(B) Three-neutrino mixing parameters

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

INSPIRE   JSON  (beta) 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
$0.307$ $\pm0.012$ 1
ABE
2024B
 FIT KamLAND+global solar; 3${{\mathit \nu}}$
• • We do not use the following data for averages, fits, limits, etc. • •
$0.306$ $\pm0.013$ 2
ABE
2024B
 FIT global solar; 3${{\mathit \nu}}$
$0.324$ ${}^{+0.027}_{-0.023}$ 3
ABE
2024B
 FIT SK-I+II+III+IV; 3${{\mathit \nu}}$
$0.318$ $\pm0.016$ 4
SALAS
2021
FIT global fit
$0.304$ $\pm0.012$ 5
ESTEBAN
2020A
 FIT Global fit
$0.320$ ${}^{+0.020}_{-0.016}$
DE-SALAS
2018
FIT Global fit
$0.307$ ${}^{+0.013}_{-0.012}$ 6
ABE
2016C
 FIT KamLAND+global solar; 3${{\mathit \nu}}$
$0.310$ $\pm0.014$ 7
ABE
2016C
 FIT SKAM+SNO; 3${{\mathit \nu}}$
$0.334$ ${}^{+0.027}_{-0.023}$ 8
ABE
2016C
 FIT SK-I+II+III+IV; 3${{\mathit \nu}}$
$0.327$ ${}^{+0.026}_{-0.031}$ 9
ABE
2016C
 FIT SK-IV; 3${{\mathit \nu}}$
$0.323$ $\pm0.016$ 10
FORERO
2014
FIT 3${{\mathit \nu}}$
$0.304$ ${}^{+0.013}_{-0.012}$ 11
GONZALEZ-GARC..
2014
FIT Either mass ordering; global fit
$0.299$ ${}^{+0.014}_{-0.014}$ 12, 13
AHARMIM
2013
FIT global solar: 2${{\mathit \nu}}$
$0.307$ ${}^{+0.016}_{-0.013}$ 14, 13
AHARMIM
2013
FIT global solar: 3${{\mathit \nu}}$
$0.304$ ${}^{+0.022}_{-0.018}$ 15, 13
AHARMIM
2013
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$0.304$ ${}^{+0.014}_{-0.013}$ 16
GANDO
2013
FIT KamLAND + global solar + SBL + accelerator: 3${{\mathit \nu}}$
$0.304$ ${}^{+0.014}_{-0.013}$ 17
GANDO
2013
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$0.325$ ${}^{+0.039}_{-0.039}$ 18
GANDO
2013
FIT KamLAND: 3${{\mathit \nu}}$
$0.30$ ${}^{+0.02}_{-0.01}$ 19
ABE
2011
FIT KamLAND + global solar: 2${{\mathit \nu}}$
$0.30$ ${}^{+0.02}_{-0.01}$ 20
ABE
2011
FIT global solar: 2${{\mathit \nu}}$
$0.31$ ${}^{+0.03}_{-0.02}$ 21
ABE
2011
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$0.31$ ${}^{+0.03}_{-0.03}$ 22
ABE
2011
FIT global solar: 3${{\mathit \nu}}$
$0.314$ ${}^{+0.015}_{-0.012}$ 23
BELLINI
2011A
 FIT KamLAND + global solar: 2${{\mathit \nu}}$
$0.319$ ${}^{+0.017}_{-0.015}$ 24
BELLINI
2011A
 FIT global solar: 2${{\mathit \nu}}$
$0.311$ ${}^{+0.016}_{-0.016}$ 25
GANDO
2011
FIT KamLAND + solar: 3${{\mathit \nu}}$
$0.304$ ${}^{+0.046}_{-0.042}$ 26
GANDO
2011
FIT KamLAND: 3${{\mathit \nu}}$
$0.314$ ${}^{+0.018}_{-0.014}$ 27, 28
AHARMIM
2010
FIT KamLAND + global solar: 2${{\mathit \nu}}$
$0.314$ ${}^{+0.017}_{-0.020}$ 27, 29
AHARMIM
2010
FIT global solar: 2${{\mathit \nu}}$
$0.319$ ${}^{+0.019}_{-0.016}$ 27, 30
AHARMIM
2010
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$0.319$ ${}^{+0.023}_{-0.024}$ 27, 31
AHARMIM
2010
FIT global solar: 3${{\mathit \nu}}$
$0.36$ ${}^{+0.05}_{-0.04}$ 32
ABE
2008A
 FIT KamLAND
$0.32$ $\pm0.03$ 33
ABE
2008A
 FIT KamLAND + global fit
$0.32$ $\pm0.02$ 34
AHARMIM
2008
FIT KamLAND + global solar
$0.31$ ${}^{+0.04}_{-0.04}$ 35
HOSAKA
2006
FIT KamLAND + global solar
$0.31$ ${}^{+0.04}_{-0.03}$ 36
HOSAKA
2006
FIT SKAM+SNO+KamLAND
$0.31$ ${}^{+0.03}_{-0.04}$ 37
HOSAKA
2006
FIT SKAM+SNO
$0.31$ ${}^{+0.02}_{-0.03}$ 38
AHARMIM
2005A
 FIT KamLAND + global solar
$\text{0.25 - 0.39}$ 39
AHARMIM
2005A
 FIT global solar
$0.29$ $\pm0.03$ 40
ARAKI
2005
FIT KamLAND + global solar
$0.29$ ${}^{+0.03}_{-0.02}$ 41
AHMED
2004A
 FIT KamLAND + global solar
$\text{0.23 - 0.37}$ 42
AHMED
2004A
 FIT global solar
$0.31$ ${}^{+0.04}_{-0.04}$ 43
SMY
2004
FIT KamLAND + global solar
$0.29$ ${}^{+0.04}_{-0.04}$ 44
SMY
2004
FIT global solar
$0.32$ ${}^{+0.06}_{-0.05}$ 45
SMY
2004
FIT SKAM + SNO
$\text{0.19 - 0.33}$ 46
AHMAD
2002B
 FIT global solar
$\text{0.19 - 0.39}$ 47
FUKUDA
2002
