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¹	ABREU 2025A report the observation of reactor anti-neutrino disappearance, using 286 ton$\cdot{}$yr of data collected by the SNO+ experiment. The result is based on an extended log likelihood fit to unbinned data performed on the prompt energy distribution.

ALLEGA 2025 use the reactor anti-neutrino signal collected during 125.4 days of data taking with the partially liquid scintillator filled SNO+ detector to determine $\Delta $m${}^{2}_{21}$ by means of a spectral fit. Because of the low signal strength of $9.53$ $\pm0.30$ inverse beta decay events, sin$^2({{\mathit \theta}_{{{12}}}})$ was fixed to the value given in PDG 2020.

ABE 2024B obtained this result by a three-neutrino oscillation analysis, with a constraint of sin$^2({{\mathit \theta}_{{{13}}}})$ = $0.0218$ $\pm0.0007$ coming from reactor neutrino experiments, using all solar and KamLAND data. The result includes the full Super-Kamiokande I to IV data. $\mathit CPT$ invariance is assumed. Supersedes ABE 2016C.

⁴	ABREU 2025A combine results from a spectral fit to 286 ton$\cdot{}$yr of SNO+ with SK solar neutrinos to obtain an improved measurement of the mass difference. $\mathit CPT$ invariance is assumed.

⁵

ABE 2024B obtained this result by a three-neutrino oscillation analysis, with a constraint of sin$^2({{\mathit \theta}_{{{13}}}})$ = $0.0218$ $\pm0.0007$ coming from reactor neutrino experiments and a constraint on ${}^{8}\mathrm {B}$(hep) flux based on the SNO neutral current event rate, using the full Super-Kamiokande I to IV data. Supersedes ABE 2016C.

⁶	ABE 2024B obtained this result by a three-neutrino oscillation analysis, with a constraint of sin$^2({{\mathit \theta}_{{{13}}}})$ = $0.0218$ $\pm0.0007$ coming from reactor neutrino experiments, using SNO and full Super-Kamiokande I to IV data. Supersedes ABE 2016C.

⁷

ABE 2024B obtained this result by a three-neutrino oscillation analysis, with a constraint of sin$^2({{\mathit \theta}_{{{13}}}})$ = $0.0218$ $\pm0.0007$ coming from reactor neutrino experiments and a constraint on ${}^{8}\mathrm {B}$(hep) flux based on the SNO neutral current event rate, using the full Super-Kamiokande IV data. Supersedes ABE 2016C.

⁸	SALAS 2021 reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference.

⁹	ESTEBAN 2020A reports results of a global fit to neutrino oscillation data available at the time of the Neutrino2020 conference.

¹⁰	ABE 2016C obtained this result by a three-neutrino oscillation analysis, with a constraint of sin$^2({{\mathit \theta}_{{{13}}}})$ = $0.0219$ $\pm0.0014$ coming from reactor neutrino experiments, using all solar data and KamLAND data. $\mathit CPT$ invariance is assumed.

¹¹	ABE 2016C obtained this result by a three-neutrino oscillation analysis, with a constraint of sin$^2({{\mathit \theta}_{{{13}}}})$ = $0.0219$ $\pm0.0014$ coming from reactor neutrino experiments, using Super-Kamiokande (I+II+III+IV) and SNO data. Superseded by ABE 2024B.

¹²	ABE 2016C obtained this result by a three-neutrino oscillation analysis, with a constraint of sin$^2({{\mathit \theta}_{{{13}}}})$ = $0.0219$ $\pm0.0014$ coming from reactor neutrino experiments, by combining the four phases of the Super-Kamiokande solar data. Superseded by ABE 2024B.

¹³	ABE 2016C obtained this result by a three-neutrino oscillation analysis, with a constraint of sin$^2({{\mathit \theta}_{{{13}}}})$ = $0.0219$ $\pm0.0014$ coming from reactor neutrino experiments, using the Super-Kamiokande-IV data.

¹⁴	FORERO 2014 performs a global fit to $\Delta $m${}^{2}_{21}$ using solar, reactor, long-baseline accelerator, and atmospheric neutrino data.

¹⁵

GONZALEZ-GARCIA 2014 result comes from a frequentist global fit. The corresponding Bayesian global fit to the same data results are reported in BERGSTROM 2015 as ($7.50$ ${}^{+0.19}_{-0.17}$) $ \times 10^{-5}$ eV${}^{2}$ for normal and ($7.50$ ${}^{+0.18}_{-0.17}$) $ \times 10^{-5}$ eV${}^{2}$ for inverted mass ordering.

