(B) Three-neutrino mixing parameters

sin$^2(\theta _{13})$ INSPIRE search

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

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

VALUE ($ 10^{-2} $) CL% DOCUMENT ID TECN  COMMENT
$\bf{ 2.12 \pm0.08}$ OUR AVERAGE
$2.149$ $\pm0.071$ $\pm0.050$ 1
AN
2017A
DAYA DayaBay, LingAo/Ao II reactors
$2.25$ ${}^{+0.87}_{-0.86}$ 2
ABE
2016B
DCHZ Chooz reactors
$1.81$ $\pm0.29$ 3
AN
2016A
DAYA DayaBay, Ling Ao/Ao II reactors
$2.09$ $\pm0.23$ $\pm0.16$ 4
CHOI
2016
RENO Yonggwang reactors
• • • We do not use the following data for averages, fits, limits, etc. • • •
$2.7$ $\pm0.7$ 5
ABE
2017F
T2K Normal mass ordering, T2K only
$2.15$ $\pm0.13$ 6
AN
2015
DAYA DayaBay, Ling Ao/Ao II reactors
$2.6$ ${}^{+1.2}_{-1.1}$ 7
ABE
2014A
DCHZ Chooz reactors
$3.0$ ${}^{+1.3}_{-1.0}$ 8
ABE
2014C
T2K Inverted mass ordering
$3.6$ ${}^{+1.0}_{-0.9}$ 8
ABE
2014C
T2K Normal mass ordering
$2.3$ ${}^{+0.9}_{-0.8}$ 9
ABE
2014H
DCHZ Chooz reactors
$2.3$ $\pm0.2$ 10
AN
2014
DAYA DayaBay, Ling Ao/Ao II reactors
$2.12$ $\pm0.47$ 11
AN
2014B
DAYA DayaBay, Ling Ao/Ao II reactors
$2.34$ $\pm0.20$ 12
FORERO
2014
FIT Normal mass ordering
$2.40$ $\pm0.19$ 12
FORERO
2014
FIT Inverted mass ordering
$2.18$ $\pm0.10$ 13
GONZALEZ-GARC..
2014
FIT Normal mass ordering; global fit
$2.19$ ${}^{+0.11}_{-0.10}$ 13
GONZALEZ-GARC..
2014
FIT Inverted mass ordering; global fit
$2.5$ $\pm0.9$ $\pm0.9$ 14
ABE
2013C
DCHZ Chooz reactors
$2.3$ ${}^{+1.3}_{-1.0}$ 15
ABE
2013E
T2K Normal mass ordering
$2.8$ ${}^{+1.6}_{-1.2}$ 15
ABE
2013E
T2K Inverted mass ordering
$1.6$ ${}^{+1.3}_{-0.9}$ 16
ADAMSON
2013A
MINS Normal mass ordering
$3.0$ ${}^{+1.8}_{-1.6}$ 16
ADAMSON
2013A
MINS Inverted mass ordering
$<13$ 90
AGAFONOVA
2013
OPER OPERA: 3${{\mathit \nu}}$
$<3.6$ 95 17
AHARMIM
2013
FIT global solar: 3${{\mathit \nu}}$
$2.3$ $\pm0.3$ $\pm0.1$ 18
AN
2013
DAYA DayaBay, LIng Ao/Ao II reactors
$2.2$ $\pm1.1$ $\pm0.8$ 19
ABE
2012
DCHZ Chooz reactors
$2.8$ $\pm0.8$ $\pm0.7$ 20
ABE
2012B
DCHZ Chooz reactors
$2.9$ $\pm0.3$ $\pm0.5$ 21
AHN
2012
RENO Yonggwang reactors
$2.4$ $\pm0.4$ $\pm0.1$ 22
AN
2012
DAYA DayaBay, Ling Ao/Ao II reactors
$2.5$ ${}^{+1.8}_{-1.6}$ 23
ABE
2011
FIT KamLAND + global solar
$\text{< 6.1}$ 95 24
ABE
2011
FIT Global solar
$1.3\text{ to }5.6 $ 68 25
ABE
2011A
T2K Normal mass ordering
$1.5\text{ to }5.6 $ 68 26
ABE
2011A
T2K Inverted mass ordering
$0.3\text{ to }2.3 $ 68 27
ADAMSON
2011D
MINS Normal mass ordering
$0.8\text{ to }3.9 $ 68 28
ADAMSON
2011D
MINS Inverted mass ordering
$8$ $\pm3$ 29
FOGLI
2011
FIT Global neutrino data
$7.8$ $\pm6.2$ 30
GANDO
2011
FIT KamLAND + solar: 3${{\mathit \nu}}$
$12.4$ $\pm13.3$ 31
GANDO
2011
FIT KamLAND: 3${{\mathit \nu}}$
$3$ ${}^{+9}_{-7}$ 90 32
