# 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
$\bf{ 2.18 \pm0.07}$ OUR AVERAGE
$2.188$ $\pm0.076$ 1
 2018 A
DAYA DayaBay, LingAo/Ao II reactors
$2.29$ $\pm0.18$ 2
 2018
RENO Yonggwang reactors
$2.25$ ${}^{+0.87}_{-0.86}$ 3
 2016 B
DCHZ Chooz reactors
$1.81$ $\pm0.29$ 4
 2016 A
DAYA DayaBay, Ling Ao/Ao II reactors
• • • We do not use the following data for averages, fits, limits, etc. • • •
$<3.9$ 68
 2019
OPER
$1.8$ ${}^{+2.9}_{-1.3}$ 5
 2018 B
SKAM 3${{\mathit \nu}}$ osc: normal mass ordering, ${{\mathit \theta}_{{13}}}$ free
$0.8$ ${}^{+1.7}_{-0.7}$ 5
 2018 B
SKAM 3${{\mathit \nu}}$ osc: inverted mass ordering, ${{\mathit \theta}_{{13}}}$ free
$<12$ 90 6
 2018 A
OPER OPERA: ${{\mathit \nu}_{{e}}}$ appearance
$2.160$ ${}^{+0.083}_{-0.069}$
 2018
FIT Normal mass ordering, global fit
$2.220$ ${}^{+0.074}_{-0.076}$
 2018
FIT Inverted mass ordering, global fit
$2.09$ $\pm0.23$ $\pm0.16$ 7
 2018
RENO Yonggwang reactors
$2.7$ $\pm0.7$ 8
 2017 F
T2K Normal mass ordering, T2K only
$2.149$ $\pm0.071$ $\pm0.050$ 9
 2017 A
DAYA DayaBay, LingAo/Ao II reactors
$2.09$ $\pm0.23$ $\pm0.16$ 10
 2016
RENO Yonggwang reactors
$2.15$ $\pm0.13$ 11
 2015
DAYA DayaBay, Ling Ao/Ao II reactors
$2.6$ ${}^{+1.2}_{-1.1}$ 12
 2014 A
DCHZ Chooz reactors
$3.0$ ${}^{+1.3}_{-1.0}$ 13
 2014 C
T2K Inverted mass ordering
$3.6$ ${}^{+1.0}_{-0.9}$ 13
 2014 C
T2K Normal mass ordering
$2.3$ ${}^{+0.9}_{-0.8}$ 14
 2014 H
DCHZ Chooz reactors
$2.3$ $\pm0.2$ 15
 2014
DAYA DayaBay, Ling Ao/Ao II reactors
$2.12$ $\pm0.47$ 16
 2014 B
DAYA DayaBay, Ling Ao/Ao II reactors
$2.34$ $\pm0.20$ 17
 2014
FIT Normal mass ordering
$2.40$ $\pm0.19$ 17
 2014
FIT Inverted mass ordering
$2.18$ $\pm0.10$ 18
 2014
FIT Normal mass ordering; global fit
$2.19$ ${}^{+0.11}_{-0.10}$ 18
 2014
FIT Inverted mass ordering; global fit
$2.5$ $\pm0.9$ $\pm0.9$ 19
 2013 C
DCHZ Chooz reactors
$2.3$ ${}^{+1.3}_{-1.0}$ 20
 2013 E
T2K Normal mass ordering
$2.8$ ${}^{+1.6}_{-1.2}$ 20
 2013 E
T2K Inverted mass ordering
$1.6$ ${}^{+1.3}_{-0.9}$ 21
 2013 A
MINS Normal mass ordering
$3.0$ ${}^{+1.8}_{-1.6}$ 21
 2013 A
MINS Inverted mass ordering
$<13$ 90
 2013
OPER OPERA: 3${{\mathit \nu}}$
$<3.6$ 95 22
 2013
FIT global solar: 3${{\mathit \nu}}$
$2.3$ $\pm0.3$ $\pm0.1$ 23
 2013
DAYA DayaBay, LIng Ao/Ao II reactors
$2.2$ $\pm1.1$ $\pm0.8$ 24
 2012
DCHZ Chooz reactors
$2.8$ $\pm0.8$ $\pm0.7$ 25
 2012 B
DCHZ Chooz reactors
$2.9$ $\pm0.3$ $\pm0.5$ 26
