub></td><td>6 ADAMSON</td><td>20A MINS</td><td>Accel., atmospheric, inverted mass ordering</td></tr><tr><td>2.50 <sup>+0.13</sup><sub>-0.20</sub></td><td>7 ABE</td><td>18B SKAM</td><td>Normal mass ordering, &theta;<sub>13</sub> constrained</td></tr><tr><td>-2.58 <sup>+0.08</sup><sub>-0.37</sub></td><td>7 ABE</td><td>18B SKAM</td><td>Inverted mass ordering, &theta;<sub>13</sub> constrained</td></tr><tr><td>2.63 &pm; 0.14</td><td>8 BAK</td><td>18 RENO</td><td>Normal mass ordering</td></tr><tr><td>-2.73 &pm; 0.14</td><td>8 BAK</td><td>18 RENO</td><td>Inverted mass ordering</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>2.48</td><td>+0.05</td><td>9 ABE</td><td>23D T2K</td><td>ν<sub>μ</sub> disappearance</td></tr><tr><td>2.53</td><td>+0.10</td><td>9 ABE</td><td>23D T2K</td><td>ν̄<sub>μ</sub> disappearance</td></tr><tr><td>2.47</td><td>+0.08</td><td>10 ABE</td><td>21A T2K</td><td>ν<sub>μ</sub> disappearance</td></tr><tr><td>2.50</td><td>+0.18</td><td>10 ABE</td><td>21A T2K</td><td>ν̄<sub>μ</sub> disappearance</td></tr><tr><td>2.45</td><td>+0.07</td><td>11 ABE</td><td>20F T2K</td><td>Normal mass ordering, &theta;<sub>13</sub> constrained</td></tr><tr><td>-2.51</td><td>+0.07</td><td>11,12 ABE</td><td>20F T2K</td><td>Inverted mass ordering, &theta;<sub>13</sub> constrained</td></tr><tr><td>2.517</td><td>+0.026</td><td>13 ESTEBAN</td><td>20A FIT</td><td>Normal mass ordering, global fit</td></tr><tr><td>-2.498</td><td>+0.028</td><td>13 ESTEBAN</td><td>20A FIT</td><td>Inverted mass ordering, global fit</td></tr><tr><td>2.55</td><td>+0.12</td><td>14 AARTSEN</td><td>19C ICCB</td><td></td></tr><tr><td>2.48</td><td>+0.11</td><td>15 ACERO</td><td>19 NOVA</td><td>Normal mass ordering, octant II for &theta;<sub>23</sub></td></tr><tr><td>-2.54</td><td>+0.06</td><td>15 ACERO</td><td>19 NOVA</td><td>Inverted mass ordering, octant II for &theta;<sub>23</sub></td></tr><tr><td>&lt; 4.1 at 90% CL</td><td></td><td>AGAFONOVA</td><td>19 OPER</td><td></td></tr><tr><td>2.0</td><td>+0.4</td><td>16 ALBERT</td><td>19 ANTR</td><td>Atmospheric ν, deep sea telescope</td></tr><tr><td>2.31</td><td>+0.11</td><td>17 AARTSEN</td><td>18A ICCB</td><td>Normal mass ordering</td></tr><tr><td>2.50</td><td>+0.13</td><td>18 ABE</td><td>18B SKAM</td><td>3ν osc: normal mass ordering, &theta;<sub>13</sub> free</td></tr></tbody></table>
<table>
  <tbody>
    <tr>
      <td>-2.28</td>
      <td>+0.33<br>-0.13</td>
      <td>18 ABE</td>
      <td>18B</td>
      <td>SKAM</td>
      <td>3ν osc; inverted mass ordering,<br>θ<sub>13</sub> free</td>
    </tr>
    <tr>
      <td>2.463</td>
      <td>+0.071<br>-0.070</td>
      <td>19 ABE</td>
      <td>18G</td>
      <td>T2K</td>
      <td>Normal mass ordering, θ<sub>13</sub><br>constrained</td>
    </tr>
    <tr>
      <td>-2.507</td>
      <td>±0.070</td>
      <td>19,20 ABE</td>
      <td>18G</td>
      <td>T2K</td>
      <td>Inverted mass ordering, θ<sub>13</sub><br>constrained</td>
    </tr>
    <tr>
      <td>2.44</td>
      <td>+0.08<br>-0.07</td>
      <td>21 ACERO</td>
      <td>18</td>
      <td>NOVA</td>
      <td>Normal mass order, octant II<br>for θ<sub>23</sub></td>
    </tr>
    <tr>
      <td>2.45</td>
      <td>+0.07<br>-0.08</td>
      <td>21,22 ACERO</td>
      <td>18</td>
      <td>NOVA</td>
      <td>Normal mass order; octant I<br>for θ<sub>23</sub></td>
    </tr>
    <tr>
      <td>2.471</td>
      <td>+0.068<br>-0.070</td>
      <td>23 ADEY</td>
      <td>18A</td>
      <td>DAYA</td>
      <td>Normal mass ordering</td>
    </tr>
    <tr>
      <td>-2.575</td>
      <td>+0.068<br>-0.070</td>
      <td>23 ADEY</td>
      <td>18A</td>
      <td>DAYA</td>
      <td>Inverted mass ordering</td>
    </tr>
    <tr>
      <td>2.7</td>
      <td>+0.7<br>-0.6</td>
      <td>24 AGAFONOVA</td>
      <td>18</td>
      <td>OPER</td>
      <td>OPERA ν<sub>τ</sub> appearance</td>
    </tr>
    <tr>
      <td>2.42</td>
      <td>±0.03</td>
      <td>DE-SALAS</td>
      <td>18</td>
      <td>FIT</td>
      <td>Normal mass ordering, global<br>fit</td>
    </tr>
    <tr>
      <td>-2.50</td>
      <td>+0.03<br>-0.04</td>
      <td>DE-SALAS</td>
      <td>18</td>
      <td>FIT</td>
      <td>Inverted mass order, global fit</td>
    </tr>
    <tr>
      <td>2.57</td>
      <td>+0.21<br>-0.23</td>
      <td>25 SEO</td>
      <td>18</td>
      <td>RENO</td>
      <td>Normal mass ordering</td>
    </tr>
    <tr>
      <td>-2.67</td>
      <td>+0.23<br>-0.21</td>
      <td>25 SEO</td>
      <td>18</td>
      <td>RENO</td>
      <td>Inverted mass ordering</td>
    </tr>
    <tr>
      <td>2.53</td>
      <td>+0.15<br>-0.13</td>
      <td>ABE</td>
      <td>17C</td>
      <td>T2K</td>
      <td>Normal mass ordering with<br>neutrinos</td>
    </tr>
    <tr>
      <td>2.55</td>
      <td>+0.33<br>-0.27</td>
      <td>ABE</td>
      <td>17C</td>
      <td>T2K</td>
      <td>Normal mass ordering with<br>antineutrinos</td>
    </tr>
    <tr>
      <td>2.55</td>
      <td>+0.08<br>-0.08</td>
      <td>ABE</td>
      <td>17C</td>
      <td>T2K</td>
      <td>Normal mass ordering with<br>neutrinos and antineutrinos</td>
    </tr>
    <tr>
      <td>-2.63</td>
      <td>+0.08<br>-0.08</td>
      <td>ABE</td>
      <td>17C</td>
      <td>T2K</td>
      <td>Inverted mass ordering with<br>neutrinos and antineutrinos</td>
    </tr>
    <tr>
      <td>2.54</td>
      <td>±0.08</td>
      <td>26 ABE</td>
      <td>17F</td>
      <td>T2K</td>
      <td>Normal mass ordering; ν+τ</td>
    </tr>
    <tr>
      <td>-2.51</td>
      <td>±0.08</td>
      <td>26 ABE</td>
      <td>17F</td>
      <td>T2K</td>
      <td>Inverted mass ordering; ν+τ</td>
    </tr>
    <tr>
      <td>2.67</td>
      <td>±0.11</td>
      <td>27 ADAMSON</td>
      <td>17A</td>
      <td>NOVA</td>
      <td>3ν osc; normal mass ordering</td>
    </tr>
    <tr>
      <td>-2.72</td>
      <td>±0.11</td>
      <td>27 ADAMSON</td>
      <td>17A</td>
      <td>NOVA</td>
      <td>3ν osc; inverted mass ordering</td>
    </tr>
    <tr>
      <td>2.45</td>
      <td>±0.06</td>
      <td>28 AN</td>
      <td>17A</td>
      <td>DAYA</td>
      <td>Normal mass ordering</td>
    </tr>
    <tr>
      <td>-2.56</td>
      <td>±0.06</td>
      <td>28 AN</td>
      <td>17A</td>
      <td>DAYA</td>
      <td>Inverted mass ordering</td>
    </tr>
    <tr>
      <td>2.51</td>
      <td>+0.29<br>-0.25</td>
      <td>29 ABE</td>
      <td>16D</td>
      <td>T2K</td>
      <td>3ν osc; normal mass ordering;<br>τ beam</td>
    </tr>
    <tr>
      <td>2.52</td>
      <td>+0.20<br>-0.18</td>
      <td>30 ADAMSON</td>
      <td>16A</td>
      <td>NOVA</td>
      <td>3ν osc; normal mass ordering</td>
    </tr>
    <tr>
      <td>-2.56</td>
      <td>±0.19</td>
      <td>30 ADAMSON</td>
      <td>16A</td>
      <td>NOVA</td>
      <td>3ν osc; inverted mass ordering</td>
    </tr>
    <tr>
      <td>2.56</td>
      <td>+0.21<br>-0.23</td>
      <td>31 CHOI</td>
      <td>16</td>
      <td>RENO</td>
      <td>3ν osc; normal mass ordering</td>
    </tr>
    <tr>
      <td>-2.69</td>
      <td>+0.23<br>-0.21</td>
      <td>31 CHOI</td>
      <td>16</td>
      <td>RENO</td>
      <td>3ν osc; inverted mass ordering</td>
    </tr>
    <tr>
      <td>2.72</td>
      <td>+0.19<br>-0.20</td>
      <td>32 AARTSEN</td>
      <td>15A</td>
      <td>ICCB</td>
      <td>Normal mass ordering</td>
    </tr>
    <tr>
      <td>-2.73</td>
      <td>+0.21<br>-0.18</td>
      <td>32 AARTSEN</td>
      <td>15A</td>
      <td>ICCB</td>
      <td>Inverted mass ordering</td>
    </tr>
    <tr>
      <td>2.0-5.0</td>
      <td></td>
      <td>33 AGAFONOVA</td>
      <td>15A</td>
      <td>OPER</td>
      <td>90% CL, 5 events</td>
    </tr>
    <tr>
      <td>2.37</td>
      <td>±0.11</td>
      <td>34 AN</td>
      <td>15</td>
      <td>DAYA</td>
      <td>3ν osc; normal mass ordering</td>
    </tr>
    <tr>
      <td>-2.47</td>
      <td>±0.11</td>
      <td>34 AN</td>
      <td>15</td>
      <td>DAYA</td>
      <td>3ν osc; inverted mass ordering</td>
    </tr>
    <tr>
      <td>2.51</td>
      <td>±0.10</td>
      <td>35 ABE</td>
      <td>14</td>
      <td>T2K</td>
      <td>3ν osc; normal mass ordering</td>
    </tr>
    <tr>
      <td>-2.56</td>
      <td>±0.10</td>
      <td>35 ABE</td>
      <td>14</td>
      <td>T2K</td>
      <td>3ν osc; inverted mass ordering</td>
    </tr>
    <tr>
      <td>2.37</td>
      <td>±0.09</td>
      <td>36 ADAMSON</td>
      <td>14</td>
      <td>MINS</td>
      <td>Accel., atmospheric, normal<br>mass ordering</td>
    </tr>
    <tr>
      <td>-2.41</td>
      <td>+0.09<br>-0.12</td>
      <td>36 ADAMSON</td>
      <td>14</td>
      <td>MINS</td>
      <td>Accel., atmospheric, inverted<br>mass ordering</td>
    </tr>
    <tr>
      <td>2.54</td>
      <td>+0.19<br>-0.20</td>
      <td>37 AN</td>
      <td>14</td>
      <td>DAYA</td>
      <td>3ν osc; normal mass ordering</td>
    </tr>
    <tr>
      <td>-2.64</td>
      <td>+0.20<br>-0.19</td>
      <td>37 AN</td>
      <td>14</td>
      <td>DAYA</td>
      <td>3ν osc; inverted mass ordering</td>
    </tr>
    <tr>
      <td>2.48</td>
      <td>+0.05<br>-0.07</td>
      <td>38 FORERO</td>
      <td>14</td>
      <td>FIT</td>
      <td>3ν; normal mass ordering</td>
    </tr>
    <tr>
      <td>-2.38</td>
      <td>+0.06<br>-0.05</td>
      <td>38 FORERO</td>
      <td>14</td>
      <td>FIT</td>
      <td>3ν; inverted mass ordering</td>
    </tr>
    <tr>
      <td>2.457</td>
      <td>±0.047</td>
      <td>39,40 GONZALEZ...</td>
      <td>14</td>
      <td>FIT</td>
      <td>Normal mass ordering; global<br>fit</td>
    </tr>
    <tr>
      <td>-2.449</td>
      <td>+0.047<br>-0.048</td>
      <td>39 GONZALEZ...</td>
      <td>14</td>
      <td>FIT</td>
      <td>Inverted mass ordering; global<br>fit</td>
    </tr>
    <tr>
      <td>2.3</td>
      <td>+0.6<br>-0.5</td>
      <td>41 AARTSEN</td>
      <td>13B</td>
      <td>ICCB</td>
      <td>DeepCore, 2ν oscillation</td>
    </tr>
    <tr>
      <td>2.44</td>
      <td>+0.17<br>-0.15</td>
      <td>42 ABE</td>
      <td>13G</td>
      <td>T2K</td>
      <td>3ν osc; normal mass ordering</td>
    </tr>
    <tr>
      <td>2.41</td>
      <td>+0.09<br>-0.10</td>
      <td>43 ADAMSON</td>
      <td>13B</td>
      <td>MINS</td>
      <td>2ν osc; beam + atmospheric;<br>identical ν &amp; τ</td>
    </tr>
    <tr>
      <td>2.2-3.1</td>
      <td></td>
      <td>44 ABE</td>
      <td>12A</td>
      <td>T2K</td>
      <td>off-axis beam</td>
    </tr>
    <tr>
      <td>2.62</td>
      <td>+0.31<br>-0.28</td>
      <td>45 ADAMSON</td>
      <td>12</td>
      <td>MINS</td>
      <td>τ beam</td>
    </tr>
    <tr>
      <td>1.35-2.55</td>
      <td></td>
      <td>46,47 ADAMSON</td>
      <td>12B</td>
      <td>MINS</td>
      <td>MINOS atmospheric</td>
    </tr>
    <tr>
      <td>1.4-5.6</td>
      <td></td>
      <td>46,48 ADAMSON</td>
      <td>12B</td>
      <td>MINS</td>
      <td>MINOS pure atmospheric ν</td>
    </tr>
    <tr>
      <td>0.9-2.5</td>
      <td></td>
      <td>46,48 ADAMSON</td>
      <td>12B</td>
      <td>MINS</td>
      <td>MINOS pure atmospheric τ</td>
    </tr>
    <tr>
      <td>1.8-5.0</td>
      <td></td>
      <td>49 ADRIAN-MAR...12</td>
      <td>ANTR</td>
      <td></td>
      <td>Atmospheric ν with deep sea<br>telescope</td>
    </tr>
    <tr>
      <td>1.3-4.0</td>
      <td></td>
      <td>50 ABE</td>
      <td>11C</td>
      <td>SKAM</td>
      <td>atmospheric τ</td>
    </tr>
    <tr>
      <td>2.32</td>
      <td>+0.12<br>-0.08</td>
      <td>ADAMSON</td>
      <td>11</td>
      <td>MINS</td>
      <td>2ν oscillation; maximal mixing</td>
    </tr>
    <tr>
      <td>3.36</td>
      <td>+0.46<br>-0.40</td>
      <td>51 ADAMSON</td>
      <td>11B</td>
      <td>MINS</td>
      <td>τ beam</td>
    </tr>
    <tr>
      <td>&lt; 3.37</td>
      <td></td>
      <td>52 ADAMSON</td>
      <td>11C</td>
      <td>MINS</td>
      <td>MINOS</td>
    </tr>
    <tr>
      <td>1.9-2.6</td>
      <td></td>
      <td>53 WENDELL</td>
      <td>10</td>
      <td>SKAM</td>
      <td>3ν osc; normal mass ordering</td>
    </tr>
    <tr>
      <td>-1.7-2.7</td>
      <td></td>
      <td>53 WENDELL</td>
      <td>10</td>
      <td>SKAM</td>
      <td>3ν osc; inverted mass ordering</td>
    </tr>
    <tr>
      <td>2.43</td>
      <td>±0.13</td>
      <td>ADAMSON</td>
      <td>08A</td>
      <td>MINS</td>
      <td>MINOS</td>
    </tr>
  </tbody>
</table>

