(B) Three-neutrino mixing parameters

sin$^2(\theta _{12})$

INSPIRE   PDGID:
S067P12
If an experiment reports sin$^2(2~\theta _{12})$ we convert the value to sin$^2(~\theta _{12})$.
VALUE DOCUMENT ID TECN  COMMENT
$0.307$ ${}^{+0.013}_{-0.012}$ 1
ABE
2016C
 FIT KamLAND+global solar; 3${{\mathit \nu}}$
• • We do not use the following data for averages, fits, limits, etc. • •
$0.318$ $\pm0.016$ 2
SALAS
2021
FIT global fit
$0.304$ $\pm0.012$ 3
ESTEBAN
2020A
 FIT Global fit
$0.320$ ${}^{+0.020}_{-0.016}$
DE-SALAS
2018
FIT Global fit
$0.310$ $\pm0.014$ 4
ABE
2016C
 FIT SKAM+SNO; 3${{\mathit \nu}}$
$0.334$ ${}^{+0.027}_{-0.023}$ 5
ABE
2016C
 FIT SK-I+II+III+IV; 3${{\mathit \nu}}$
$0.327$ ${}^{+0.026}_{-0.031}$ 6
ABE
2016C
 FIT SK-IV; 3${{\mathit \nu}}$
$0.323$ $\pm0.016$ 7
FORERO
2014
FIT 3${{\mathit \nu}}$
$0.304$ ${}^{+0.013}_{-0.012}$ 8
GONZALEZ-GARC..
2014
FIT Either mass ordering; global fit
$0.299$ ${}^{+0.014}_{-0.014}$ 9, 10
AHARMIM
2013
FIT global solar: 2${{\mathit \nu}}$
$0.307$ ${}^{+0.016}_{-0.013}$ 11, 10
AHARMIM
2013
FIT global solar: 3${{\mathit \nu}}$
$0.304$ ${}^{+0.022}_{-0.018}$ 12, 10
AHARMIM
2013
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$0.304$ ${}^{+0.014}_{-0.013}$ 13
GANDO
2013
FIT KamLAND + global solar + SBL + accelerator: 3${{\mathit \nu}}$
$0.304$ ${}^{+0.014}_{-0.013}$ 14
GANDO
2013
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$0.325$ ${}^{+0.039}_{-0.039}$ 15
GANDO
2013
FIT KamLAND: 3${{\mathit \nu}}$
$0.30$ ${}^{+0.02}_{-0.01}$ 16
ABE
2011
FIT KamLAND + global solar: 2${{\mathit \nu}}$
$0.30$ ${}^{+0.02}_{-0.01}$ 17
ABE
2011
FIT global solar: 2${{\mathit \nu}}$
$0.31$ ${}^{+0.03}_{-0.02}$ 18
ABE
2011
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$0.31$ ${}^{+0.03}_{-0.03}$ 19
ABE
2011
FIT global solar: 3${{\mathit \nu}}$
$0.314$ ${}^{+0.015}_{-0.012}$ 20
BELLINI
2011A
 FIT KamLAND + global solar: 2${{\mathit \nu}}$
$0.319$ ${}^{+0.017}_{-0.015}$ 21
BELLINI
2011A
 FIT global solar: 2${{\mathit \nu}}$
$0.311$ ${}^{+0.016}_{-0.016}$ 22
GANDO
2011
FIT KamLAND + solar: 3${{\mathit \nu}}$
$0.304$ ${}^{+0.046}_{-0.042}$ 23
GANDO
2011
FIT KamLAND: 3${{\mathit \nu}}$
$0.314$ ${}^{+0.018}_{-0.014}$ 24, 25
AHARMIM
2010
FIT KamLAND + global solar: 2${{\mathit \nu}}$
$0.314$ ${}^{+0.017}_{-0.020}$ 24, 26
AHARMIM
2010
FIT global solar: 2${{\mathit \nu}}$
$0.319$ ${}^{+0.019}_{-0.016}$ 24, 27
AHARMIM
2010
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$0.319$ ${}^{+0.023}_{-0.024}$ 24, 28
AHARMIM
2010
FIT global solar: 3${{\mathit \nu}}$
$0.36$ ${}^{+0.05}_{-0.04}$ 29
ABE
2008A
 FIT KamLAND
$0.32$ $\pm0.03$ 30
ABE
2008A
 FIT KamLAND + global fit
$0.32$ $\pm0.02$ 31
AHARMIM
2008
FIT KamLAND + global solar
$0.31$ ${}^{+0.04}_{-0.04}$ 32
HOSAKA
2006
FIT KamLAND + global solar
$0.31$ ${}^{+0.04}_{-0.03}$ 33
HOSAKA
2006
FIT SKAM+SNO+KamLAND
$0.31$ ${}^{+0.03}_{-0.04}$ 34
HOSAKA
2006
FIT SKAM+SNO
$0.31$ ${}^{+0.02}_{-0.03}$ 35
AHARMIM
2005A
 FIT KamLAND + global solar
$\text{0.25 - 0.39}$ 36
AHARMIM
2005A
 FIT global solar
$0.29$ $\pm0.03$ 37
ARAKI
2005
FIT KamLAND + global solar
$0.29$ ${}^{+0.03}_{-0.02}$ 38
AHMED
2004A
 FIT KamLAND + global solar
$\text{0.23 - 0.37}$ 39
AHMED
2004A
 FIT global solar
$0.31$ ${}^{+0.04}_{-0.04}$ 40
SMY
2004
FIT KamLAND + global solar
$0.29$ ${}^{+0.04}_{-0.04}$ 41
SMY
2004
FIT global solar
$0.32$ ${}^{+0.06}_{-0.05}$ 42
SMY
2004
FIT SKAM + SNO
$\text{0.19 - 0.33}$ 43
AHMAD
2002B
 FIT global solar
$\text{0.19 - 0.39}$ 44
FUKUDA
2002
FIT global solar
1  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.
