(B) Three-neutrino mixing parameters

$\Delta $m${}^{2}_{21}$

INSPIRE   JSON  (beta) PDGID:
S067DM3
VALUE ($ 10^{-5} $ eV${}^{2}$) DOCUMENT ID TECN  COMMENT
$7.50$ ${}^{+0.19}_{-0.18}$ 1
ABE
2024B
 FIT KamLAND + global solar; 3${{\mathit \nu}}$
• • We do not use the following data for averages, fits, limits, etc. • •
$6.10$ ${}^{+1.26}_{-0.86}$ 2
ABE
2024B
 FIT SK-I+II+III+IV; 3${{\mathit \nu}}$
$6.10$ ${}^{+1.04}_{-0.75}$ 3
ABE
2024B
 FIT SKAM+SNO; 3${{\mathit \nu}}$
$6.9$ ${}^{+1.6}_{-1.2}$ 4
ABE
2024B
 FIT SK-IV; 3${{\mathit \nu}}$
$7.50$ ${}^{+0.22}_{-0.20}$ 5
SALAS
2021
FIT global fit
$7.42$ ${}^{+0.21}_{-0.20}$ 6
ESTEBAN
2020A
 FIT Global fit
$7.55$ ${}^{+0.20}_{-0.16}$
DE-SALAS
2018
FIT Global fit
$7.49$ ${}^{+0.19}_{-0.18}$ 7
ABE
2016C
 FIT KamLAND+global solar; 3${{\mathit \nu}}$
$4.8$ ${}^{+1.3}_{-0.6}$ 8
ABE
2016C
 FIT SKAM+SNO; 3${{\mathit \nu}}$
$4.8$ ${}^{+1.5}_{-0.8}$ 9
ABE
2016C
 FIT SK-I+II+III+IV; 3${{\mathit \nu}}$
$3.2$ ${}^{+2.8}_{-0.2}$ 10
ABE
2016C
 FIT SK-IV; 3${{\mathit \nu}}$
$7.6$ ${}^{+0.19}_{-0.18}$ 11
FORERO
2014
FIT 3${{\mathit \nu}}$
$7.50$ ${}^{+0.19}_{-0.17}$ 12
GONZALEZ-GARC..
2014
FIT Either mass ordering; global fit
$5.13$ ${}^{+1.29}_{-0.96}$ 13, 14
AHARMIM
2013
FIT global solar: 2${{\mathit \nu}}$
$5.13$ ${}^{+1.49}_{-0.98}$ 15, 14
AHARMIM
2013
FIT global solar: 3${{\mathit \nu}}$
$7.46$ ${}^{+0.20}_{-0.19}$ 16, 14
AHARMIM
2013
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$7.53$ $\pm0.18$ 17
GANDO
2013
FIT KamLAND + global solar + SBL + accelerator: 3${{\mathit \nu}}$
$7.53$ ${}^{+0.19}_{-0.18}$ 18
GANDO
2013
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$7.54$ ${}^{+0.19}_{-0.18}$ 19
GANDO
2013
FIT KamLAND: 3${{\mathit \nu}}$
$7.6$ $\pm0.2$ 20
ABE
2011
FIT KamLAND + global solar: 2${{\mathit \nu}}$
$6.2$ ${}^{+1.1}_{-1.9}$ 21
ABE
2011
FIT global solar: 2${{\mathit \nu}}$
$7.7$ $\pm0.3$ 22
ABE
2011
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$6.0$ ${}^{+2.2}_{-2.5}$ 23
ABE
2011
FIT global solar: 3${{\mathit \nu}}$
$7.50$ ${}^{+0.16}_{-0.24}$ 24
BELLINI
2011A
 FIT KamLAND + global solar: 2${{\mathit \nu}}$
$5.2$ ${}^{+1.5}_{-0.9}$ 25
BELLINI
2011A
 FIT global solar: 2${{\mathit \nu}}$
$7.50$ ${}^{+0.19}_{-0.20}$ 26
GANDO
2011
FIT KamLAND + solar: 3${{\mathit \nu}}$
$7.49$ $\pm0.20$ 27
GANDO
2011
FIT KamLAND: 3${{\mathit \nu}}$
$7.59$ ${}^{+0.20}_{-0.21}$ 28, 29
AHARMIM
2010
FIT KamLAND + global solar: 2${{\mathit \nu}}$
$5.89$ ${}^{+2.13}_{-2.16}$ 28, 30
AHARMIM
2010
FIT global solar: 2${{\mathit \nu}}$
$7.59$ $\pm0.21$ 28, 31
AHARMIM
2010
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$6.31$ ${}^{+2.49}_{-2.58}$ 28, 32
AHARMIM
2010
FIT global solar: 3${{\mathit \nu}}$
$7.58$ ${}^{+0.14}_{-0.13}$ $\pm0.15$ 33
ABE
2008A
 FIT KamLAND
$7.59$ $\pm0.21$ 34
ABE
2008A
 FIT KamLAND + global solar
$7.59$ ${}^{+0.19}_{-0.21}$ 35
AHARMIM
2008
FIT KamLAND + global solar
$8.0$ $\pm0.3$ 36
HOSAKA
2006
FIT KamLAND + global solar
$8.0$ $\pm0.3$ 37
HOSAKA
2006
FIT SKAM+SNO+KamLAND
$6.3$ ${}^{+3.7}_{-1.5}$ 38
HOSAKA
2006
FIT SKAM+SNO
$\text{5 - 12}$ 39
HOSAKA
2006
FIT SKAM day/night in the LMA region
$8.0$ ${}^{+0.4}_{-0.3}$ 40
AHARMIM
2005A
 FIT KamLAND + global solar LMA
$\text{3.3 - 14.4}$ 41
AHARMIM
2005A
 FIT global solar
$7.9$ ${}^{+0.4}_{-0.3}$ 42
ARAKI
2005
FIT KamLAND + global solar
$7.1$ ${}^{+1.0}_{-0.3}$ 43
AHMED
2004A
 FIT KamLAND + global solar
$\text{3.2 - 13.7}$ 44
AHMED
2004A
 FIT global solar
$7.1$ ${}^{+0.6}_{-0.5}$ 45
SMY
2004
FIT KamLAND + global solar
$6.0$ ${}^{+1.7}_{-1.6}$ 46
SMY
2004
FIT global solar
$6.0$ ${}^{+2.5}_{-1.6}$ 47
SMY
2004
FIT SKAM + SNO
$\text{2.8 - 12.0}$ 48
AHMAD
2002B
 FIT global solar
$\text{3.2 - 19.1}$ 49
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 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.
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, using SNO and full Super-Kamiokande I to IV data. Supersedes ABE 2016C.