<table>
  <tbody>
    <tr>
      <td>0.07-50</td>
      <td>54 ADAMSON</td>
      <td>06</td>
      <td>MINS</td>
      <td>atmospheric ν with far detector</td>
    </tr>
    <tr>
      <td>1.9-4.0</td>
      <td>55,56 AHN</td>
      <td>06A</td>
      <td>K2K</td>
      <td>KEK to Super-K</td>
    </tr>
    <tr>
      <td>2.2-3.8</td>
      <td>57 MICHAEL</td>
      <td>06</td>
      <td>MINS</td>
      <td>MINOS</td>
    </tr>
    <tr>
      <td>1.9-3.6</td>
      <td>55 ALIU</td>
      <td>05</td>
      <td>K2K</td>
      <td>KEK to Super-K</td>
    </tr>
    <tr>
      <td>0.3-12</td>
      <td>58 ALLISON</td>
      <td>05</td>
      <td>SOU2</td>
      <td></td>
    </tr>
    <tr>
      <td>1.5-3.4</td>
      <td>59 ASHIE</td>
      <td>05</td>
      <td>SKAM</td>
      <td>atmospheric neutrino</td>
    </tr>
    <tr>
      <td>0.6-8.0</td>
      <td>60 AMBROSIO</td>
      <td>04</td>
      <td>MCRO</td>
      <td>MACRO</td>
    </tr>
    <tr>
      <td>1.9 to 3.0</td>
      <td>61 ASHIE</td>
      <td>04</td>
      <td>SKAM</td>
      <td>L/E distribution</td>
    </tr>
    <tr>
      <td>1.5-3.9</td>
      <td>62 AHN</td>
      <td>03</td>
      <td>K2K</td>
      <td>KEK to Super-K</td>
    </tr>
    <tr>
      <td>0.25-9.0</td>
      <td>63 AMBROSIO</td>
      <td>03</td>
      <td>MCRO</td>
      <td>MACRO</td>
    </tr>
    <tr>
      <td>0.6-7.0</td>
      <td>64 AMBROSIO</td>
      <td>03</td>
      <td>MCRO</td>
      <td>MACRO</td>
    </tr>
    <tr>
      <td>0.15-15</td>
      <td>65 SANCHEZ</td>
      <td>03</td>
      <td>SOU2</td>
      <td>Soudan-2 Atmospheric</td>
    </tr>
    <tr>
      <td>0.6-15</td>
      <td>66 AMBROSIO</td>
      <td>01</td>
      <td>MCRO</td>
      <td>upward μ</td>
    </tr>
    <tr>
      <td>1.0-6.0</td>
      <td>67 AMBROSIO</td>
      <td>01</td>
      <td>MCRO</td>
      <td>upward μ</td>
    </tr>
    <tr>
      <td>1.0-50</td>
      <td>68 FUKUDA</td>
      <td>99c</td>
      <td>SKAM</td>
      <td>upward μ</td>
    </tr>
    <tr>
      <td>1.5-15.0</td>
      <td>69 FUKUDA</td>
      <td>99d</td>
      <td>SKAM</td>
      <td>upward μ</td>
    </tr>
    <tr>
      <td>0.7-18</td>
      <td>70 FUKUDA</td>
      <td>99d</td>
      <td>SKAM</td>
      <td>stop μ / through</td>
    </tr>
    <tr>
      <td>0.5-6.0</td>
      <td>71 FUKUDA</td>
      <td>98c</td>
      <td>SKAM</td>
      <td>Super-Kamiokande</td>
    </tr>
    <tr>
      <td>0.55-50</td>
      <td>72 HATAKEYAMA98</td>
      <td>98</td>
      <td>KAMI</td>
      <td>Kamiokande</td>
    </tr>
    <tr>
      <td>4-23</td>
      <td>73 HATAKEYAMA98</td>
      <td>98</td>
      <td>KAMI</td>
      <td>Kamiokande</td>
    </tr>
    <tr>
      <td>5-25</td>
      <td>74 FUKUDA</td>
      <td>94</td>
      <td>KAMI</td>
      <td>Kamiokande</td>
    </tr>
  </tbody>
</table>

¹ABBASI 23 uses atmospheric neutrino data measured between 2011 and 2019 with the low-energy subdetector DeepCore of the IceCube neutrino telescope. Supersedes AARTSEN 18A.

²ABE 23F results are based on data collected between 2010 and 2020 in (anti)neutrino mode and include a neutrino beam exposure of 1.97 × 10²¹ (1.63 × 10²¹) protons on target. Supersedes ABE 20r.

³ABE 23F reports $\Delta m_{13}^2 = (2.463^{+0.042}_{-0.056}) \times 10^{-3}$ eV² for inverted mass ordering. We convert to $\Delta m_{21}^2$ using PDG 23 value of $\Delta m_{21}^2 = (7.53 \pm 0.18) \times 10^{-5}$ eV².

⁴AN 23 reports results derived from the complete data collected by the Daya-Bay experiment, corresponding to 3158 days of operation, resulting in 5.55 × 10⁶ $\bar{\nu}_e$ candidate events. Solar oscillation parameters are fixed in the analysis to $\sin^2(\theta_{12}) = 0.307 \pm 0.013$, $\Delta m_{21}^2 = (7.53 \pm 0.18) \times 10^{-5}$ eV² from PDG 20. Supersedes ADEY 18A.

⁵ACERO 22 uses data from Jun 29, 2016 to Feb 26, 2019 (12.5 × 10²⁰ POT) and Feb 6, 2014 to Mar 20, 2020 (13.6 × 10²⁰ POT). For normal mass ordering and $\theta_{23}$ octant I (lower octant), best fit is 0.00239 eV²; for inverted mass ordering and octant I, best fit is -0.00244 eV². Supersedes ACERO 19.

⁶ADAMSON 20A uses the complete dataset from MINOS and MINOS+ experiments. The data were collected using a total exposure of 23.76 × 10²⁰ protons on target and 60.75 kton-yr exposure to atmospheric neutrinos. Supersedes ADAMSON 14.

⁷ABE 18B uses 328 kton-years of Super-Kamiokande I-IV atmospheric neutrino data to obtain this result. The fit is performed over the three parameters, $\Delta m_{32}^2$, $\sin^2(\theta_{23})$, and $\delta$, while the solar parameters and $\sin^2(\theta_{13})$ are fixed to $\Delta m_{21}^2 = (7.53 \pm 0.18) \times 10^{-5}$ eV², $\sin^2(\theta_{12}) = 0.304 \pm 0.014$, and $\sin^2(\theta_{13}) = 0.0219 \pm 0.0012$.

⁸BAK 18 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 $\Delta m_{32}^2$ using the PDG 18 values of $\sin^2(\theta_{12}) = 0.307^{+0.013}_{-0.012}$ and $\Delta m_{21}^2 = (7.53 \pm 0.18) \times 10^{-5}$ eV². Supersedes SEO 18.

⁹ABE 23D uses the same dataset as ABE 23F. The measurement of $\Delta m_{32}^2$ is performed independently for $\nu_μ$ and $\bar{\nu}_μ$.

¹⁰ABE 21A results are based on 1.49 × 10²¹ POT in neutrino mode and 1.64 × 10²¹ POT in antineutrino mode.

¹¹ABE 20F results are based on data collected between 2009 and 2018 in (anti)neutrino mode and include a neutrino beam exposure of 1.49 × 10²¹ (1.64 × 10²¹) protons on target. Supersedes ABE 18g.

¹²ABE 20F reports $\Delta m_{13}^2 = (2.43 \pm 0.07) \times 10^{-3}$ eV² for inverted mass ordering. We convert to $\Delta m_{21}^2$ using PDG 20 value of $\Delta m_{21}^2 = (7.53 \pm 0.18) \times 10^{-5}$ eV².

¹³ESTEBAN 20A reports results of a global fit to neutrino oscillation data available at the time of the Neutrino2020 conference.

¹⁴AARTSEN 19c 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 18A also reports the best fit values for the inverted mass ordering as $\Delta m_{32}^2 = -2.32 \times 10^{-3}$ eV² and $\sin^2(\theta_{23}) = 0.51$. Uncertainties for the inverted mass ordering fits were not provided. Supersedes AARTSEN 15A.

¹⁵ACERO 19 is based on a sample size of 12.33 × 10²⁰ 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 σ and $\theta_{23}$ values in octant II by 1.6 σ. Superseded by ACERO 22.

¹⁶ALBERT 19 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 12.

¹⁷AARTSEN 18A 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 18A also reports the best fit values for the inverted mass ordering as $\Delta m_{32}^2 = -2.32 \times 10^{-3}$ eV² and $\sin^2(\theta_{23}) = 0.51$. Uncertainties for the inverted mass ordering fits were not provided. Supersedes AARTSEN 15A.

¹⁸ABE 18B uses 328 kton-years of Super-Kamiokande I-IV atmospheric neutrino data to obtain this result. The fit is performed over the four parameters, $\Delta m_{32}^2$, $\sin^2(\theta_{23})$, $\sin^2(\theta_{13})$, and $\delta$, while the solar parameters are fixed to $\Delta m_{21}^2 = (7.53 \pm 0.18) \times 10^{-5}$ eV² and $\sin^2(\theta_{12}) = 0.304 \pm 0.014$.
19 ABE 18g data prefers normal ordering with a posterior probability of 87%. Supersedes ABE 17f.