ADAMSON
2010A
MINS Normal mass ordering
$6$ ${}^{+14}_{-6}$ 90 33
ADAMSON
2010A
MINS Inverted mass ordering
$8$ ${}^{+8}_{-7}$ 34, 35
AHARMIM
2010
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$\text{< 30}$ 95 34, 36
AHARMIM
2010
FIT global solar: 3${{\mathit \nu}}$
$\text{< 15}$ 90 37
WENDELL
2010
SKAM 3${{\mathit \nu}}$ osc.; normal $\mathit m$ ordering
$\text{< 33}$ 90 37
WENDELL
2010
SKAM 3${{\mathit \nu}}$ osc.; inverted $\mathit m$ ordering
$11$ ${}^{+11}_{-8}$ 38
ADAMSON
2009
MINS Normal mass ordering
$18$ ${}^{+15}_{-11}$ 39
ADAMSON
2009
MINS Inverted mass ordering
$6$ $\pm4$ 40
FOGLI
2008
FIT Global neutrino data
$8$ $\pm7$ 41
FOGLI
2008
FIT Solar + KamLAND data
$5$ $\pm5$ 42
FOGLI
2008
FIT Atmospheric + LBL + CHOOZ
$\text{< 36}$ 90 43
YAMAMOTO
2006
K2K Accelerator experiment
$\text{< 48}$ 90 44
AHN
2004
K2K Accelerator experiment
$\text{< 36}$ 90 45
BOEHM
2001
Palo Verde react.
$\text{< 45}$ 90 46
BOEHM
2000
Palo Verde react.
$\text{< 15}$ 90 47
APOLLONIO
1999
CHOZ Reactor Experiment
1  AN 2017A report 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 ${}^{}\mathrm {Gd}$. A simultaneous fit to ${{\mathit \theta}_{{13}}}$ and $\Delta $m${}^{2}_{ee}$ is performed. Supersedes AN 2015 .
2  ABE 2016B 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$^2(2{{\mathit \theta}_{{13}}})$. This analysis uses 7.15 reactor-off days for constraining backgrounds. A rate and shape analysis is performed on combined neutron captures on ${}^{}\mathrm {H}$ and ${}^{}\mathrm {Gd}$. Supersedes ABE 2014H and ABE 2013C.
3  AN 2016A uses data from the eight antineutrino detectors (404 days) and six antineutrino detectors (217 days) runs to determine the mixing parameter sin$^2(2{{\mathit \theta}_{{13}}})$ using the neutron capture on ${}^{}\mathrm {H}$ only. Supersedes AN 2014B.
4  CHOI 2016 reports results of the RENO experiment using about 500 days of data, performing a rate and shape analysis. Compared to AHN 2012 , 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 2012 .
5  Using T2K data only. For inverted mass ordering, all values of ${{\mathit \theta}_{{13}}}$ are ruled out at 68$\%$ CL.
6  AN 2015 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 ${{\overline{\mathit \nu}}_{{e}}}$ observed interaction rates with neutron capture on ${}^{}\mathrm {Gd}$ and energy spectra. The result corresponds to the exposure of $6.9 \times 10^{5}$ GW$_{th}$-ton-days. Superseded by AN 2017A.
7  ABE 2014A 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$^2(2 {{\mathit \theta}_{{13}}})$. The Bugey4 data (DECLAIS 1994 ) is used to constrain the neutrino flux. The data set includes 7.24 reactor-off days. A "rate-modulation" analysis is performed. Supercedes ABE 2012B.