FIT global solar
1  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.
2  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 data. $\mathit CPT$ invariance is assumed. Supersedes ABE 2016C.
3  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 full Super-Kamiokande (I+II+III+IV) data. $\mathit CPT$ invariance is assumed. Supersedes ABE 2016C.
4  SALAS 2021 reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference.
5  ESTEBAN 2020A reports results of a global fit to neutrino oscillation data available at the time of the Neutrino2020 conference.
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 all solar data and KamLAND data. $\mathit CPT$ invariance is assumed. Superseded by ABE 2024B.
7  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.
8  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.
9  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. Superseded by ABE 2024B.
10  FORERO 2014 performs a global fit to neutrino oscillations using solar, reactor, long-baseline accelerator, and atmospheric neutrino data.
11  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.
12  AHARMIM 2013 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data.
13  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.
14  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.
15  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.
16  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.
17  GANDO 2013 obtained this result by a three-neutrino oscillation analysis using KamLAND and global solar neutrino data, assuming CPT invariance. Supersedes GANDO 2011.
18  GANDO 2013 obtained this result by a three-neutrino oscillation analysis using KamLAND data. Supersedes GANDO 2011.
19  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.
20  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.
21  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.
22  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.
23  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.
24  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.
25  GANDO 2011 obtain this result with three-neutrino fit using the KamLAND + solar data. Superseded by GANDO 2013.
26  GANDO 2011 obtain this result with three-neutrino fit using the KamLAND data only. Superseded by GANDO 2013.
27  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).
28  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.
29  AHARMIM 2010 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data.
30  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.
31  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.
32  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.
33  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.
34  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.
35  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.
36  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.
37  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.
38  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 $ = $0.86$ ${}^{+0.05}_{-0.06}$.
39  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 $ = $0.86$ ${}^{+0.05}_{-0.07}$.
40  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.
41  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 $ = $0.82$ $\pm0.06$.
42  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 $ = $0.82$).
43  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.
44  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.
45  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.
46  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).
47  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