20 ABE 18g reports $\Delta m_{13}^2 = (2.432 \pm 0.070) \times 10^{-3}$ eV$^2$ for inverted mass ordering. We convert to $\Delta m_{32}^2$ using PDG 18 value of $\Delta m_{21}^2 = (7.53 \pm 0.18) \times 10^{-5}$ eV$^2$.

21 ACERO 18 performs a joint fit to the data for $\nu_\mu$ disappearance and $\nu_e$ appearance. The overall best fit favors normal mass ordering and $\theta_{23}$ in octant II. No $1\sigma$ confidence intervals are presented for the inverted mass ordering scenarios. Superseded by ACERO 19.

22 The error for octant I is taken from the result for octant II.

23 ADEY 18A reports results from analysis of 1958 days of data taking with the Daya-Bay experiment, with $3.9 \times 10^6 \bar{\nu}_e$ candidates. The fit to the data gives $\Delta m_{ee}^2 = (2.522^{+0.068}_{-0.070}) \times 10^{-3}$ eV$^2$. Solar oscillation parameters are fixed in the analysis using the global averages, $\sin^2(\theta_{12}) = 0.307^{+0.013}_{-0.012}$, $\Delta m_{21}^2 = (7.53 \pm 0.18) \times 10^{-5}$ eV$^2$, from PDG 18. Supersedes AN 17a.

24 AGAFONOVA 18 assumes maximal $\theta_{23}$ mixing.

25 SEO 18 reports result of the RENO experiment from a rate and shape analysis of 500 days of data. A simultaneous fit to $\theta_{13}$ and $\Delta m_{ee}^2$ yields $\Delta m_{ee}^2 = (2.62^{+0.21}_{-0.23} \pm 0.12) \times 10^{-3}$ eV$^2$. We convert the results to $\Delta m_{32}^2$ using PDG 18 values of $\sin^2\theta_{12}$ and $\Delta m_{21}^2$. SEO 18 is a detailed description of the results published in CHOI 16, which it supersedes. Superseded by BAK 18

26 ABE 17f confidence intervals are obtained using a frequentium analysis including $\theta_{13}$ constraint from reactor experiments. Bayesian intervals based on Markov Chain Monte Carlo method are also provided by the authors. Superseded by ABE 18g.

27 Superseded by ACERO 18.

28 AN 17A report results from combined rate and spectral shape analysis of 1230 days of data taken with the Daya Bay reactor experiment. The data contains more than $2.5 \times 10^6$ inverse beta-decay events with neutron capture on Gd. The fit to the data gives $\Delta \epsilon^2 = (2.50 \pm 0.06 \pm 0.06) \times 10^{-3}$ eV. Superseded by ADEY 18A.

29 ABE 16D reports oscillation results using $\bar{\nu}_\mu$ disappearance in an off-axis beam.

30 Superseded by ADAMSON 17A.

31 CHOI 16 reports result of the RENO experiment from a rate and shape analysis of 500 days of data. A simultaneous fit to $\theta_{13}$ and $\Delta m_{ee}^2$ yields $\Delta m_{ee}^2 = (2.62^{+0.21}_{-0.23} \pm 0.12) \times 10^{-3}$ eV. We convert the results to $\Delta m_{32}^2$ using PDG 18 values of $\sin^2(\theta_{12})$ and $\Delta m_{21}^2$.

32 AARTSEN 15A obtains this result by a three-neutrino oscillation analysis using 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 18A.

33 AGAFONOVA 15A result is based on $5 \nu_\mu \rightarrow \nu_\tau$ appearance candidates with an expected background of $0.25 \pm 0.05$ events. The best fit is for $\Delta m_{32}^2 = 3.3 \times 10^{-3}$ eV$^2$.

34 AN 15 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 $\Delta m_{ee}^2 = (2.42 \pm 0.11) \times 10^{-3}$ eV$^2$. Assuming the normal (inverted) ordering, the fitted $\Delta m_{32}^2 = (2.37 \pm 0.11) \times 10^{-3}$ ((2.47 $\pm$ 0.11) $\times 10^{-3}$) eV$^2$. Superseded by AN 17A.

35 ABE 14 results are based on $\nu_\mu$ disappearance using three-neutrino oscillation fit. The confidence intervals are derived from one dimensional profiled likelihoods. In ABE 14 the inverted mass ordering result is reported as $\Delta m_{13}^2 = (2.48 \pm 0.10) \times 10^{-3}$ eV$^2$ which we converted to $\Delta m_{32}^2$ by adding PDG 14 value of $\Delta m_{21}^2 = (7.53 \pm 0.18) \times 10^{-5}$ eV$^2$. Superseded by ABE 17c.

36 ADAMSON 14 uses a complete set of accelerator and atmospheric data. The analysis combines the analysis combines the $\nu_\mu$ disappearance and $\nu_e$ appearance data using three-neutrino oscillation fit. The fit results are obtained for normal and inverted mass ordering assumptions.

37 AN 14 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 $\Delta m_{ee}^2 = (2.59^{+0.19}_{-0.20}) \times 10^{-3}$ eV$^2$. Assuming the normal (inverted) ordering, the fitted $\Delta m_{32}^2 = (2.54^{+0.19}_{-0.20}) \times 10^{-3}$ ((2.64 $\pm$ 0.19) $\times 10^{-3}$) eV$^2$. Superseded by AN 15.

38 FORERO 14 performs a global fit to $\Delta m_{31}^2$ using solar, reactor, long-baseline accelerator, and atmospheric neutrino data.

39 GONZALEZ-GARCIA 14 result comes from a frequentium fit. The corresponding Bayesian global fit to the same data results are reported in BERGSTROM 15 as (2.460 $\pm$ 0.046) $\times 10^{-3}$ 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 $\Delta m_{31}^2$ which differs from $\Delta m_{32}^2$ by a much smaller value of $\Delta m_{12}^2$.

41 AARTSEN 13b 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 $\nu_\mu$ events with 205 $\pm$ 17(syst) expected in the absence of neutrino oscillations. Superseded by ABE 14.

43 ADAMSON 13b obtained this result from $\nu_\mu$ and $\bar{\nu}_\mu$ disappearance using $\nu_\mu$ (10.71 $\times$ 10$^20$ POT) and $\bar{\nu}_\mu$ (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 $\nu_\mu$ and $\bar{\nu}_\mu$ oscillation parameters.

44 ABE 12A obtained this result by a two-neutrino oscillation analysis. The best-fit point is $\Delta m_{32}^2 = 2.65 \times 10^{-3}$ eV$^2$.

45 ADAMSON 12 is a two-neutrino oscillation analysis using antineutrinos.

46 ADAMSON 12b obtained this result by a two-neutrino oscillation analysis of the L/E distribution using 37.9 kton-yr atmospheric neutrino data with the MINOS far detector.

47 The 90% single-parameter confidence interval at the best fit point is $\Delta m^2 = 0.0019 \pm 0.0004$ eV$^2$.

48 The data are separated into pure samples of $\nu_s$ and $\bar{\nu}_s$, and separate oscillation parameters for $\nu_s$ and $\bar{\nu}_s$ to the data. The best fit point is ($\Delta m^2$, $\sin^2\theta$) = (0.0022 eV$^2$, 0.99) and ($\Delta m^2$, $\sin^22\theta$) = (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 12 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 19

50 ABE 11c 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 $\Delta m^2 = 1.7-3.0 \times 10^{-3}$ eV$^2$.

51 ADAMSON 11b 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 11 at 2% C.L.

52 ADAMSON 11c obtains this result based on a study of antineutrinos in a neutrino beam and assumes maximal mixing in the two-flavor approximation.

53 WENDELL 10 obtained this result by a three-neutrino oscillation analysis with one mass scale dominance ($\Delta m_{21}^2 = 0$) using the Super-Kamiokande-I+II+III atmospheric neutrino data, and updates the HOSAKA 06A result.

54 ADAMSON 06 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 $\Delta m^2 = 2.8 \times 10^{-3}$ eV$^2$.

56 Supersedes ALIU 05.

57 MICHAEL 06 best fit is $2.74 \times 10^{-3}$ eV$^2$. See also ADAMSON 08.

58 ALLISON 05 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 $\Delta m^2 = 0.0017$ eV$^2$ and $\sin^2 2\theta = 0.97$.

59 ASHIE 05 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 $\Delta m^2 = 2.1 \times 10^{-3}$ eV$^2$.

60 AMBROSIO 04 obtained this result, without using the absolute normalization of the neutrino flux, by combining the angular distribution of upward through-going muon tracks with $E_\mu > 1$ GeV, $N_{Ilow}$ and $N_{high}$, and the numbers of InDown + UpStop and InUp events. Here, $N_{Ilow}$ 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 $\Delta m^2 = 2.3 \times 10^{-3}$ eV$^2$.

61 ASHIE 04 obtained this result from the L(flight length)/E(estimated neutrino energy) distribution of $\nu_\mu$ disappearance probability, using the Super-Kamiokande-I 1489 live-day atmospheric neutrino data. The best fit is for $\Delta m^2 = 2.4 \times 10^{-3}$ eV$^2$.

62 There are several islands of allowed region from this K2K analysis, extending to high values of $\Delta m^2$. We only include the one that overlaps atmospheric neutrino analyses. The best fit is for $\Delta m^2 = 2.8 \times 10^{-3}$ eV$^2$.

63 AMBROSIO 03 obtained this result on the basis of the ratio $R = N_{Ilow}/N_{high}$, where $N_{Ilow}$ 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 98 is used to obtain the limits. The best fit is for $\Delta m^2 = 2.5 \times 10^{-3}$ eV$^2$.

64 AMBROSIO 03 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 01. The method of FELDMAN 98 is used to obtain the limits. The best fit is for $\Delta m^2 = 2.5 \times 10^{-3}$ eV$^2$.

65 SANCHEZ 03 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 $\mu$ flavor sample while the e-flavor sample provides flux normalization. The method of FELDMAN 98 is used to obtain the allowed region. The best fit is for $\Delta m^2 = 5.2 \times 10^{-3}$ eV$^2$.

66 AMBROSIO 01 result is based on the angular distribution of upward through-going muon tracks with $E_\mu > 1$ 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 98 is used to obtain the limits.

67 AMBROSIO 01 result is based on the angular distribution and normalization of upward through-going muon tracks with $E_\mu > 1$ GeV. See the previous footnote.

68 FUKUDA 99c 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 $E_\mu > 1.6$ GeV, the observed flux is $(1.74 \pm 0.07 \pm 0.02) \times 10^{-13} \text{ cm}^{-2}\text{s}^{-1}\text{sr}^{-1}$. The best fit is for $\Delta m^2 = 5.9 \times 10^{-3}$ eV$^2$.

69 FUKUDA 99d 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 $\pm$ 0.04 $\pm$ 0.02) $\times 10^{-13} \text{ cm}^{-2}\text{s}^{-1}\text{sr}^{-1}$. This is compared to the expected flux of (0.73 $\pm$ 0.16 (theoretical error)) $\times 10^{-13} \text{ cm}^{-2}\text{s}^{-1}\text{sr}^{-1}$. The best fit is for $\Delta m^2 = 3.9 \times 10^{-3}$ eV$^2$.

70 FUKUDA 99d obtained this result from the zenith dependence of the upward-stopping/through-going flux ratio. The best fit is for $\Delta m^2 = 3.1 \times 10^{-3}$ eV$^2$.
71 FUKUDA 98C obtained this result by an analysis of 33.0 kton yr atmospheric neutrino data. The best fit is for $\Delta m^2 = 2.2 \times 10^{-3}$ eV$^2$.

72 HATAKEYAMA 98 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 $E_{\mu} > 1.6$ GeV, the observed flux of upward-going muons is $(1.94 \pm 0.10^{+0.07}_{-0.06}) \times 10^{-13} \text{ cm}^{-2}\text{s}^{-1}\text{sr}^{-1}$. This is compared to the expected flux of $(2.46 \pm 0.54)$ (theoretical error)) $\times 10^{-13} \text{ cm}^{-2}\text{s}^{-1}\text{sr}^{-1}$. The best fit is for $\Delta m^2 = 2.2 \times 10^{-3}$ eV$^2$.

73 HATAKEYAMA 98 obtained this result from a combined analysis of Kamiokande contained events (FUKUDA 94) and upward going muon events. The best fit is for $\Delta m^2 = 13 \times 10^{-3}$ eV$^2$.

74 FUKUDA 94 obtained the result by a combined analysis of sub- and multi-GeV atmospheric neutrino events in Kamiokande. The best fit is for $\Delta m^2 = 16 \times 10^{-3}$ eV$^2$.