8  ABE 2014C result is for ${{\mathit \nu}_{{e}}}$ appearance and assumes $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ = $2.4 \times 10^{-3}$ eV${}^{2}$, sin$^2( \theta _{23})$ = 0.5, and $\delta $ = 0.
9  ABE 2014H 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$^2(2 {{\mathit \theta}_{{13}}})$. The Bugey4 data (DECLAIS 1994 ) is used to constrain the neutrino flux. The data set includes 7.24 reactor-off days. A rate and shape analysis is performed. Superceded by ABE 2016B.
10  AN 2014 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 ${{\overline{\mathit \nu}}_{{e}}}$ observed interaction rates with neutron capture on ${}^{}\mathrm {Gd}$ and energy spectra. Supersedes AN 2013 and superseded by AN 2015 .
11  AN 2014B uses six identical anti-neutrino detectors with flux-weighted baselines of $\sim{}$500 m and $\sim{}$1.6 km to six power reactors. This rate analysis uses a 217-day data set and neutron capture on protons (not ${}^{}\mathrm {Gd}$) only. $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$= $2.32 \times 10^{-3}$ eV${}^{2}$ is assumed. Superseded by AN 2016A.
12  FORERO 2014 performs a global fit to neutrino oscillations using solar, reactor, long-baseline accelerator, and atmospheric neutrino data.
13  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 $0.0218$ ${}^{+.0010}_{-.0011}$ eV${}^{2}$ for normal and $0.0219$ ${}^{+.0012}_{-.0010}$ eV${}^{2}$ for inverted mass ordering.
14  ABE 2013C uses delayed neutron capture on hydrogen instead of on ${}^{}\mathrm {Gd}$ used previously. The physical volume is thus three times larger. The fit is based on the rate and shape analysis as in ABE 2012B. The Bugey4 data (DECLAIS 1994 ) is used to constrain the neutrino flux. Superseded by ABE 2016B.
15  ABE 2013E assumes maximal $\theta _{23}$ mixing and $\mathit CP$ phase $\delta $ = 0.
16  ADAMSON 2013A results obtained from ${{\mathit \nu}_{{e}}}$ appearance, assuming $\delta $ = 0, and sin$^2(2 \theta _{23})$ = 0.957.
17  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. 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. AHARMIM 2013 also reported a result combining global solar and KamLAND data, which is sin${}^{2}$(2 ${{\mathit \theta}_{{13}}}$) = $0.091$ ${}^{+.029}_{-.031}$.
18  AN 2013 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 ${{\overline{\mathit \nu}}_{{e}}}$ interaction rate ratios. Superseded by AN 2014 .
19  ABE 2012 determines the ${{\overline{\mathit \nu}}_{{e}}}$ 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 $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$ = $2.4 \times 10^{-3}$ eV${}^{2}$ is used in the analysis. Superseded by ABE 2012B.
20  ABE 2012B determines the neutrino mixing angle ${{\mathit \theta}_{{13}}}$ 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 1994 ) is used to constrain the neutrino flux. Superseded by ABE 2014A.
21  AHN 2012 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 ${{\mathit \theta}_{{13}}}$. This rate-only analysis excludes the no-oscillation hypothesis at 4.9 standard deviations. The value of $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$ = $0.00232$ ${}^{+.00012}_{-.00008}$ eV${}^{2}$ was assumed in the analysis. Superseded by CHOI 2016 .
22  AN 2012 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 ${{\mathit \theta}_{{13}}}$ using the ${{\overline{\mathit \nu}}_{{e}}}$ observed interaction rate ratios. This rate-only analysis excludes the no-oscillation hypothesis at 5.2 standard deviations. The value of $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$ = $0.00232$ ${}^{+.00012}_{-.00008}$ eV${}^{2}$ was assumed in the analysis. Superseded by AN 2013 .
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, GALLEX/GNO, SAGE, and KamLAND data. This result implies an upper bound of sin$^2{{\mathit \theta}_{{13}}}<$ 0.059 (95$\%$ CL) or sin$^22{{\mathit \theta}_{{13}}}<$ 0.22 (95$\%$ CL). The normal neutrino mass ordering and CPT invariance are assumed.
24  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.