 2012
RENO Yonggwang reactors
$2.4$ $\pm0.4$ $\pm0.1$ 27
 2012
DAYA DayaBay, Ling Ao/Ao II reactors
$2.5$ ${}^{+1.8}_{-1.6}$ 28
 2011
FIT KamLAND + global solar
$\text{< 6.1}$ 95 29
 2011
FIT Global solar
$1.3\text{ to }5.6$ 68 30
 2011 A
T2K Normal mass ordering
$1.5\text{ to }5.6$ 68 31
 2011 A
T2K Inverted mass ordering
$0.3\text{ to }2.3$ 68 32
 2011 D
MINS Normal mass ordering
$0.8\text{ to }3.9$ 68 33
 2011 D
MINS Inverted mass ordering
$8$ $\pm3$ 34
 2011
FIT Global neutrino data
$7.8$ $\pm6.2$ 35
 2011
FIT KamLAND + solar: 3${{\mathit \nu}}$
$12.4$ $\pm13.3$ 36
 2011
FIT KamLAND: 3${{\mathit \nu}}$
$3$ ${}^{+9}_{-7}$ 90 37
 2010 A
MINS Normal mass ordering
$6$ ${}^{+14}_{-6}$ 90 38
 2010 A
MINS Inverted mass ordering
$8$ ${}^{+8}_{-7}$ 39, 40
 2010
FIT KamLAND + global solar: 3${{\mathit \nu}}$
$\text{< 30}$ 95 39, 41
 2010
FIT global solar: 3${{\mathit \nu}}$
$\text{< 15}$ 90 42
 2010
SKAM 3${{\mathit \nu}}$ osc.; normal $\mathit m$ ordering
$\text{< 33}$ 90 42
 2010
SKAM 3${{\mathit \nu}}$ osc.; inverted $\mathit m$ ordering
$11$ ${}^{+11}_{-8}$ 43
 2009
MINS Normal mass ordering
$18$ ${}^{+15}_{-11}$ 44
 2009
MINS Inverted mass ordering
$6$ $\pm4$ 45
 2008
FIT Global neutrino data
$8$ $\pm7$ 46
 2008
FIT Solar + KamLAND data
$5$ $\pm5$ 47
 2008
FIT Atmospheric + LBL + CHOOZ
$\text{< 36}$ 90 48
 2006
K2K Accelerator experiment
$\text{< 48}$ 90 49
 2004
K2K Accelerator experiment
$\text{< 36}$ 90 50
 2001
Palo Verde react.
$\text{< 45}$ 90 51
 2000
Palo Verde react.
$\text{< 15}$ 90 52
 1999
CHOZ Reactor Experiment
1  ADEY 2018A reports results from analysis of 1958 days of data taking with the Daya-Bay experiment, with $3.9 \times 10^{6}{{\overline{\mathit \nu}}_{{e}}}$ candidates. The fit to the data gives $\Delta$m${}^{2}_{ee}$ = $0.002522$ ${}^{+0.000068}_{-0.000070}$ eV${}^{2}$. Solar oscillation parameters are fixed in the analysis using the global averages, sin$^2({{\mathit \theta}_{{12}}})$ = $0.307$ ${}^{+0.013}_{-0.012}$, $\Delta$m${}^{2}_{21}$ = ($7.53$ $\pm0.18$) $\times 10^{-5}$ eV${}^{2}$, from PDG 2018 . Supersedes AN 2017A.
2  BAK 2018 reports results of the RENO experiment using about 2200 live-days of data taken with detectors placed at 410.6 and 1445.7 m from reactors of the Hanbit Nuclear Power Plant. Supersedes SEO 2018 .
3  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.
4  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.