## $\sin^2(\theta_{13})$

At present time direct measurements of $\sin^2(\theta_{13})$ are derived from the reactor $\bar{\nu}_e$ disappearance at distances corresponding to the $\Delta m^2_{32}$ value, i.e. $L \sim 1$ km. Alternatively, limits can also be obtained from the analysis of the solar neutrino data and accelerator-based $\nu_{\mu} \to \nu_{e}$ experiments.

If an experiment reports $\sin^2(2\theta_{13})$ we convert the value to $\sin^2(\theta_{13})$.

<table><thead><tr><th>VALUE (units 10<sup>-2</sup>)</th><th>CL<sup>2</sup></th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td><strong>2.19 ± 0.07</strong></td><td><strong>OUR AVERAGE</strong></td><td></td><td></td><td>Error includes scale factor of 1.2.</td></tr><tr><td>2.80 ± 0.28</td><td></td><td>1 ABE</td><td>23F</td><td>Normal mass ordering</td></tr><tr><td>0.65</td><td></td><td></td><td></td><td></td></tr><tr><td>2.170 ± 0.063</td><td></td><td>2 AN</td><td>23</td><td>DAYA DayaBay, Ling Ao/Ao II reactors</td></tr><tr><td>2.70 ± 0.37</td><td></td><td>3 DE-KERRET</td><td>20</td><td>DCHZ Chooz reactors</td></tr><tr><td>2.22 ± 0.21 ± 0.37</td><td></td><td>4 SHIN</td><td>20</td><td>RENO Yonggwang reactors</td></tr><tr><td>2.29 ± 0.18</td><td></td><td>5 BAK</td><td>18</td><td>RENO Yonggwang reactors</td></tr><tr><td>1.81 ± 0.29</td><td></td><td>6 AN</td><td>16A</td><td>DAYA DayaBay, Ling Ao/Ao II reactors</td></tr></tbody></table>

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>3.10 ± 0.30</td><td></td><td>1 ABE</td><td>23F</td><td>T2K Inverted mass ordering</td></tr><tr><td>0.69</td><td></td><td></td><td></td><td></td></tr><tr><td>2.41 ± 0.45</td><td></td><td>7 ABRAHAO</td><td>21</td><td>DCHZ Chooz reactors</td></tr><tr><td>2.200 ± 0.069</td><td></td><td>8 SALAS</td><td>21</td><td>FIT Normal mass ordering, global fit</td></tr><tr><td>0.062</td><td></td><td></td><td></td><td></td></tr><tr><td>2.225 ± 0.064</td><td></td><td>8 SALAS</td><td>21</td><td>FIT Inverted mass ordering, global fit</td></tr><tr><td>0.070</td><td></td><td></td><td></td><td></td></tr><tr><td>2.219 ± 0.062</td><td></td><td>9 ESTEBAN</td><td>20A</td><td>FIT Normal mass ordering, global fit</td></tr><tr><td>0.063</td><td></td><td></td><td></td><td></td></tr><tr><td>2.238 ± 0.063</td><td></td><td>9 ESTEBAN</td><td>20A</td><td>FIT Inverted mass ordering, global fit</td></tr><tr><td>0.062</td><td></td><td></td><td></td><td></td></tr><tr><td>&lt; 3.9</td><td>68</td><td>AGAFONOVA</td><td>19</td><td>OPER</td></tr><tr><td>1.8 ± 2.9</td><td></td><td>10 ABE</td><td>18B</td><td>SKAM 3ν osc: normal mass ordering, θ<sub>13</sub> free</td></tr><tr><td>1.3</td><td></td><td></td><td></td><td></td></tr><tr><td>0.8 ± 1.7</td><td></td><td>10 ABE</td><td>18B</td><td>SKAM 3ν osc: inverted mass ordering, θ<sub>13</sub> free</td></tr><tr><td>0.7</td><td></td><td></td><td></td><td></td></tr><tr><td>2.188 ± 0.076</td><td></td><td>11 ADEY</td><td>18A</td><td>DAYA DayaBay, LingAo/Ao II reactors OPERA: ν<sub>e</sub> appearance</td></tr><tr><td>&lt; 12</td><td>90</td><td>12 AGAFONOVA</td><td>18A</td><td>OPER</td></tr><tr><td>2.160 ± 0.083</td><td></td><td>DE-SALAS</td><td>18</td><td>FIT Normal mass ordering, global fit</td></tr><tr><td>0.069</td><td></td><td></td><td></td><td></td></tr><tr><td>2.220 ± 0.074</td><td></td><td>DE-SALAS</td><td>18</td><td>FIT Inverted mass ordering, global fit</td></tr><tr><td>0.076</td><td></td><td></td><td></td><td></td></tr><tr><td>2.09 ± 0.23 ± 0.16</td><td></td><td>13 SEO</td><td>18</td><td>RENO Yonggwang reactors</td></tr><tr><td>0.7</td><td></td><td>14 ABE</td><td>17F</td><td>T2K Normal mass ordering, T2K only</td></tr><tr><td>2.149 ± 0.071 ± 0.050</td><td></td><td>15 AN</td><td>17A</td><td>DAYA DayaBay, LingAo/Ao II reactors</td></tr><tr><td>0.87</td><td></td><td></td><td></td><td></td></tr><tr><td>0.86</td><td></td><td>16 ABE</td><td>16B</td><td>DCHZ Chooz reactors</td></tr><tr><td>2.09 ± 0.23 ± 0.16</td><td></td><td>17 CHOI</td><td>16</td><td>RENO Yonggwang reactors</td></tr><tr><td>0.13</td><td></td><td>18 AN</td><td>15</td><td>DAYA DayaBay, Ling Ao/Ao II reactors</td></tr><tr><td>0.13</td><td></td><td></td><td></td><td></td></tr><tr><td>2.6 ± 1.2</td><td></td><td>19 ABE</td><td>14A</td><td>DCHZ Chooz reactors</td></tr><tr><td>1.1</td><td></td><td></td><td></td><td></td></tr><tr><td>3.0 ± 1.3</td><td></td><td>20 ABE</td><td>14C</td><td>T2K Inverted mass ordering</td></tr><tr><td>1.0</td><td></td><td></td><td></td><td></td></tr><tr><td>3.6 ± 1.0</td><td></td><td>20 ABE</td><td>14C</td><td>T2K Normal mass ordering</td></tr><tr><td>0.9</td><td></td><td></td><td></td><td></td></tr><tr><td>2.3 ± 0.9</td><td></td><td>21 ABE</td><td>14H</td><td>DCHZ Chooz reactors</td></tr><tr><td>0.8</td><td></td><td></td><td></td><td></td></tr><tr><td>2.3 ± 0.2</td><td></td><td>22 AN</td><td>14</td><td>DAYA DayaBay, Ling Ao/Ao II reactors</td></tr><tr><td>2.12 ± 0.47</td><td></td><td>23 AN</td><td>14B</td><td>DAYA DayaBay, Ling Ao/Ao II reactors</td></tr><tr><td>2.34 ± 0.20</td><td></td><td>24 FORERO</td><td>14</td><td>FIT Normal mass ordering</td></tr><tr><td>2.40 ± 0.19</td><td></td><td>24 FORERO</td><td>14</td><td>FIT Inverted mass ordering</td></tr><tr><td>2.18 ± 0.10</td><td></td><td>25 GONZALEZ...</td><td>14</td><td>FIT Normal mass ordering; global fit</td></tr><tr><td>2.19 ± 0.11</td><td></td><td>25 GONZALEZ...</td><td>14</td><td>FIT Inverted mass ordering; global fit</td></tr><tr><td>0.10</td><td></td><td></td><td></td><td></td></tr><tr><td>2.5 ± 0.9 ± 0.9</td><td></td><td>26 ABE</td><td>13C</td><td>DCHZ Chooz reactors</td></tr><tr><td>1.3</td><td></td><td></td><td></td><td></td></tr><tr><td>1.0</td><td></td><td>27 ABE</td><td>13E</td><td>T2K Normal mass ordering</td></tr><tr><td>2.8 ± 1.6</td><td></td><td>27 ABE</td><td>13E</td><td>T2K Inverted mass ordering</td></tr></tbody></table>

<table><tbody><tr><td>1.6</td><td>+ 1.3</td><td>28 ADAMSON</td><td>13A</td><td>MINS Normal mass ordering</td></tr><tr><td>0.9</td><td>-</td><td></td><td></td><td></td></tr><tr><td>3.0</td><td>+ 1.8</td><td>28 ADAMSON</td><td>13A</td><td>MINS Inverted mass ordering</td></tr><tr><td>1.6</td><td>-</td><td></td><td></td><td></td></tr><tr><td>&lt; 13</td><td></td><td>AGAFONOVA</td><td>13</td><td>OPER OPERA: 3ν</td></tr><tr><td>&lt; 3.6</td><td></td><td>29 AHARMIM</td><td>13</td><td>FIT global solar: 3ν</td></tr><tr><td>2.3</td><td>± 0.3</td><td>30 AN</td><td>13</td><td>DAYA DayaBay, Ling Ao/Ao II reactors</td></tr><tr><td>2.2</td><td>± 1.1</td><td>31 ABE</td><td>12</td><td>DCHZ Chooz reactors</td></tr><tr><td>2.8</td><td>± 0.8</td><td>32 ABE</td><td>12B</td><td>DCHZ Chooz reactors</td></tr><tr><td>2.9</td><td>± 0.3</td><td>33 AHN</td><td>12</td><td>RENO Yonggwang reactors</td></tr><tr><td>2.4</td><td>± 0.4</td><td>34 AN</td><td>12</td><td>DAYA DayaBay, Ling Ao/Ao II reactors</td></tr><tr><td>2.5</td><td>+ 1.8</td><td>35 ABE</td><td>11</td><td>FIT KamLAND + global solar</td></tr><tr><td>1.6</td><td>-</td><td></td><td></td><td></td></tr><tr><td>&lt; 6.1</td><td></td><td>36 ABE</td><td>11</td><td>FIT Global solar</td></tr><tr><td>1.3</td><td>to 5.6</td><td>37 ABE</td><td>11A</td><td>T2K Normal mass ordering</td></tr><tr><td>1.5</td><td>to 5.6</td><td>38 ABE</td><td>11A</td><td>T2K Inverted mass ordering</td></tr><tr><td>0.3</td><td>to 2.3</td><td>39 ADAMSON</td><td>11D</td><td>MINS Normal mass ordering</td></tr><tr><td>0.8</td><td>to 3.9</td><td>40 ADAMSON</td><td>11D</td><td>MINS Inverted mass ordering</td></tr><tr><td>8</td><td>± 3</td><td>41 FOGLI</td><td>11</td><td>FIT Global neutrino data</td></tr><tr><td>7.8</td><td>± 6.2</td><td>42 GANDO</td><td>11</td><td>FIT KamLAND + solar: 3ν</td></tr><tr><td>12.4</td><td>± 13.3</td><td>43 GANDO</td><td>11</td><td>FIT KamLAND: 3ν</td></tr><tr><td>3</td><td>+ 9</td><td>44 ADAMSON</td><td>10A</td><td>MINS Normal mass ordering</td></tr><tr><td>7</td><td>-</td><td></td><td></td><td></td></tr><tr><td>6</td><td>+14</td><td>45 ADAMSON</td><td>10A</td><td>MINS Inverted mass ordering</td></tr><tr><td>6</td><td>-</td><td></td><td></td><td></td></tr><tr><td>8</td><td>+ 8</td><td>46.47 AHARMIM</td><td>10</td><td>FIT KamLAND + global solar: 3ν</td></tr><tr><td>7</td><td>-</td><td></td><td></td><td></td></tr><tr><td>&lt; 30</td><td></td><td>46.48 AHARMIM</td><td>10</td><td>FIT global solar: 3ν</td></tr><tr><td>&lt; 15</td><td></td><td>49 WENDELL</td><td>10</td><td>SKAM 3ν osc.; normal mass ordering</td></tr><tr><td>&lt; 33</td><td></td><td>49 WENDELL</td><td>10</td><td>SKAM 3ν osc.; inverted mass ordering</td></tr><tr><td>11</td><td>+11</td><td>50 ADAMSON</td><td>09</td><td>MINS Normal mass ordering</td></tr><tr><td>8</td><td>-</td><td></td><td></td><td></td></tr><tr><td>18</td><td>+15</td><td>51 ADAMSON</td><td>09</td><td>MINS Inverted mass ordering</td></tr><tr><td>11</td><td>-</td><td></td><td></td><td></td></tr><tr><td>6</td><td>± 4</td><td>52 FOGLI</td><td>08</td><td>FIT Global neutrino data</td></tr><tr><td>8</td><td>± 7</td><td>53 FOGLI</td><td>08</td><td>FIT Solar + KamLAND data</td></tr><tr><td>5</td><td>± 5</td><td>54 FOGLI</td><td>08</td><td>FIT Atmospheric + LBL + CHOOZ</td></tr><tr><td>&lt; 36</td><td></td><td>55 YAMAMOTO</td><td>06</td><td>K2K Accelerator experiment</td></tr><tr><td>&lt; 48</td><td></td><td>56 AHN</td><td>04</td><td>K2K Accelerator experiment</td></tr><tr><td>&lt; 36</td><td></td><td>57 BOEHM</td><td>01</td><td>Palo Verde react.</td></tr><tr><td>&lt; 45</td><td></td><td>58 BOEHM</td><td>00</td><td>Palo Verde react.</td></tr><tr><td>&lt; 15</td><td></td><td>59 APOLLONIO</td><td>99</td><td>CHOZ Reactor Experiment</td></tr></tbody></table>

1 ABE 23F 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.

2 AN 23 reports results derived from the complete data set collected by the Daya-Bay experiment, corresponding to 3158 days of operation, resulting in $5.55 \times 10^6 \bar{\nu}_e$ candidate events. Solar oscillation parameters are fixed in the analysis to $\sin^2(\theta_{12}) = 0.307 \pm 0.013$, $\Delta m^2_{21} = (7.53 \pm 0.18) \times 10^{-5}$ eV$^2$ from PDG 20. Supersedes ADEY 18A.