25  The quoted limit is for $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ = $2.4 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = ${{\mathit \pi}}$/2, ${{\mathit \delta}}$ = 0, and the normal mass ordering. For other values of ${{\mathit \delta}}$, the 68$\%$ region spans from 0.03 to 0.25, and the 90$\%$ region from 0.02 to 0.32.
26  The quoted limit is for $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ = $2.4 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = ${{\mathit \pi}}$/2, ${{\mathit \delta}}$ = 0, and the inverted mass ordering. For other values of ${{\mathit \delta}}$, the 68$\%$ region spans from 0.04 to 0.30, and the 90$\%$ region from 0.02 to 0.39.
27  The quoted limit is for $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ = $2.32 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = ${{\mathit \pi}}$/2, ${{\mathit \delta}}$ = 0, and the normal mass ordering. For other values of ${{\mathit \delta}}$, the 68$\%$ region spans from 0.02 to 0.12, and the 90$\%$ region from 0 to 0.16.
28  The quoted limit is for $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ = $2.32 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = ${{\mathit \pi}}$/2, ${{\mathit \delta}}$ = 0, and the inverted mass ordering. For other values of ${{\mathit \delta}}$, the 68$\%$ region spans from 0.02 to 0.16, and the 90$\%$ region from 0 to 0.21.
29  FOGLI 2011 obtained this result from an analysis using the atmospheric, accelerator long baseline, CHOOZ, solar, and KamLAND data. Recently, MUELLER 2011 suggested an average increase of about 3.5$\%$ in normalization of the reactor ${{\overline{\mathit \nu}}_{{e}}}$ fluxess, and using these fluxes, the fitted result becomes $0.10$ $\pm0.03$.
30  GANDO 2011 report sin$^2{{\mathit \theta}_{{13}}}$ = $0.020$ $\pm0.016$. This result was obtained with three-neutrino fit using the KamLAND + solar data.
31  GANDO 2011 report sin$^2{{\mathit \theta}_{{13}}}$ = $0.032$ $\pm0.037$. This result was obtained with three-neutrino fit using the KamLAND data only.
32  This result corresponds to the limit of $<$0.12 at 90$\%$ CL for $\Delta {{\mathit m}}{}^{2}_{32}$ = $2.43 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = $\pi $/2, and $\delta $ = 0. For other values of $\delta $, the 90$\%$ CL region spans from 0 to 0.16.
33  This result corresponds to the limit of $<$0.20 at 90$\%$ CL for $\Delta {{\mathit m}}{}^{2}_{32}$ = $2.43 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = $\pi $/2, and $\delta $ = 0. For other values of $\delta $, the 90$\%$ CL region spans from 0 to 0.21.
34  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 ).
35  AHARMIM 2010 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta $ fixed to $2.3 \times 10^{-3}$ eV${}^{2}$, using global solar neutrino data and KamLAND data (ABE 2008A). $\mathit CPT$ invariance is assumed. This result implies an upper bound of sin$^2{{\mathit \theta}_{{13}}}<$ 0.057 (95$\%$ CL) or sin$^22{{\mathit \theta}_{{13}}}<$ 0.22 (95$\%$ CL).
36  AHARMIM 2010 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta $ fixed to $2.3 \times 10^{-3}$ eV${}^{2}$, using global solar neutrino data.
37  WENDELL 2010 obtained this result 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 2006A result.
38  The quoted limit is for $\Delta {{\mathit m}}{}^{2}_{32}$ = $2.43 \times 10^{-3}$ 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.
39  The quoted limit is for $\Delta {{\mathit m}}{}^{2}_{32}$ = $2.43 \times 10^{-3}$ 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.
40  FOGLI 2008 obtained this result from a global analysis of all neutrino oscillation data, that is, solar + KamLAND + atmospheric + accelerator long baseline + CHOOZ.
41  FOGLI 2008 obtained this result from an analysis using the solar and KamLAND neutrino oscillation data.
42  FOGLI 2008 obtained this result from an analysis using the atmospheric, accelerator long baseline, and CHOOZ neutrino oscillation data.