¹⁶	AHARMIM 2013 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data.

¹⁷

AHARMIM 2013 global solar neutrino data include SNO's all-phases-combined analysis results on the total active ${}^{8}\mathrm {B}$ neutrino flux and energy-dependent ${{\mathit \nu}_{{{e}}}}$ survival probability parameters, measurements of ${}^{}\mathrm {Cl}$ (CLEVELAND 1998), ${}^{}\mathrm {Ga}$ (ABDURASHITOV 2009 which contains combined analysis with GNO (ALTMANN 2005 and Ph.D. thesis of F. Kaether)), and ${}^{7}\mathrm {Be}$ (BELLINI 2011A) rates, and ${}^{8}\mathrm {B}$ solar-neutrino recoil electron measurements of SK-I (HOSAKA 2006) zenith, SK-II (CRAVENS 2008), and SK-III (ABE 2011) day/night spectra, and Borexino (BELLINI 2010A) spectra.

¹⁸	AHARMIM 2013 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$ fixed to $2.45 \times 10^{-3}$ eV${}^{2}$, using global solar neutrino data.

¹⁹	AHARMIM 2013 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$ fixed to $2.45 \times 10^{-3}$ eV${}^{2}$, using global solar neutrino and KamLAND data (GANDO 2011). CPT invariance is assumed.

²⁰	GANDO 2013 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 2011.

²¹	GANDO 2013 obtained this result by a three-neutrino oscillation analysis using KamLAND and global solar neutrino data, assuming CPT invariance. Supersedes GANDO 2011.

²²	GANDO 2013 obtained this result by a three-neutrino oscillation analysis using KamLAND data. Supersedes GANDO 2011.

²³	ABE 2011 obtained this result by a two-neutrino oscillation analysis using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 2008A), Homestake, GALLEX/GNO, SAGE, and KamLAND data. CPT invariance is assumed.

²⁴	ABE 2011 obtained this result by a two-neutrino oscillation analysis using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 2008A), Homestake, GALLEX/GNO, and SAGE data.

²⁵

ABE 2011 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ fixed to $2.4 \times 10^{-3}$ eV${}^{2}$, using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 2008A), Homestake, GALLEX/GNO, SAGE, and KamLAND data. The normal neutrino mass ordering and CPT invariance are assumed.

²⁶

ABE 2011 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ fixed to $2.4 \times 10^{-3}$ eV${}^{2}$, using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 2008A), Homestake, and GALLEX/GNO data. The normal neutrino mass ordering is assumed.

²⁷

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

²⁸

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

²⁹	GANDO 2011 obtain this result with three-neutrino fit using the KamLAND + solar data. Superseded by GANDO 2013.

³⁰	GANDO 2011 obtain this result with three-neutrino fit using the KamLAND data only. Supersedes ABE 2008A.

³¹

AHARMIM 2010 global solar neutrino data include SNO's low-energy-threshold analysis survival probability day/night curves, SNO Phase III integral rates (AHARMIM 2008), Cl (CLEVELAND 1998), SAGE (ABDURASHITOV 2009), Gallex/GNO (HAMPEL 1999, ALTMANN 2005), Borexino (ARPESELLA 2008A), SK-I zenith (HOSAKA 2006), and SK-II day/night spectra (CRAVENS 2008).

³²	AHARMIM 2010 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data and KamLAND data (ABE 2008A). $\mathit CPT$ invariance is assumed.

³³	AHARMIM 2010 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data.

³⁴	AHARMIM 2010 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{{{\mathit 31}}}$ fixed to $2.3 \times 10^{-3}$ eV${}^{2}$, using global solar neutrino data and KamLAND data (ABE 2008A). $\mathit CPT$ invariance is assumed.

³⁵	AHARMIM 2010 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{{{\mathit 31}}}$ fixed to $2.3 \times 10^{-3}$ eV${}^{2}$, using global solar neutrino data.

³⁶	ABE 2008A obtained this result by a rate + shape + time combined geoneutrino and reactor two-neutrino fit for $\Delta {{\mathit m}^{2}}_{{{\mathit 21}}}$ and tan$^2\theta _{12}$, using KamLAND data only. Superseded by GANDO 2011.