4  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.
5  SALAS 2021 reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference.
6  ESTEBAN 2020A reports results of a global fit to neutrino oscillation data available at the time of the Neutrino2020 conference.
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 all solar data and KamLAND data. $\mathit CPT$ invariance is assumed.
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, using Super-Kamiokande (I+II+III+IV) and SNO 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, by combining the four phases of the Super-Kamiokande solar data. Superseded by ABE 2024B.
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 the Super-Kamiokande-IV data.
11  FORERO 2014 performs a global fit to $\Delta $m${}^{2}_{21}$ using solar, reactor, long-baseline accelerator, and atmospheric neutrino data.
12  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.
13  AHARMIM 2013 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data.
14  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.
15  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.
16  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.
17  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.
18  GANDO 2013 obtained this result by a three-neutrino oscillation analysis using KamLAND and global solar neutrino data, assuming CPT invariance. Supersedes GANDO 2011.
19  GANDO 2013 obtained this result by a three-neutrino oscillation analysis using KamLAND data. Supersedes GANDO 2011.
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, SAGE, and KamLAND data. CPT invariance is assumed.
21  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.
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, GALLEX/GNO, SAGE, and KamLAND data. The normal neutrino mass ordering and CPT invariance are assumed.
23  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.
24  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.
25  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.
26  GANDO 2011 obtain this result with three-neutrino fit using the KamLAND + solar data. Superseded by GANDO 2013.
27  GANDO 2011 obtain this result with three-neutrino fit using the KamLAND data only. Supersedes ABE 2008A.
28  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).
29  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.
30  AHARMIM 2010 obtained this result by a two-neutrino oscillation analysis using global solar neutrino data.
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 and KamLAND data (ABE 2008A). $\mathit CPT$ invariance is assumed.
32  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.
33  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.
34  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.
35  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.
36  HOSAKA 2006 obtained this result by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (ARAKI 2005). $\mathit CPT$ invariance is assumed.
37  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.
38  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.
39  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.
40  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.
41  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.
42  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.
43  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.
44  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 $ = $0.82$).
45  SMY 2004 obtained this result by a two-neutrino oscillation analysis using solar neutrino and KamLAND data (IANNI 2003). $\mathit CPT$ invariance is assumed.
46  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.
47  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.
48  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).
49  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