43  YAMAMOTO 2006 searched for ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ appearance. Assumes 2 sin$^2(2\theta _{ {{\mathit \mu}} {{\mathit e}} })$ = sin$^2(2\theta _{13})$. The quoted limit is for ${{\mathit \Delta}}{{\mathit m}}{}^{2}_{32}$ = $1.9 \times 10^{-3}$ eV${}^{2}$. That value of ${{\mathit \Delta}}{{\mathit m}}{}^{2}_{32}$ is the one-$\sigma $ low value for AHN 2006A. For the AHN 2006A best fit value of $2.8 \times 10^{-3}$ eV${}^{2}$, the sin$^2(2\theta _{13})$ limit is $<$ 0.26. Supersedes AHN 2004 .
44  AHN 2004 searched for ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ appearance. Assuming 2 sin$^2(2 \theta _{{{\mathit \mu}_{{e}}}})$ = sin$^2(2 \theta _{13})$, a limit on sin$^2(2 \theta _{{{\mathit \mu}_{{e}}}})$ is converted to a limit on sin$^2(2 \theta _{13})$.The quoted limit is for ${{\mathit \Delta}}{{\mathit m}}{}^{2}_{32}$ = $1.9 \times 10^{-3}$ eV${}^{2}$. That value of ${{\mathit \Delta}}{{\mathit m}}{}^{2}_{32}$ is the one-${{\mathit \sigma}}$ low value for ALIU 2005 . For the ALIU 2005 best fit value of $2.8 \times 10^{-3}$ eV${}^{2}$, the sin$^2(2 \theta _{13})$ limit is $<$ 0.30.
45  The quoted limit is for $\Delta \mathit m{}^{2}_{32}$ = $1.9 \times 10^{-3}$ eV${}^{2}$. That value of $\Delta \mathit m{}^{2}_{32}$ is the 1-${{\mathit \sigma}}$ low value for ALIU 2005 . For the ALIU 2005 best fit value of $2.8 \times 10^{-3}$ eV${}^{2}$, the sin$^22 {{\mathit \theta}}_{13}$ limit is $<$ 0.19. In this range, the ${{\mathit \theta}}_{13}$ limit is larger for lower values of $\Delta \mathit m{}^{2}_{32}$, and smaller for higher values of $\Delta \mathit m{}^{2}_{32}$.
46  The quoted limit is for $\Delta \mathit m{}^{2}_{32}$ = $1.9 \times 10^{-3}$ eV${}^{2}$. That value of $\Delta \mathit m{}^{2}_{32}$ is the 1-${{\mathit \sigma}}$ low value for ALIU 2005 . For the ALIU 2005 best fit value of $2.8 \times 10^{-3}$ eV${}^{2}$, the sin$^22 {{\mathit \theta}}_{13}$ limit is $<$ 0.23.
47  The quoted limit is for $\Delta \mathit m{}^{2}_{32}$ = $2.43 \times 10^{-3}$ eV${}^{2}$. That value of $\Delta \mathit m{}^{2}_{32}$ is the central value for ADAMSON 2008 . For the ADAMSON 2008 1-$\sigma $ low value of $2.30 \times 10^{-3}$ eV${}^{2}$, the sin$^22 {{\mathit \theta}}_{13}$ limit is $<$ 0.16. See also APOLLONIO 2003 for a detailed description of the experiment.