5  ABE 2018B uses 328 kton$\cdot{}$years of Super-Kamiokande I-IV atmospheric neutrino data to obtain this result. The fit is performed over the four parameters, $\Delta$m${}^{2}_{32}$, sin$^2{{\mathit \theta}_{{23}}}$, sin$^2{{\mathit \theta}_{{13}}}$, and $\delta$, while the solar parameters are fixed to $\Delta$m${}^{2}_{21}$= ($7.53$ $\pm0.18$) $\times 10^{-5}$ eV${}^{2}$ and sin$^2{{\mathit \theta}_{{12}}}$ = $0.304$ $\pm0.014$.
6  AGAFONOVA 2018A reports sin$^2(2{{\mathit \theta}_{{13}}})$ $<$ 0.43 at 90$\%$ C.L. The result on the sterile neutrino search in the context of 3+1 model is also reported. A 90$\%$ C.L. upper limit on sin$^2(2\theta _{ {{\mathit \mu}} {{\mathit e}} )}$ = $0.021$ for $\Delta$m${}^{2}_{41}{}\geq{}$ 0.1 eV${}^{2}$ is set.
7  SEO 2018 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. SEO 2018 is a detailed description of the results published in CHOI 2016 , which it supersedes. Superseded by BAK 2018 .
8  Using T2K data only. For inverted mass ordering, all values of ${{\mathit \theta}_{{13}}}$ are ruled out at 68$\%$ CL.
9  AN 2017A reports 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. Superseded by ADEY 2018A.
10  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 .
11  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.
12  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.
13  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.
14  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.
15  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 .
16  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.
17  FORERO 2014 performs a global fit to neutrino oscillations using solar, reactor, long-baseline accelerator, and atmospheric neutrino data.
18  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 $0.0218$ ${}^{+0.0010}_{-0.0011}$ eV${}^{2}$ for normal and $0.0219$ ${}^{+0.0012}_{-0.0010}$ eV${}^{2}$ for inverted mass ordering.
19  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.
20  ABE 2013E assumes maximal $\theta _{23}$ mixing and $\mathit CP$ phase $\delta$ = 0.
21  ADAMSON 2013A results obtained from ${{\mathit \nu}_{{e}}}$ appearance, assuming $\delta$ = 0, and sin$^2(2 \theta _{23})$ = 0.957.
22  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 ${{\mathit \theta}_{{13}}}$) = $0.091$ ${}^{+0.029}_{-0.031}$.
23  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 .
24  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.
25  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.
26  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 $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$ = $0.00232$ ${}^{+0.00012}_{-0.00008}$ eV${}^{2}$ was assumed in the analysis. Superseded by CHOI 2016 .
27  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 $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$ = $0.00232$ ${}^{+0.00012}_{-0.00008}$ eV${}^{2}$ was assumed in the analysis. Superseded by AN 2013 .
28  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.
29  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.
30  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.
31  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.
32  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.
33  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.
34  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 $0.10$ $\pm0.03$.
35  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.
36  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.
37  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.
38  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.
39  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 ).
40  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).
41  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.
42  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.
43  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.
44  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.
45  FOGLI 2008 obtained this result from a global analysis of all neutrino oscillation data, that is, solar + KamLAND + atmospheric + accelerator long baseline + CHOOZ.
46  FOGLI 2008 obtained this result from an analysis using the solar and KamLAND neutrino oscillation data.
47  FOGLI 2008 obtained this result from an analysis using the atmospheric, accelerator long baseline, and CHOOZ neutrino oscillation data.
48  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 .
49  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.
50  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 $\Delta \mathit m{}^{2}_{32}$.
51  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.
52  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:
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 ABE 2018B
PR D97 072001 Atmospheric neutrino oscillation analysis with external constraints in Super-Kamiokande I-IV
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 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
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
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
PRL 101 141801 Hints of $\theta _{13}$ > 0 from Global Neutrino Data Analysis
PRL 96 181801 Improved Search for ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ Oscillation in a Long-Baseline Accelerator Experiment