3 DE-KERRET 20 uses 481 days of data from single detector operation and also 384 days of data with both near and far detectors operating. A rate and shape analysis is performed on combined neutron captures on H and Gd. Supersedes ABE 16B.

4 SHIN 20 uses the RENO detector and 1500 live days of data. The near (far) detector observed 567,690 (90,747) $\bar{\nu}_e$ candidate events with a delayed neutron capture on hydrogen. The extracted value of $\sin^2\theta_{13}$ is consistent with the previous analysis with neutron capture on Gd in BAK 18.

5 BAK 18 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. Supersedes SEO 18.

6 AN 16A uses data from the eight antineutrino detectors (404 days) and six antineutrino detectors (217 days) runs to determine the mixing parameter $\sin^2(2\theta_{13})$ using the neutron capture on H only. Supersedes AN 14B.

7 ABRAHAO 21 uses 865 days of data collected in both near and far detectors with at least one reactor in operation. The analysis is based on a background model independent approach, so called Reactor Rate Modulation, to determine the mixing angle $\theta_{13}$. Adding the background model reduces the uncertainty to 0.0041. Supersedes ABE 16B.

8 SALAS 21 reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference.

9 ESTEBAN 20A reports results of a global fit to neutrino oscillation data available at the time of the Neutrino2020 conference.

10 ABE 18B uses 328 kton-years of Super-Kamiokande I-IV atmospheric neutrino data to obtain this result. The fit is performed over the four parameters, $\Delta m^2_{32}$, $\sin^2\theta_{23}$, $\sin^2\theta_{13}$, and $\delta$, while the solar parameters are fixed to $\Delta m^2_{21} = (7.53 \pm 0.18) \times 10^{-5}$ eV$^2$ and $\sin^2\theta_{12} = 0.304 \pm 0.014$.

11 ADEY 18A reports results from analysis of 1958 days of data taking with the Daya-Bay experiment, with $3.9 \times 10^6 \bar{\nu}_e$ 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, $\sin^2(\theta_{12}) = 0.307^{+0.013}_{-0.012}$, $\Delta m^2_{21} = (7.53 \pm 0.18) \times 10^{-5}$ eV$^2$, from PDG 18. Supersedes AN 17A.

12 AGAFONOVA 18A reports $\sin^2(2\theta_{13}) < 0.43$ at 90% C.L. The result on the sterile neutrino search in the context of 3+1 model is also reported. A 90% C.L. upper limit on $\sin^2(2\theta_{\mu e}) = 0.021$ for $\Delta m^2_{41} \ge 0.1$ eV$^2$ is set.
¹³SEO 18 reports results of the RENO experiment using about 500 days of data, performing a rate and shape analysis. Compared to AHN 12, a significant reduction of the systematic uncertainties is reported. A 3% excess of events near 5 MeV of the prompt energy is observed. SEO 18 is a detailed description of the results published in CHOI 16, which it supersedes. Superseded by BAK 18.

¹⁴Using T2K data only. For inverted mass ordering, all values of $\theta_{13}$ are ruled out at 68% CL.

¹⁵AN 17A reports 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 Gd. A simultaneous fit to $\theta_{13}$ and $\Delta m^2_{ee}$ is performed. Superseded by ADEY 18A.

¹⁶ABE 16B uses 455.57 live days of data from a detector 1050 m away from two reactor cores of the Chooz nuclear power station, to determine the mixing parameter $\sin^2(2\theta_{13})$. This analysis uses 7.15 reactor-off days for constraining backgrounds. A rate and shape analysis is performed on combined neutron captures on H and Gd. Supersedes ABE 14H and ABE 13C.

¹⁷CHOI 16 reports results of the RENO experiment using about 500 days of data, performing a rate and shape analysis. Compared to AHN 12, a significant reduction of the systematic uncertainties is reported. A 3% excess of events near 5 MeV of the prompt energy is observed. Supersedes AHN 12.

¹⁸AN 15 uses all eight identical detectors, with four placed near the reactor cores and the remaining four at the far hall to determine the mixing angle $\theta_{13}$ using the $\bar{\tau}_e$ observed interaction rates with neutron capture on Gd and energy spectra. The result corresponds to the exposure of $6.9 \times 10^5$ GW$_{Ih}$-ton-days. Superseded by AN 17A.

¹⁹ABE 14A uses 467.9 live days of one detector, 1050 m away from two reactor cores of the Chooz nuclear power station, to determine the mixing parameter $\sin^2(2\theta_{13})$. The Bugey4 data (DECLAIS 94) is used to constrain the neutrino flux. The data set includes 7.24 reactor-off days. A "rate-modulation" analysis is performed. Supersedes ABE 12B.

²⁰ABE 14c result is for $\nu_e$ appearance and assumes $\Delta m^2_{32} = 2.4 \times 10^{-3} \text{ eV}^2, \sin^2(\theta_{23}) = 0.5$, and $\delta = 0$.

²¹ABE 14h uses 467.9 live days of one detector, 1050 m away from two reactor cores of the Chooz nuclear power station, to determine the mixing parameter $\sin^2(2\theta_{13})$. The Bugey4 data (DECLAIS 94) is used to constrain the neutrino flux. The data set includes 7.24 reactor-off days. A rate and shape analysis is performed. Superseded by ABE 16B.

²²AN 14 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 the mixing angle $\theta_{13}$ using the $\bar{\tau}_e$ observed interaction rates with neutron capture on Gd and energy spectra. Supersedes AN 13 and superseded by AN 15.

²³AN 14B uses six identical anti-neutrino detectors with flux-weighted baselines of ~500 m and ~1.6 km to six power reactors. This rate analysis uses a 217-day data set and neutron capture on protons (not Gd) only. $\Delta m^2_{31} = 2.32 \times 10^{-3} \text{ eV}^2$ is assumed. Superseded by AN 16A.

²⁴FORERO 14 performs a global fit to neutrino oscillations using solar, reactor, long-baseline accelerator, and atmospheric neutrino data.

²⁵GONZALEZ-GARCIA 14 result comes from a frequentist global fit. The corresponding Bayesian global fit to the same data results are reported in BERGSTROM 15 as $(2.18^{+0.10}_{-0.11}) \times 10^{-2} \text{ eV}^2$ for normal and $(2.19^{+0.12}_{-0.10}) \times 10^{-2} \text{ eV}^2$ for inverted mass ordering.

²⁶ABE 13c uses delayed neutron capture on hydrogen instead of on Gd used previously. The physical volume is thus three times larger. The fit is based on the rate and shape analysis as in ABE 12b. The Bugey4 data (DECLAIS 94) is used to constrain the neutrino flux. Superseded by ABE 16b.

²⁷ABE 13e assumes maximal $\theta_{23}$ mixing and CP phase $\delta = 0$.

²⁸ADAMSON 13A results obtained from $\nu_e$ appearance, assuming $\delta = 0$, and $\sin^2(2\theta_{23}) = 0.957$.

²⁹AHARMIM 13 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m^2_{32}$ fixed to $2.45 \times 10^{-3} \text{ eV}^2$, using global solar neutrino data. AHARMIM 13 global solar neutrino data include SNO's all-phases-combined analysis results on the total active ⁸B neutrino flux and energy-dependent $\nu_e$ survival probability parameters, measurements of CI (CLEVELAND 98), Ga (ABDURASHITOV 99 which contains combined analysis with GNO (ALTMANN 05 and Ph.D. thesis of F. Kaether)), and ⁷Be (BELLINI 11A) rates, and ⁸B solar-neutrino recoil electron measurements of SK-I (HOSAKA 06) zenith, SK-II (CRAVENS 08) and SK-III (ABE 11) day/night spectra, and Borexino (BELLINI 10A) spectra. AHARMIM 13 also reported a result combining global solar and KamLAND data, which is $\sin^2(2\theta_{13}) = (9.1^{+2.9}_{-3.1}) \times 10^{-2}$.

³⁰AN 13 uses six identical detectors, with three placed near the reactor cores (flux-weighted baselines of 498 and 555 m) and the remaining three at the far hall (at the flux averaged distance of 1628 m from all six reactor cores) to determine the $\bar{\tau}_e$ interaction rate ratios. Superseded by AN 14.

³¹ABE 12 determines the $\bar{\tau}_e$ interaction rate in a single detector, located 1050 m from the cores of two reactors. A rate and shape analysis is performed. The rate normalization is fixed by the results of the Bugey4 reactor experiment, thus avoiding any dependence on possible very short baseline oscillations. The value of $\Delta m^2_{31} = 2.4 \times 10^{-3} \text{ eV}^2$ is used in the analysis. Superseded by ABE 12b.

³²ABE 12b determines the neutrino mixing angle $\theta_{13}$ using a single detector, located 1050 m from the cores of two reactors. This result is based on a spectral shape and rate analysis. The Bugey4 data (DECLAIS 94) is used to constrain the neutrino flux. Superseded by ABE 14A.

³³AHN 12 uses two identical detectors, placed at flux weighted distances of 408.56 m and 1433.99 m from six reactor cores, to determine the mixing angle $\theta_{13}$. This rate-only analysis excludes the no-oscillation hypothesis at 4.9 standard deviations. The value of $\Delta m^2_{31} = (2.32^{+0.12}_{-0.08}) \times 10^{-3} \text{ eV}^2$ was assumed in the analysis. Superseded by CHOI 16.

³⁴AN 12 uses six identical detectors with three placed near the reactor cores (flux-weighted baselines of 470 m and 576 m) and the remaining three at the far hall (at the flux averaged

distance of 1648 m from all six reactor cores) to determine the mixing angle $\theta_{13}$ using the $\bar{\tau}_e$ observed interaction rate ratios. This rate-only analysis excludes the no-oscillation hypothesis at 5.2 standard deviations. The value of $\Delta m^2_{31} = (2.32^{+0.12}_{-0.08}) \times 10^{-3} \text{ eV}^2$ was assumed in the analysis. Superseded by AN 13.

³⁵ABE 11 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m^2_{32}$ fixed to $2.4 \times 10^{-3} \text{ eV}^2$, using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake, GALLEX/GNO, SAGE, and KamLAND data. This result implies an upper bound of $\sin^2(2\theta_{13} < 0.059$ (95% CL) or $\sin^2(2\theta_{13} < 0.22$ (95% CL). The normal neutrino mass ordering and CPT invariance are assumed.

³⁶ABE 11 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m^2_{32}$ fixed to $2.4 \times 10^{-3} \text{ eV}^2$, using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 08A), Homestake, and GALLEX/GNO data. The normal neutrino mass ordering is assumed.

³⁷The quoted limit is for $\Delta m^2_{32} = 2.4 \times 10^{-3} \text{ eV}^2, \theta_{23} = \pi/2, \delta = 0$, and the normal mass ordering. For other values of $\delta$, the 68% region spans from 0.03 to 0.25, and the 90% region from 0.02 to 0.32.

³⁸The quoted limit is for $\Delta m^2_{32} = 2.4 \times 10^{-3} \text{ eV}^2, \theta_{23} = \pi/2, \delta = 0$, and the inverted mass ordering. For other values of $\delta$, the 68% region spans from 0.04 to 0.30, and the 90% region from 0.02 to 0.39.

³⁹The quoted limit is for $\Delta m^2_{32} = 2.32 \times 10^{-3} \text{ eV}^2, \theta_{23} = \pi/2, \delta = 0$, and the normal mass ordering. For other values of $\delta$, the 68% region spans from 0.02 to 0.12, and the 90% region from 0 to 0.16.

⁴⁰The quoted limit is for $\Delta m^2_{32} = 2.32 \times 10^{-3} \text{ eV}^2, \theta_{23} = \pi/2, \delta = 0$, and the inverted mass ordering. For other values of $\delta$, the 68% region spans from 0.02 to 0.16, and the 90% region from 0 to 0.21.

⁴¹FOGLI 11 obtained this result from an analysis using the atmospheric, accelerator long baseline, CHOOZ, solar, and KamLAND data. Recently, MUELLER 11 suggested an average increase of about 3.5% in normalization of the reactor $\bar{\tau}_e$ fluxess, and using these fluxes, the fitted result becomes $0.10 \pm 0.03$.

⁴²GANDO 11 report $\sin^2\theta_{13} = 0.020 \pm 0.016$. This result was obtained with three-neutrino fit using the KamLAND + solar data.