2  SALAS 2021 reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference.
3  ESTEBAN 2020A reports results of a global fit to neutrino oscillation data available at the time of the Neutrino2020 conference.
4  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.
5  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.
6  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.
7  FORERO 2014 performs a global fit to neutrino oscillations using solar, reactor, long-baseline accelerator, and atmospheric neutrino data.
8  GONZALEZ-GARCIA 2014 result comes from a frequentist global fit. The corresponding Bayesian global fit to the same data results are reported in BERGSTROM 2015 as $0.304$ ${}^{+0.013}_{-0.012}$ for normal and $0.305$ ${}^{+0.012}_{-0.013}$ for inverted mass ordering.
9  AHARMIM 2013 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data.
10  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.
11  AHARMIM 2013 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ fixed to $2.45 \times 10^{-3}$ eV${}^{2}$, using global solar neutrino data.
12  AHARMIM 2013 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ fixed to $2.45 \times 10^{-3}$ eV${}^{2}$, using global solar neutrino and KamLAND (GANDO 2011 ) data. CPT invariance is assumed.
13  GANDO 2013 obtained this result by a three-neutrino oscillation analysis using KamLAND, global solar neutrino, short-baseline (SBL) reactor, and accelerator data, assuming $\mathit CPT$ invariance. Supersedes GANDO 2011 .
14  GANDO 2013 obtained this result by a three-neutrino oscillation analysis using KamLAND and global solar neutrino data, assuming CPT invariance. Supersedes GANDO 2011 .
15  GANDO 2013 obtained this result by a three-neutrino oscillation analysis using KamLAND data. Supersedes GANDO 2011 .
16  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.
17  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.
18  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.
19  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.
20  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.
21  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.
22  GANDO 2011 obtain this result with three-neutrino fit using the KamLAND + solar data. Superseded by GANDO 2013 .
23  GANDO 2011 obtain this result with three-neutrino fit using the KamLAND data only. Superseded by GANDO 2013 .
24  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 ).
25  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.
26  AHARMIM 2010 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data.
27  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.
28  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.
29  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 .
30  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 .
31  The result given by AHARMIM 2008 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 2008A) and Super-Kamiokande-I (HOSAKA 2006 ), and KamLAND data (ABE 2008A). $\mathit CPT$ invariance is assumed.
32  HOSAKA 2006 obtained this result by a two-neutrino oscillation analysis using SK ${{\mathit \nu}_{{{e}}}}$ data, CC data from other solar neutrino experiments, and KamLAND data (ARAKI 2005 ). $\mathit CPT$ invariance is assumed.
33  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.
34  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.
35  The result given by AHARMIM 2005A is $\theta $ = ($33.9$ $\pm1.6)^\circ{}$. This result is obtained by a two-neutrino oscillation analysis using SNO pure deuteron and salt phase data, SK ${{\mathit \nu}_{{{e}}}}$ data, ${}^{}\mathrm {Cl}$ and ${}^{}\mathrm {Ga}$ CC data, and KamLAND data (ARAKI 2005 ). $\mathit CPT$ invariance is assumed. AHARMIM 2005A also quotes $\theta $ = ($33.9$ ${}^{+2.4}_{-2.2})^\circ{}$ as the error enveloping the 68$\%$ CL two-dimensional region. This translates into sin$^22 \theta $ = $0.86$ ${}^{+0.05}_{-0.06}$.
36  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 tan $^2\theta $ = $0.45$ ${}^{+0.09}_{-0.08}$ as the error enveloping the 68$\%$ CL two-dimensional region. This translates into sin$^22 \theta $ = $0.86$ ${}^{+0.05}_{-0.07}$.