  Conservation Laws:
LEPTON FAMILY NUMBER
  References:
ABE 2017F
PR D96 092006 Measurement of Neutrino and Antineutrino Oscillations by the T2K Experiment Including a New Additional Sample of ${{\mathit \nu}_{{e}}}$ Interactions at the Far Detector
AN 2017A
PR D95 072006 Measurement of Electron Antineutrino Oscillation Based on 1230 Days of Operation of the Daya Bay Experiment
ABE 2016B
JHEP 1601 163 Measurement of $\mathit \theta _{13}$ in Double Chooz using Neutron Captures on Hydrogen with Novel Background Rejection Techniques
AN 2016A
PR D93 072011 New Measurement of $\mathit \theta _{13}$ via Neutron Capture on Hydrogen at Daya Bay
CHOI 2016
PRL 116 211801 Observation of Energy and Baseline Dependent Reactor Antineutrino Disappearance in the RENO Experiment
AN 2015
PRL 115 111802 A New Measurement of Antineutrino Oscillation with the Full Detector Configuration at Daya Bay
ABE 2014H
JHEP 1410 086 Improved Measurements of the Neutrino Mixing Angle ${{\mathit \theta}_{{13}}}$ with the Double Chooz Detector
ABE 2014C
PRL 112 061802 Observation of Electron Neutrino Appearance in a Muon Neutrino Beam
ABE 2014A
PL B735 51 Background-Independent Measurement of $\mathit \theta _{13}$ in Double Chooz
AN 2014B
PR D90 071101 Independent Measurement of the Neutrino Mixing Angle ${{\mathit \theta}_{{13}}}$ via Neutron Capture on Hydrogen at Daya Bay
AN 2014
PRL 112 061801 Spectral Measurement of Electron Antineutrino Oscillation Amplitude and Frequency at Daya Bay
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
ABE 2013E
PR D88 032002 Evidence of Electron Neutrino Appearance in a Muon Neutrino Beam
ABE 2013C
PL B723 66 First Measurement of $\mathit \theta _{13}$ from Delayed Neutron Capture on Hydrogen in the Double Chooz Experiment
ADAMSON 2013A
PRL 110 171801 Electron Neutrino and Antineutrino Appearance in the Full MINOS Data Sample
AGAFONOVA 2013
JHEP 1307 004 Search for ${{\mathit \nu}_{{\mu}}}\rightarrow{{\mathit \nu}_{{e}}}$ Oscillations with the OPERA Experiment in the CNGS Beam
AHARMIM 2013
PR C88 025501 Combined Analysis of all Three Phases of Solar Neutrino Data from the Sudbury Neutrino Observatory
AN 2013
CP C37 011001 Improved Measurement of Electron Antineutrino Disappearance at Daya Bay
ABE 2012
PRL 108 131801 Indication for the Disappearance of Reactor Electron Antineutrinos in the Double Chooz Experiment
ABE 2012B
PR D86 052008 Reactor ${{\mathit \nu}_{{e}}}$ Disappearance in the Double Chooz Experiment
AHN 2012
PRL 108 191802 Observation of Reactor Electron Antineutrino Disappearance in the RENO Experiment
AN 2012
PRL 108 171803 Observation of Electron-Antineutrino Disappearance at Daya Bay
ABE 2011A
PRL 107 041801 Indication of Electron Neutrino Appearance from an Accelerator-Produced Off-Axis Muon Neutrino Beam
ABE 2011
PR D83 052010 Solar Neutrino Results in Super-Kamiokande-III
ADAMSON 2011D
PRL 107 181802 Improved Search for Muon-Neutrino to Electron-Neutrino Oscillations in MINOS
FOGLI 2011
PR D84 053007 Evidence of $\mathit \theta _{13}$ > 0 from Global Neutrino Data Analysis
GANDO 2011
PR D83 052002 Constraints on $\theta _{13}$ from a Three-Flavor Oscillation Analysis of Reactor Antineutrinos at KamLAND
ADAMSON 2010A
PR D82 051102 New Constraints on muon-neutrino to electron-neutrino Transitions in MINOS
AHARMIM 2010
PR C81 055504 Low-Energy-Threshold Analysis of the Phase I and Phase II Data Sets of the Sudbury Neutrino Observatory
WENDELL 2010
PR D81 092004 Atmospheric Neutrino Oscillation Analysis with Subleading Effects in Super-Kamiokande I, II, and III
ADAMSON 2009
PRL 103 261802 Search for Muon-Neutrino to Electron-Neutrino Transitions in MINOS
FOGLI 2008
PRL 101 141801 Hints of $\theta _{13}$ > 0 from Global Neutrino Data Analysis
YAMAMOTO 2006
PRL 96 181801 Improved Search for ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ Oscillation in a Long-Baseline Accelerator Experiment
AHN 2004
PRL 93 051801 Search for Electron Neutrino Appearance in 250 km Long-baseline Experiment
BOEHM 2001
PR D64 112001 Final Results from the Palo Verde Neutrino Oscillation Experiment
BOEHM 2000
PRL 84 3764 Search for Neutrino Oscillations at the Palo Verde Nuclear Reactors
APOLLONIO 1999
PL B466 415 Limits on Neutrino Oscillations from the CHOOZ Experiment