⁴³GANDO 11 report $\sin^2\theta_{13} = 0.032 \pm 0.037$. This result was obtained with three-neutrino fit using the KamLAND data only.

⁴⁴This result corresponds to the limit of <0.12 at 90% CL for $\Delta m^2_{32} = 2.43 \times 10^{-3} \text{ eV}^2, \theta_{23} = \pi/2$, and $\delta = 0$. For other values of $\delta$, the 90% CL region spans from 0 to 0.16.

⁴⁵This result corresponds to the limit of <0.20 at 90% CL for $\Delta m^2_{32} = 2.43 \times 10^{-3} \text{ eV}^2, \theta_{23} = \pi/2$, and $\delta = 0$. For other values of $\delta$, the 90% CL region spans from 0 to 0.21.

⁴⁶AHARMIM 10 global solar neutrino data include SNO's low-energy-threshold analysis survival probability day/night curves, SNO Phase III integral rates (AHARMIM 08), CI (CLEVELAND 98), SAGE (ABDURASHITOV 99), Gallex/GNO (HAMPEL 99, ALT-MANN 05), Borexino (ARPESELLA 08A), SK-I zenith (HOSAKA 06), and SK-II day/night spectra (CRAVENS 08).

⁴⁷AHARMIM 10 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m^2_{31}$ fixed to $2.3 \times 10^{-3} \text{ eV}^2$, using global solar neutrino data and KamLAND data (ABE 08A). CPT invariance is assumed. This result implies an upper bound of $\sin^2(2\theta_{13} < 0.057$ (95% CL) or $\sin^2(2\theta_{13} < 0.22$ (95% CL)).

⁴⁸AHARMIM 10 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta m^2_{31}$ fixed to $2.3 \times 10^{-3} \text{ eV}^2$, using global solar neutrino data.

⁴⁹WENDELL 10 obtained this result by a three-neutrino oscillation analysis with one mass scale dominance ($\Delta m^2_{31} = 0$) using the Super-Kamiokande-I+II+III atmospheric neutrino data, and updates the HOSAKA 06A result.

⁵⁰The quoted limit is for $\Delta m^2_{32} = 2.43 \times 10^{-3} \text{ eV}^2, \theta_{23} = \pi/2$, and $\delta = 0$. For other values of $\delta$, the 68% CL region spans from 0.02 to 0.26.

⁵¹The quoted limit is for $\Delta m^2_{32} = 2.43 \times 10^{-3} \text{ eV}^2, \theta_{23} = \pi/2$, and $\delta = 0$. For other values of $\delta$, the 68% CL region spans from 0.04 to 0.34.

⁵²FOGLI 08 obtained this result from a global analysis of all neutrino oscillation data, that is, solar + KamLAND + atmospheric + accelerator long baseline + CHOOZ.

⁵³FOGLI 08 obtained this result from an analysis using the solar and KamLAND neutrino oscillation data.

⁵⁴FOGLI 08 obtained this result from an analysis using the atmospheric, accelerator long baseline, and CHOOZ neutrino oscillation data.

⁵⁵YAMAMOTO 6 search for $\nu_\mu \rightarrow \nu_e$ appearance. Assumes $2 \sin^2(2\theta_{\mu e}) = \sin^2(2\theta_{13})$. The quoted limit is for $\Delta m^2_{32} = 1.9 \times 10^{-3} \text{ eV}^2$. That value of $\Delta m^2_{32}$ is the one-$\sigma$ low value for AHN 06A. For the AHN 06A best fit value of $2.8 \times 10^{-3} \text{ eV}^2$, the $\sin^2(2\theta_{13})$ limit is < 0.26. Supersedes AHN 04.

⁵⁶AHN 04 searched for $\nu_\mu \rightarrow \nu_e$ appearance. Assuming $2 \sin^2(2 \theta_{\mu e}) = \sin^2(2 \theta_{13})$, a limit on $\sin^2(2 \theta_{\mu e})$ is converted to a limit on $\sin^2(2 \theta_{13})$. The quoted limit is for $\Delta m^2_{32} = 1.9 \times 10^{-3} \text{ eV}^2$. That value of $\Delta m^2_{32}$ is the one-$\sigma$ low value for ALIU 05. For the ALIU 05 best fit value of $2.8 \times 10^{-3} \text{ eV}^2$, the $\sin^2(2 \theta_{13})$ limit is < 0.30.

⁵⁷The quoted limit is for $\Delta m^2_{32} = 1.9 \times 10^{-3} \text{ eV}^2$. That value of $\Delta m^2_{32}$ is the 1-$\sigma$ low value for ALIU 05. For the ALIU 05 best fit value of $2.8 \times 10^{-3} \text{ eV}^2$, the $\sin^2(2 \theta_{13})$ limit is < 0.19. In this range, the $\theta_{13}$ limit is larger for lower values of $\Delta m^2_{32}$, and smaller for higher values of $\Delta m^2_{32}$.

⁵⁸The quoted limit is for $\Delta m^2_{32} = 1.9 \times 10^{-3} \text{ eV}^2$. That value of $\Delta m^2_{32}$ is the 1-$\sigma$ low value for ALIU 05. For the ALIU 05 best fit value of $2.8 \times 10^{-3} \text{ eV}^2$, the $\sin^2(2 \theta_{13})$ limit is < 0.23.

⁵⁹The quoted limit is for $\Delta m^2_{32} = 2.43 \times 10^{-3} \text{ eV}^2$. That value of $\Delta m^2_{32}$ is the central value for ADAMSON 08. For the ADAMSON 08 1-$\sigma$ low value of $2.30 \times 10^{-3} \text{ eV}^2$,
the $\sin^2\theta_{13}$ limit is < 0.16. See also APOLLONIO 03 for a detailed description of the experiment.

CP violating phase

Measurements of $\delta$ come from atmospheric and accelerator experiments looking at $\nu_e$ appearance. We encode values between 0 and $2\pi$, though it is equivalent to use $-\pi$ to $\pi$.

<table><thead><tr><th>VALUE (π rad)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td colspan="5"><strong>1.19±0.22 OUR AVERAGE</strong> Error includes scale factor of 1.2.</td></tr><tr><td>1.37<sup>+0.31</sup><sub>-0.20</sub></td><td>1 ABE</td><td>23F</td><td>T2K</td><td>Normal mass ordering, θ<sub>13</sub> constrained</td></tr><tr><td>0.82<sup>+0.27</sup><sub>-0.87</sub></td><td>2,3 ACERO</td><td>22</td><td>NOVA</td><td>Normal mass ordering, octant II for θ<sub>23</sub>, θ<sub>13</sub> constrained</td></tr><tr><td>1.33<sup>+0.45</sup><sub>-0.51</sub></td><td>4 ABE</td><td>18B</td><td>SKAM</td><td>Normal mass ordering, θ<sub>13</sub> constrained</td></tr><tr><td colspan="5">• • • We do not use the following data for averages, fits, limits, etc. • • •</td></tr><tr><td>1.52<sup>+0.30</sup><sub>-0.41</sub></td><td>2,5 ACERO</td><td>22</td><td>NOVA</td><td>Inverted mass ordering, octant II for θ<sub>23</sub>, θ<sub>13</sub> constrained</td></tr><tr><td>1.08<sup>+0.13</sup><sub>-0.12</sub></td><td>6 SALAS</td><td>21</td><td>FIT</td><td>Normal mass ordering, global fit</td></tr><tr><td>1.58<sup>+0.15</sup><sub>-0.16</sub></td><td>6 SALAS</td><td>21</td><td>FIT</td><td>Inverted mass ordering, global fit</td></tr><tr><td>1.40<sup>+0.22</sup><sub>-0.18</sub></td><td>7 ABE</td><td>20F</td><td>T2K</td><td>Normal mass ordering</td></tr><tr><td>1.09<sup>+0.15</sup><sub>-0.13</sub></td><td>8 ESTEBAN</td><td>20A</td><td>FIT</td><td>Normal mass ordering, global fit</td></tr><tr><td>1.57<sup>+0.14</sup><sub>-0.17</sub></td><td>8 ESTEBAN</td><td>20A</td><td>FIT</td><td>Inverted mass ordering, global fit</td></tr><tr><td>0.0<sup>+1.3</sup><sub>-0.4</sub></td><td>9 ACERO</td><td>19</td><td>NOVA</td><td>Normal mass ordering, octant II for θ<sub>23</sub></td></tr><tr><td>1.33<sup>+0.46</sup><sub>-0.53</sub></td><td>10 ABE</td><td>18B</td><td>SKAM</td><td>3ν osc: normal mass ordering, θ<sub>13</sub> free</td></tr><tr><td>1.22<sup>+0.76</sup><sub>-0.67</sub></td><td>10 ABE</td><td>18B</td><td>SKAM</td><td>3ν osc: inverted mass ordering, θ<sub>13</sub> free</td></tr><tr><td>1.33<sup>+0.48</sup><sub>-0.53</sub></td><td>4 ABE</td><td>18B</td><td>SKAM</td><td>3ν osc: inverted mass ordering, θ<sub>13</sub> constrained</td></tr><tr><td>1.40<sup>+0.20</sup></td><td>11 ABE</td><td>18G</td><td>T2K</td><td>Normal mass ordering, θ<sub>13</sub> constrained</td></tr><tr><td>1.54<sup>+0.14</sup><sub>-0.12</sub></td><td>11 ABE</td><td>18G</td><td>T2K</td><td>Inverted mass ordering, θ<sub>13</sub> constrained</td></tr><tr><td>1.21<sup>+0.91</sup><sub>-0.30</sub></td><td>12 ACERO</td><td>18</td><td>NOVA</td><td>Normal mass ordering, octant II for θ<sub>23</sub></td></tr><tr><td>1.46<sup>+0.56</sup><sub>-0.42</sub></td><td>12 ACERO</td><td>18</td><td>NOVA</td><td>Normal mass order; octant I for θ<sub>23</sub></td></tr><tr><td>1.32<sup>+0.21</sup><sub>-0.15</sub></td><td>DE-SALAS</td><td>18</td><td>FIT</td><td>Normal mass ordering, global fit</td></tr><tr><td>1.56<sup>+0.13</sup><sub>-0.15</sub></td><td>DE-SALAS</td><td>18</td><td>FIT</td><td>Inverted mass ordering, global fit</td></tr><tr><td>1.45<sup>+0.27</sup><sub>-0.26</sub></td><td>13 ABE</td><td>17F</td><td>T2K</td><td>Normal mass ordering</td></tr><tr><td>1.54<sup>+0.22</sup><sub>-0.23</sub></td><td>13 ABE</td><td>17F</td><td>T2K</td><td>Inverted mass ordering</td></tr><tr><td>1.50<sup>+0.53</sup><sub>-0.57</sub></td><td>14 ADAMSON</td><td>17B</td><td>NOVA</td><td>Inverted mass ordering; θ<sub>23</sub> in octant II</td></tr><tr><td>0.74<sup>+0.57</sup><sub>-0.93</sub></td><td>14 ADAMSON</td><td>17B</td><td>NOVA</td><td>Normal mass ordering; θ<sub>23</sub> in octant II</td></tr><tr><td>1.48<sup>+0.69</sup><sub>-0.58</sub></td><td>14 ADAMSON</td><td>17B</td><td>NOVA</td><td>Normal mass ordering; θ<sub>23</sub> in octant I</td></tr><tr><td>0.0 to 0.1, 0.5 to 2.0</td><td>14,15 ADAMSON</td><td>16</td><td>NOVA</td><td>Inverted mass ordering</td></tr><tr><td>0.0 to 2.0 to 90</td><td>15 ADAMSON</td><td>16</td><td>NOVA</td><td>Normal mass ordering</td></tr><tr><td>0 to 0.15, 0.83 to 2</td><td>ABE</td><td>15D</td><td>T2K</td><td>Normal mass ordering</td></tr><tr><td>1.09 to 1.92</td><td>ABE</td><td>15D</td><td>T2K</td><td>Inverted mass ordering</td></tr><tr><td>0.05 to 1.2</td><td>16 ADAMSON</td><td>14</td><td>MINS</td><td>Normal mass ordering</td></tr><tr><td>1.34<sup>+0.64</sup><sub>-0.38</sub></td><td>FORERO</td><td>14</td><td>FIT</td><td>Normal mass ordering</td></tr><tr><td>1.48<sup>+0.34</sup><sub>-0.32</sub></td><td>FORERO</td><td>14</td><td>FIT</td><td>Inverted mass ordering</td></tr><tr><td>1.70<sup>+0.22</sup><sub>-0.39</sub></td><td>17 GONZALEZ...</td><td>14</td><td>FIT</td><td>Normal mass ordering; global fit</td></tr><tr><td>1.41<sup>+0.35</sup><sub>-0.34</sub></td><td>17 GONZALEZ...</td><td>14</td><td>FIT</td><td>Inverted mass ordering; global fit</td></tr><tr><td>0 to 1.5 or 1.9 to 2</td><td>18 ADAMSON</td><td>13A</td><td>MINS</td><td>Normal mass ordering</td></tr></tbody></table>