37  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 translated from the number provided by the KamLAND collaboration, tan $^2\theta $ = $0.40$ ${}^{+0.07}_{-0.05}$. The corresponding number quoted in ARAKI 2005 is tan $^2\theta $ = $0.40$ ${}^{+0.10}_{-0.07}$ (sin$^22 \theta $ = $0.82$ $\pm0.07$), which envelops the 68$\%$ CL two-dimensional region.
38  The result given by AHMED 2004A 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 2003 ). $\mathit CPT$ invariance is assumed. AHMED 2004A also quotes $\theta $ = ($32.5$ ${}^{+2.4}_{-2.3})^\circ{}$ as the error enveloping the 68$\%$ CL two-dimensional region. This translates into sin$^22 \theta $ = $0.82$ $\pm0.06$.
39  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 $ = $0.82$).
40  The result given by SMY 2004 is tan $^2\theta $ = $0.44$ $\pm0.08$. This result is obtained by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (IANNI 2003 ). $\mathit CPT$ invariance is assumed.
41  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 .
42  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 .
43  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).
44  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).
Conservation Laws:
LEPTON FAMILY NUMBER
References:
SALAS 2021
JHEP 2102 071 2020 global reassessment of the neutrino oscillation picture
ESTEBAN 2020A
JHEP 2009 178 The fate of hints: updated global analysis of three-flavor neutrino oscillations
DE-SALAS 2018
PL B782 633 Status of neutrino oscillations 2018: 3$\sigma$ hint for normal mass ordering and improved CP sensitivity
ABE 2016C
PR D94 052010 Solar Neutrino Measurements in Super-Kamiokande-IV
FORERO 2014
PR D90 093006 Neutrino Oscillations Refitted
GONZALEZ-GARCIA 2014
JHEP 1411 052 Updated Fit to Three Neutrino Mixing: Status of Leptonic $\mathit CP$ Violation
AHARMIM 2013
PR C88 025501 Combined Analysis of all Three Phases of Solar Neutrino Data from the Sudbury Neutrino Observatory
GANDO 2013
PR D88 033001 Reactor On-Off Antineutrino Measurement with KamLAND
ABE 2011
PR D83 052010 Solar Neutrino Results in Super-Kamiokande-III
BELLINI 2011A
PRL 107 141302 Precision Measurement of the ${}^{7}\mathrm {Be}$ Solar Neutrino Interaction Rate in Borexino
GANDO 2011
PR D83 052002 Constraints on $\theta _{13}$ from a Three-Flavor Oscillation Analysis of Reactor Antineutrinos at KamLAND
AHARMIM 2010
PR C81 055504 Low-Energy-Threshold Analysis of the Phase I and Phase II Data Sets of the Sudbury Neutrino Observatory
ABE 2008A
PRL 100 221803 Precision Measurement of Neutrino Oscillation Parameters with KamLAND
Also
PRL 101 119904E Hagino et al. Reply: to the Comment by N. T. Zinner and A. S. Jensen.Coexistence of BCS- and BEC-Like Pair Structures in Halo Nuclei[Phys. Rev. Lett. 101, 179201 (2008)]
AHARMIM 2008
PRL 101 111301 Independent Measurement of the Total Active ${}^{8}\mathrm {B}$ Solar Neutrino Flux Using an Array of ${}^{3}\mathrm {He}$ Proportional Counters at the Sudbury Neutrino Observatory
Also
PR C87 015502 Measurement of the ${{\mathit \nu}_{{{e}}}}$ and Total ${}^{8}\mathrm {B}$ Solar Neutrino Fluxes with the Sudbury Neutrino Observatory Phase-III Data Set
HOSAKA 2006
PR D73 112001 Solar Neutrino Measurements in Super-Kamiokande-I
AHARMIM 2005A
PR C72 055502 Search for Periodicities in the ${}^{8}\mathrm {B}$ Solar Neutrino Flux Measured by the Sudbury Neutrino Observatory
ARAKI 2005
PRL 94 081801 Measurement on Neutrino Oscillation with KamLAND: Evidence of Spectral Distortion
AHMED 2004A
PRL 92 181301 Measurement of the Total Active ${}^{8}\mathrm {B}$ Solar Neutrino Flux at the Sudbury Neutrino Observatory with Enhanced Neutral Current Sensitivity
SMY 2004
PR D69 011104 Precise Measurement of the Solar Neutrino Day/Night and Seasonal Variation in Super-Kamiokande-1
AHMAD 2002B
PRL 89 011302 Measurement of Day and Night Neutrino Energy Spectra at SNO and Constraints on Neutrino Mixing Parameters
FUKUDA 2002
PL B539 179 Determination of Solar Neutrino Oscillation Parameters using 1496 Days of Super-Kamiokande I Data