³⁷	ABE 2008A 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. $\mathit CPT$ invariance is assumed. Superseded by GANDO 2011.

³⁸	AHARMIM 2008 obtained this result by a two-neutrino oscillation analysis using all solar neutrino data including those of Borexino (ARPESELLA 2008A) and Super-Kamiokande-I (HOSAKA 2006), and KamLAND data (ABE 2008A). $\mathit CPT$ invariance is assumed.

³⁹	HOSAKA 2006 obtained this result by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (ARAKI 2005). $\mathit CPT$ invariance is assumed.

⁴⁰	HOSAKA 2006 obtained this result by a two-neutrino oscillation analysis using the data from Super-Kamiokande, SNO (AHMAD 2002 and AHMAD 2002B), and KamLAND (ARAKI 2005) experiments. $\mathit CPT$ invariance is assumed.

⁴¹	HOSAKA 2006 obtained this result by a two-neutrino oscillation analysis using the Super-Kamiokande and SNO (AHMAD 2002 and AHMAD 2002B) solar neutrino data.

⁴²

HOSAKA 2006 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.

⁴³

AHARMIM 2005A obtained this result by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (ARAKI 2005). $\mathit CPT$ invariance is assumed. AHARMIM 2005A also quotes $\Delta \mathit m{}^{2}$ = ($8.0$ ${}^{+0.6}_{-0.4}$) $ \times 10^{-5}$ eV${}^{2}$ as the error enveloping the 68$\%$ CL two-dimensional region.

⁴⁴

AHARMIM 2005A 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 2005A. AHARMIM 2005A also quotes $\Delta \mathit m{}^{2}$ = ($6.5$ ${}^{+4.4}_{-2.3}$) $ \times 10^{-5}$ eV${}^{2}$ as the error enveloping the 68$\%$ CL two-dimensional region.

⁴⁵

ARAKI 2005 obtained this result by a two-neutrino oscillation analysis using KamLAND and solar neutrino data. $\mathit CPT$ invariance is assumed. The 1$\sigma $ error shown here is provided by the KamLAND collaboration. The error quoted in ARAKI 2005, $\Delta \mathit m{}^{2}$ = ($7.9$ ${}^{+0.6}_{-0.5}$) $ \times 10^{-5}$, envelops the 68$\%$ CL two-dimensional region.

⁴⁶

AHMED 2004A obtained this result by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (EGUCHI 2003). $\mathit CPT$ invariance is assumed. AHMED 2004A also quotes $\Delta \mathit m{}^{2}$ = ($7.1$ ${}^{+1.2}_{-0.6}$) $ \times 10^{-5}$ eV${}^{2}$ as the error enveloping the 68$\%$ CL two-dimensional region.

⁴⁷

AHMED 2004A 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 2004A. The best-fit point is $\Delta \mathit m{}^{2}$ = $6.5 \times 10^{-5}$ eV${}^{2}$, tan$^2\theta $ = $0.40$ (sin$^22 \theta $ = $0.82$).

⁴⁸	SMY 2004 obtained this result by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (IANNI 2003). $\mathit CPT$ invariance is assumed.

⁴⁹	SMY 2004 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 2004.

⁵⁰	SMY 2004 obtained this result by a two-neutrino oscillation analysis using the Super-Kamiokande and SNO (AHMAD 2002 and AHMAD 2002B) solar neutrino data. The 1$\sigma $ errors are read from Fig. 6(a) of SMY 2004.

⁵¹

AHMAD 2002B 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 2002B. The best fit point is $\Delta \mathit m{}^{2}$ = $5.0 \times 10^{-5}$ eV${}^{2}$ and tan $\theta $ = $0.34$ (sin$^22 \theta $ = 0.76).

⁵²

FUKUDA 2002 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 2002. The best fit point is $\Delta \mathit m{}^{2}$ = $6.9 \times 10^{-5}$ eV${}^{2}$ and tan$^2\theta $ = $0.38$ (sin$^22 \theta $ = 0.80).

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Except where otherwise noted, content of the 2025 Review of Particle Physics is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license. The publication of the Review of Particle Physics is supported by US DOE, MEXT and KEK (Japan), INFN (Italy) and CERN. Individual collaborators receive support for their PDG activities from their respective institutes or funding agencies. © 2025. See LBNL disclaimers.

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