(C) Other neutrino mixing results

The LSND collaboration reported in AGUILAR 01 a signal which is consistent with $\bar{\nu}_\mu \to \bar{\nu}_e$ oscillations. In a three neutrino framework, this would be a measurement of $\theta_{12}$ and $\Delta m^2_{21}$. This does not appear to be consistent with most of the other neutrino data. The following listings include results from $\nu_\mu \to \nu_e, \bar{\nu}_\mu \to \bar{\nu}_e$ appearance and $\nu_\mu, \bar{\nu}_\mu, \nu_e, \bar{\nu}_e$ disappearance experiments, and searches for CPT violation.

$$ \Delta(m^2) \text{ for } \sin^2(2\theta) = 1 \quad (\nu_\mu \to \nu_e) $$

<table><thead><tr><th>VALUE (eV<sup>2</sup>)</th><th>CL%</th><th>DOCUMENT ID</th><th>TECN</th><th>COMMENT</th></tr></thead><tbody><tr><td>0.03 to 0.55</td><td>90</td><td>1 AGUILAR-AR...21</td><td>MBNE MiniBooNE $\nu_e, \bar{\nu}_e$ combined</td><td></td></tr><tr><td>0.03 to 0.05</td><td>90</td><td>2 AGUILAR-AR...18c</td><td>MBNE MiniBooNE $\nu_e, \bar{\nu}_e$ combined</td><td></td></tr><tr><td>0.015 to 0.050</td><td>90</td><td>3 AGUILAR-AR...13a</td><td>MBNE MiniBooNE</td><td></td></tr><tr><td>&lt;0.34</td><td>90</td><td>4 MAHN</td><td>12 MBNE MiniBooNE/SciBooNE</td><td></td></tr><tr><td>&lt;0.034</td><td>90</td><td>AGUILAR-AR...07</td><td>MBNE MiniBooNE</td><td></td></tr><tr><td>&lt;0.0008</td><td>90</td><td>AHN</td><td>04 K2K Water Cherenkov</td><td></td></tr><tr><td>&lt;0.4</td><td>90</td><td>ASTIER</td><td>03 NOMD CERN SPS</td><td></td></tr><tr><td>&lt;2.4</td><td>90</td><td>AVVAKUMOV</td><td>02 NTEV NUTEV FNAL</td><td></td></tr><tr><td></td><td></td><td>5 AGUILAR</td><td>01 LSND $\nu_\mu \to \nu_e$ osc-prob.</td><td></td></tr><tr><td>0.03 to 0.3</td><td>95</td><td>6 ATHANASSO...98</td><td>LSND $\nu_\mu \to \nu_e$</td><td></td></tr><tr><td>&lt;2.3</td><td>90</td><td>7 LOVERRE</td><td>96 CHARM/CDHS</td><td></td></tr><tr><td>&lt;0.9</td><td>90</td><td>VILAIN</td><td>94C CHM2 CERN SPS</td><td></td></tr><tr><td>&lt;0.09</td><td>90</td><td>ANGELINI</td><td>86 HLBC BEBC CERN PS</td><td></td></tr></tbody></table>

<footnote n="1">1 ABE 23f 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. For inverted mass ordering, the quoted result is $1.54^{+0.18}_{-0.19} \pi$ rad. Supersedes ABE 20f.</footnote>

<footnote n="2">2 ACERO 22 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). Results for normal and inverted mass ordering, and $\theta_{23}$ octant I and II are presented. Supersedes ACERO 19.</footnote>

<footnote n="3">3 For the octant I (lower octant), the 68% CL allowed region is discontinuous, and all delta values are allowed at 90% CL.</footnote>

<footnote n="4">4 ABE 18b uses 328 kton-years of Super-Kamiokande I-IV atmospheric neutrino data to obtain this result. The fit is performed over the three parameters, $\Delta m^2_{32}$, $\sin^2\theta_{23}$, and</footnote>

<footnote>$\delta$, while the solar parameters and $\sin^2\theta_{23}$ are fixed to $\Delta m^2_{21} = (7.53 \pm 0.18) \times 10^{-5}$ eV$^2$, $\sin^2\theta_{12} = 0.304 \pm 0.014$, and $\sin^2\theta_{13} = 0.0219 \pm 0.0012$.</footnote>

<footnote n="5">5 The inverted mass ordering is rejected at $1.0 \sigma$. The quoted error bars are based on the local best-fit point.</footnote>

<footnote n="6">6 SALAS 21 reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference.</footnote>

<footnote n="7">7 ABE 20f 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. For inverted mass ordering, the quoted result is $1.56^{+0.15}_{-0.17} \pi$ rad. Supersedes ABE 18g.</footnote>

<footnote n="8">8 ESTEBAN 20a reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference.</footnote>

<footnote n="9">9 ACERO 19 is based on a sample size of $1.33 \times 10^{20}$ protons on target with combined antineutrino and neutrino data. Superseded by ACERO 22.</footnote>

<footnote n="10">10 ABE 18b uses 328 kton-years of Super-Kamiokande I-IV atmospheric neutrino data to obtain this result. The fit is performed over the four parameters, $\Delta m^2_{32}$, $\sin^2\theta_{23}$, $\sin^2\theta_{13}$, and $\delta$, while the solar parameters are fixed to $\Delta m^2_{21} = (7.53 \pm 0.18) \times 10^{-5}$ eV$^2$ and $\sin^2\theta_{12} = 0.304 \pm 0.014$.</footnote>

<footnote n="11">11 ABE 18g confidence intervals are marginalized over both mass orderings. Normal order preferred with a posterior probability of 87%. The 1-sigma result for normal mass ordering used in the average was provided by the experiment via private communications. Supersedes ABE 17f.</footnote>

<footnote n="12">12 ACERO 18 performs a joint fit to the data for $\nu_\mu$ disappearance and $\nu_e$ appearance. The overall best fit favors normal mass ordering and $\theta_{23}$ in octant II. No $1\sigma$ confidence intervals are presented for the inverted mass ordering scenarios. Superseded by ACERO 19.</footnote>

<footnote n="13">13 ABE 17f confidence intervals are obtained using a frequentist analysis including $\theta_{13}$ constraint from reactor experiments. Bayesian intervals based on Markov Chain Monte Carlo method are also provided by the authors. Superseded by ABE 18g.</footnote>

<footnote n="14">14 Errors are projections of 68% C.L. curve of $\delta_{CP}$ vs. $\sin^2\theta_{23}$.</footnote>

<footnote n="15">15 ADAMSON 16 result is based on a data sample with $2.74 \times 10^{20}$ protons on target. The likelihood-based analysis observed 6 $\nu_e$ events with an expected background of 0.99 ± 0.11 events.</footnote>

<footnote n="16">16 ADAMSON 14 result is based on three-flavor formalism and $\theta_{23} > \pi/4$. Likelihood as a function of $\delta$ is also shown for the other three combinations of hierarchy and $\theta_{23}$ octants; all values of $\delta$ are allowed at 90% C.L.</footnote>

<footnote n="17">17 GONZALEZ-GARCIA 14 result comes from a frequentist global fit. The corresponding Bayesian global fit to the same data results are reported in BERGSTROM 15 as 68% CL intervals of 1.24–1.94 for normal and 1.15–1.77 for inverted mass ordering.</footnote>

<footnote n="18">18 ADAMSON 13a result is based on $\nu_e$ appearance in MINOS and the calculated $\sin^2(2\theta_{23}) = 0.957, \theta_{23} > \pi/4$, and normal mass hierarchy. Likelihood as a function of $\delta$ is also shown for the other three combinations of hierarchy and $\theta_{23}$ octants; all values of $\delta$ are allowed at 90% C.L.</footnote>

<footnote n="1">1 AGUILAR-AREVALO 21 result is based on a total of $18.75 \times 10^{20}$ POT in neutrino mode, and $11.27 \times 10^{20}$ POT in anti-neutrino mode. Best fit at 0.043 eV$^2$. The allowed region does not extend to large $\Delta m^2$. The quoted value is the entire allowed region of $\Delta m^2$ at 90% C.L. for all values of $\sin^2(2\theta)$. Supersedes AGUILAR-AREVALO 18c.</footnote>

<footnote n="2">2 AGUILAR-AREVALO 18c result is based on $\nu_\mu \to \nu_e$ appearance of 460.5 ± 99.0 events; The best fit value is $\Delta m^2 = 0.041$ eV$^2$. Superseded by AGUILAR-AREVALO 21.</footnote>

<footnote n="3">3 AGUILAR-AREVALO 13a result is based on $\nu_\mu \to \nu_e$ appearance of $162.0 \pm 47.8$ events; marginally compatible with two-neutrino oscillations. The best fit value is $\Delta m^2 = 3.14$ eV$^2$.</footnote>

<footnote n="4">4 MAHN 12 is a combined spectral fit of MiniBooNE and SciBooNE neutrino data with the range of $\Delta m^2$ up to 25 eV$^2$. The best limit is 0.04 at 7 eV$^2$.</footnote>
5 AGUILAR 01 is the final analysis of the LSND full data set. Search is made for the $\nu_\mu \to \nu_e$ oscillations using $\nu_\mu$ from $\pi^+$ decay in flight by observing beam-on electron events from $\nu_e C \to e^-X$. Present analysis results in 8.1 $\pm$ 12.2 $\pm$ 1.7 excess events in the $60 < E_e < 200$ MeV energy range, corresponding to oscillation probability of 0.10 $\pm$ 0.16 $\pm$ 0.04%. This is consistent, though less significant, with the previous result of ATHANASSOPOULOS 98, which supersedes. The present analysis uses selection criteria developed for the decay at rest, and is less effective in removing the background above 60 MeV than ATHANASSOPOULOS 98.

6 ATHANASSOPOULOS 98 is a search for the $\nu_\mu \to \nu_e$ oscillations using $\nu_\mu$ from $\pi^+$ decay in flight. The 40 observed beam-on electron events are consistent with $\nu_e C \to e^-X$; the expected background is 21.9 $\pm$ 2.1. Authors interpret this excess as evidence for an oscillation signal corresponding to oscillations with probability (0.26 $\pm$ 0.10 $\pm$ 0.05)%. Although the significance is only 2.3 $\sigma$, this measurement is an important and consistent cross check of ATHANASSOPOULOS 96 who reported evidence for $\bar{\nu}_\mu \to \bar{\nu}_e$ oscillations from $\mu^+$ decay at rest. See also ATHANASSOPOULOS 98b.

7 LOVERRE 96 uses the charged-current to neutral-current ratio from the combined CHARM (ALLABY 86) and CDHS (ABRAMOWICZ 86) data from 1986.

$$ \sin^2(2\theta) \text{ for "Large" } \Delta(m^2) \quad (\nu_\mu \to \nu_e) $$

VALUE (units $10^{-3}$) CL% DOCUMENT ID TECN COMMENT

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>6 to 1000</td><td>90</td><td>1 AGUILAR-AR...21</td><td>MBNE MiniBooNE; ν + ν̄</td></tr><tr><td>&lt; 5</td><td>90</td><td>2 AGUILAR-AR...18c</td><td>MBNE MiniBooNE; ν + ν̄</td></tr><tr><td>&lt; 7.2</td><td>90</td><td>AGAFONOVA 13</td><td>OPER Δ(m<sup>2</sup>) &gt; 0.1 eV<sup>2</sup></td></tr><tr><td>0.8 to 3</td><td>90</td><td>3 AGUILAR-AR...13A</td><td>MBNE MiniBooNE</td></tr><tr><td>&lt; 11</td><td>90</td><td>4 ANTONELLO 13</td><td>ICAR ν<sub>μ</sub> → ν<sub>e</sub></td></tr><tr><td>&lt; 6.8</td><td>90</td><td>5 ANTONELLO 13A</td><td>ICAR ν<sub>μ</sub> → ν<sub>e</sub></td></tr><tr><td>&lt;100</td><td>90</td><td>6 MAHN</td><td>12 MBNE MiniBooNE/SciBooNE</td></tr><tr><td>&lt; 1.8</td><td>90</td><td>7 AGUILAR-AR...07</td><td>MBNE MiniBooNE</td></tr><tr><td>&lt;110</td><td>90</td><td>8 AHN</td><td>04 K2K Water Cherenkov</td></tr><tr><td>&lt; 1.4</td><td>90</td><td>ASTIER</td><td>03 NOMD CERN SPS</td></tr><tr><td>&lt; 1.6</td><td>90</td><td>AVVAKUMOV 02</td><td>NTEV NUTEV FNAL</td></tr><tr><td>0.5 to 30</td><td>95</td><td>9 AGUILAR 01</td><td>LSND ν<sub>μ</sub> → ν<sub>e</sub> osc-prob.</td></tr><tr><td>&lt; 3.0</td><td>90</td><td>10 ATHANASSO...98</td><td>LSND ν<sub>μ</sub> → ν<sub>e</sub></td></tr><tr><td>&lt; 9.4</td><td>90</td><td>11 LOVERRE 96</td><td>96 CHARM/CDHS</td></tr><tr><td>&lt; 5.6</td><td>90</td><td>12 VILAIN</td><td>94c CHM2 CERN SPS</td></tr><tr><td></td><td></td><td>12 VILAIN</td><td>94c CHM2 CERN SPS</td></tr></tbody></table>

1 AGUILAR-AREVALO 21 result is based on a total of $18.75 \times 10^{20}$ POT in neutrino mode, and $11.27 \times 10^{20}$ POT in anti-neutrino mode. The best fit value is $\sin^2(2\theta) = 0.807$. The allowed region does not extend to large $\Delta m^2$. The quoted value is the entire allowed region of $\sin^2(2\theta)$ at 90% C.L. for all values of $\Delta m^2$. Supersedes AGUILAR-AREVALO 18c.

2 AGUILAR-AREVALO 18c result is based on $\nu_\mu \to \nu_e$ appearance of $460.5 \pm 99.0$ events; The best fit value is $\sin^2(2\theta) = 0.92$. The quoted limit for the two-neutrino mixing angle $\theta$ is valid above $\Delta m^2 = 0.59$ eV$^2$. Supersedes by AGUILAR-AREVALO 21.

3 AGUILAR-AREVALO 13A result is based on $\nu_\mu \to \nu_e$ appearance of $162.0 \pm 47.8$ events; marginally compatible with two neutrino oscillations. The best fit value is $\sin^2(2\theta) = 0.002$.

4 ANTONELLO 13 use the ICARUS T600 detector at LNGS and ~ 20 GeV beam of $\nu_\mu$ from CERN 730 km away to search for an excess of $\nu_e$ events. Two events are found with 3.7 $\pm$ 0.6 expected from conventional sources. This result excludes some parts of the parameter space affected by LSND. Supersedes by ANTONELLO 13A.

5 Based on four events with a background of 6.4 $\pm$ 0.9 from conventional sources with an average energy of 20 GeV and 730 km from the source of $\nu_\mu$.

6 MAHN 12 is a combined fit of MiniBooNE and SciBooNE neutrino data.

7 The limit is $\sin^2 2\theta < 0.9 \times 10^{-3}$ at $\Delta m^2 = 2$ eV$^2$. That value of $\Delta m^2$ corresponds to the smallest mixing angle consistent with the reported signal from LSND in AGUILAR 01.

8 The limit becomes $\sin^2 2\theta < 0.15$ at $\Delta m^2 = 2.8 \times 10^{-3}$ eV$^2$, the bets-fit value of the $\nu_\mu$ disappearance analysis in K2K.

9 AGUILAR 01 is the final analysis of the LSND full data set of the search for the $\nu_\mu \to \nu_e$ oscillations. See footnote in preceding table for further details.

10 ATHANASSOPOULOS 98 report (0.26 $\pm$ 0.10 $\pm$ 0.05)% for the oscillation probability; the value of $\sin^2 2\theta$ for large $\Delta m^2$ is deduced from this probability. See footnote in preceding table for further details, and see the paper for a plot showing allowed regions. If effect is due to oscillation, it is most likely to be intermediate $\sin^2 2\theta$ and $\Delta m^2$. See also ATHANASSOPOULOS 98b.

11 LOVERRE 96 uses the charged-current to neutral-current ratio from the combined CHARM (ALLABY 86) and CDHS (ABRAMOWICZ 86) data from 1986.

12 VILAIN 94c limit derived by combining the $\nu_\mu$ and $\bar{\nu}_\mu$ data assuming CP conservation.

$$ \Delta(m^2) \text{ for } \sin^2(2\theta) = 1 \quad (\bar{\nu}_\mu \to \bar{\nu}_e) $$

VALUE (eV$^2$) CL% DOCUMENT ID TECN COMMENT

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>0.023 to 0.060</td><td>90</td><td>1 AGUILAR-AR...13A</td><td>MBNE MiniBooNE</td></tr><tr><td>&lt;0.16</td><td>90</td><td>2 CHENG 12</td><td>MBNE MiniBooNE/SciBooNE</td></tr><tr><td>0.03-0.09</td><td>90</td><td>3 AGUILAR-AR...10</td><td>MBNE E<sub>μ</sub> &gt; 475 MeV</td></tr><tr><td>0.03-0.07</td><td>90</td><td>4 AGUILAR-AR...10</td><td>MBNE E<sub>μ</sub> &gt; 200 MeV</td></tr><tr><td>&lt;0.06</td><td>90</td><td>AGUILAR-AR...09B</td><td>MBNE MiniBooNE</td></tr><tr><td>&lt;0.055</td><td>90</td><td>5 ARMBRUSTER02</td><td>KAR2 Liquid Sci. calor.</td></tr><tr><td>&lt;2.6</td><td>90</td><td>AVVAKUMOV 02</td><td>NTEV NUTEV FNAL</td></tr></tbody></table>

<table><tbody><tr><td>0.03-0.05</td><td></td><td>6 AGUILAR 01</td><td>LSND LAMPF</td></tr><tr><td>0.05-0.08</td><td>90</td><td>7 ATHANASSO...96</td><td>LSND LAMPF</td></tr><tr><td>0.048-0.090</td><td>80</td><td>8 ATHANASSO...95</td><td></td></tr><tr><td>&lt;0.07</td><td>90</td><td>9 HILL</td><td>95</td></tr><tr><td>&lt;0.9</td><td>90</td><td>VILAIN 94c</td><td>CHM2 CERN SPS</td></tr><tr><td>&lt;0.14</td><td>90</td><td>10 FREEDMAN 93</td><td>CNTR LAMPF</td></tr></tbody></table>

1 Based on $\bar{\nu}_\mu \to \bar{\nu}_e$ appearance of $78.4 \pm 28.5$ events. The best fit values are $\Delta m^2 = 0.043$ eV$^2$ and $\sin^2 2\theta = 0.88$.

2 CHENG 12 is a combined fit of MiniBooNE and SciBooNE antineutrino data.

3 This value is for a two neutrino oscillation analysis for excess antineutrino events with $E_\mu > 475$ MeV. The best fit is at 0.07. The allowed region is consistent with LSND reported by AGUILAR 01. Supersedes AGUILAR-AREVALO 09b.

4 This value is for a two neutrino oscillation analysis for excess antineutrino events with $E_\nu > 200$ MeV with subtraction of the expected 12 events low energy excess seen in the neutrino component of the beam. The best fit value is 0.007 for $\Delta(m^2) = 4.4$ eV$^2$.

5 ARMBRUSTER 02 is the final analysis of the KARMEN 2 data for 17.7 m distance from the ISIS stopped pion and muon neutrino source. It is a search for $\bar{\nu}_e$, detected by the inverse $\beta$-decay reaction on protons and $^{12}$C. 15 candidate events are observed, and 15.8 $\pm$ 0.5 background events are expected, hence no oscillation signal is detected. The results exclude large regions of the parameter area favored by the LSND experiment.

6 AGUILAR 01 is the final analysis of the LSND full data set. It is a search for $\bar{\nu}_e$ 30 m from LAMPF beam stop. Neutrinos originate mainly for $\pi^+$ decay at rest. $\bar{\nu}_e$ are detected through $\bar{\nu}_e p \to e^+ n$ ($20 < E^+ < 60$ MeV) in delayed coincidence with $np \to d\gamma$. Authors observe $87.9 \pm 22.4 \pm 6.0$ total excess events. The observation is attributed to $\bar{\nu}_\mu \to \bar{\nu}_e$ oscillations with the oscillation probability of $0.264 \pm 0.067 \pm 0.045\%$, consistent with the previously published result. Taking into account all constraints, the most favored allowed region of oscillation parameters is a band of $\Delta(m^2)$ from 0.2-2.0 eV$^2$. Supersedes ATHANASSOPOULOS 95, ATHANASSOPOULOS 96, and ATHANASSOPOULOS 98.

7 ATHANASSOPOULOS 96 is a search for $\bar{\nu}_e$ 30 m from LAMPF beam stop. Neutrinos originate mainly from $\pi^+$ decay at rest. $\bar{\nu}_e$ could come from either $\bar{\nu}_\mu \to \bar{\nu}_e$ or $\nu_e \to \bar{\nu}_e$; our entry assumes the first interpretation. They are detected through $\bar{\nu}_e p \to e^+ n$ (20 MeV $< E^+ < 60$ MeV) in delayed coincidence with $np \to d\gamma$. Authors observe $51 \pm 20 \pm 8$ total excess events over an estimated background $12.5 \pm 2.9$. ATHANASSOPOULOS 96b is a shorter version of this paper.

8 ATHANASSOPOULOS 95 error corresponds to the $1.6\sigma$ band in the plot. The expected background is $2.7 \pm 0.4$ events. Corresponds to an oscillation probability of $(0.34^{+0.20}_{-0.18} \pm 0.07)\%$. For a different interpretation, see HILL 95. Replaced by ATHANASSOPOULOS 96.

9 HILL 95 is a report by one member of the LSND Collaboration, reporting a different conclusion from the analysis of the data of this experiment (see ATHANASSOPOULOS 95). Contrary to the rest of the LSND Collaboration, Hill finds no evidence for the neutrino oscillation $\bar{\nu}_\mu \to \bar{\nu}_e$ and obtains only upper limits.

10 FREEDMAN 93 is a search at LAMPF for $\bar{\nu}_e$ generated from any of the three neutrino types $\nu_\mu$, $\bar{\nu}_\mu$, and $\nu_e$ which come from the beam stop. The $\bar{\nu}_e$'s would be detected by the reaction $\bar{\nu}_e p \to e^+ n$. FREEDMAN 93 replaces DURKIN 88.

$$ \sin^2(2\theta) \text{ for "Large" } \Delta(m^2) \quad (\bar{\nu}_\mu \to \bar{\nu}_e) $$

VALUE (units $10^{-3}$) CL% DOCUMENT ID TECN COMMENT

• • • We do not use the following data for averages, fits, limits, etc. • • •

<table><tbody><tr><td>&lt;640</td><td>90</td><td>1 ANTONELLO 13A</td><td>ICAR ν̄e appearance</td></tr><tr><td>&lt;150</td><td>90</td><td>2 CHENG 12</td><td>MBNE MiniBooNE/SciBooNE</td></tr><tr><td>0.4-9.0</td><td>99</td><td>3 AGUILAR-AR...10</td><td>MBNE E<sub>μ</sub> &gt; 475 MeV</td></tr><tr><td>0.4-9.0</td><td>99</td><td>4 AGUILAR-AR...10</td><td>MBNE E<sub>μ</sub> &gt; 200 MeV</td></tr><tr><td>&lt; 3.3</td><td>90</td><td>5 AGUILAR-AR...09B</td><td>MBNE MiniBooNE</td></tr><tr><td>&lt; 1.7</td><td>90</td><td>6 ARMBRUSTER02</td><td>KAR2 Liquid Sci. calor.</td></tr><tr><td>&lt; 1.1</td><td>90</td><td>AVVAKUMOV 02</td><td>NTEV NUTEV FNAL</td></tr><tr><td>5.3+1.3±9.0</td><td></td><td>7 AGUILAR 01</td><td>LSND LAMPF</td></tr><tr><td>6.2+2.4±1.0</td><td></td><td>8 ATHANASSO...96</td><td>LSND LAMPF</td></tr><tr><td>3-12</td><td>80</td><td>9 ATHANASSO...95</td><td></td></tr><tr><td>&lt; 6</td><td>90</td><td>10 HILL</td><td>95</td></tr></tbody></table>

1 ANTONELLO 13A obtained the limit by assuming $\bar{\nu}_\mu \to \bar{\nu}_e$ oscillation from the $\sim 2\%$ of $\bar{\nu}_\mu$ events contamination in the CNGS beam.

2 CHENG 12 is a combined fit of MiniBooNE and SciBooNE antineutrino data.

3 This value is for a two neutrino oscillation analysis for excess antineutrino events with $E_\mu > 475$ MeV. At 90% CL there is no solution at high $\Delta(m^2)$. The best fit is at maximal mixing. The allowed region is consistent with LSND reported by AGUILAR 01. Supersedes AGUILAR-AREVALO 09b.

4 This value is for a two neutrino oscillation analysis for excess antineutrino events with $E_\nu > 200$ MeV with subtraction of the expected 12 events low energy excess seen in the neutrino component of the beam. At 90% CL there is no solution at high $\Delta(m^2)$. The best fit value is 0.007 for $\Delta(m^2) = 4.4$ eV$^2$.

5 This result is inconclusive with respect to small amplitude mixing suggested by LSND.

6 ARMBRUSTER 02 is the final analysis of the KARMEN 2 data. See footnote in the preceding table for further details, and the paper for the exclusion plot.

7 AGUILAR 01 is the final analysis of the LSND full data set. The deduced oscillation probability is $0.264 \pm 0.067 \pm 0.045\%$; the value of $\sin^2 2\theta$ for large $\Delta(m^2)$ is twice this probability (although these values are excluded by other constraints). See footnote in preceding table for further details, and the paper for a plot showing allowed regions. Supersedes ATHANASSOPOULOS 95, ATHANASSOPOULOS 96, and ATHANASSOPOULOS 98.